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Derivation Algebras of Centerless Perfect Lie Algebras Are Complete 1(appeared in J.Algebra ,285(2005),508–515.)Yucai Su ?,Linsheng Zhu ??Department of Mathematics,Shanghai Jiaotong University,Shanghai 200030,China ?Department of Mathematics,Changshu Institute of Technology,Jiangsu 215500,China Abstract:It is proved that the derivation algebra of a centerless perfect Lie algebra of arbitrary dimension over any ?eld of arbitrary characteristic is complete and that the holomorph of a centerless perfect Lie algebra is complete if and only if its outer derivation algebra is centerless.Key works:Derivation,complete Lie algebra,holomorph of Lie algebra Mathematics Subject Classi?cation (1991):17B05§1.Introduction A Lie algebra is called complete if its center is zero,and all its derivations are inner.This de?nition of a complete Lie algebra was given by Jacobson in 1962[3].In [12],Schenkman proved a theorem,the so-called derivation tower theorem ,that the last term of the derivation tower of a centerless Lie algebra is complete.It is also known that the holomorph of an abelian Lie algebra is complete.Suggested by the derivation tower theorem,complete Lie algebras occur
naturally in the study of Lie algebras and would provide interesting objects for investigation.In 1963,Leger [6]presented some interesting examples of complete Lie algebras.However since then,the study of complete Lie algebras had become dormant for decades,partly due to the fact that the structure theory of complete Lie algebras was not well developed.In recent years,much progress has been obtained on the structure theory of complete Lie algebras in ?nite dimensional case (see for example,the references at the end of this paper).
It is known that a simple Lie algebra is not always complete(e.g.in some in?nite dimensional cases[14]).In this case,a natural question is:how big is the length of the derivation tower of a simple Lie algebra?
In this paper,we answer the above question.Precisely,we prove that the derivation algebra of a centerless perfect Lie algebra(i.e.,a Lie algebra g with zero center and[g,g]=g)of arbitrary dimension over any?eld of arbitrary characteristic is complete,thus as a consequence, the length of the derivation tower of any simple Lie algebra is≤1.
Let F be any?eld.First we recall the de?nitions of a derivation and the holomorph of a Lie algebra g over the?eld F.A derivation of a Lie algebra g is an F-linear transformation d:g→g such that
d([x,y])=[d(x),y]+[x,d(y)]for x,y∈g.(1.1) We denote by Der g the vector space of derivations of g,which forms a Lie algebra with respect to the commutator of linear transformations,called the derivation algebra of g.Clearly,the space ad g={ad x|x∈g}of inner derivations is an ideal of Der g.We call Der g/ad g the outer derivation algebra of g.
The holomorph h(g)of a Lie algebra g is the direct sum of the vector spaces h(g)=g⊕Der g with the following bracket
[(x,d),(y,e)]=([x,y]+d(y)?e(x),[d,e])for x,y∈g,d,e∈Der g.(1.2)
An element(x,d)of h(g)is also written as x+d.Obviously,g is an ideal of h(g)and h(g)/g～= Der g.Thus we write
h(g)=g×|Der g.(1.3) For a Lie algebra g,we denote by C(g)the center of g,i.e.,C(g)={x∈g|[x,g]=0}.
The main result of this paper is the following
Theorem1.1.Let g be a perfect Lie algebra with zero center(i.e.,[g,g]=g,C(g)=0). Then we have
(i)The derivation algebra Der g is complete.
(ii)The holomorph h(g)is complete if and only if the center of outer derivation algebra is zero,i.e.,C(Der g/ad g)=0.
We shall prove Theorem1.1in Section2,then we give some interesting example in Section
3.
§2.Proof of the main result
Proof of Theorem 1.1(i).Assume that d∈C(Der g).Then in particular we have [d,ad x](y)=0for all x,y∈g.Thus d([x,y])=[x,d(y)].Hence by(1.1),[d(x),y]=0for all x,y∈g.Since g has zero center,we obtain d(x)=0,i.e.,d=0.Therefore
C(Der g)=0.(2.1) Now we prove that all derivations of the Lie algebra Der g are inner.First we have
Claim1.Let D∈Der(Der g).If D(ad g)=0,then D=0.
Let d∈Der g,x∈g.Note from(1.1)that in the Lie algebra Der g,we have
[d,ad x]=ad d(x)∈ad g.(2.2)
Using this,noting that D(d)∈Der g and the fact that D(ad g)=0,we have
ad D(d)(x)=[D(d),ad x]
=D([d,ad x])?[d,D(ad x)]
(2.3)
=D(ad d(x))
=0.
Since g has zero center,(2.3)gives D(d)(x)=0for all x∈g,which means that D(d)=0as a derivation of g.But d is arbitrary,we obtain D=0.This proves the claim.
Since g is perfect,for any x∈g,we can write x as
x= i∈I[x i,y i]for some x i,y i∈g,(2.4) and for some?nite index set I.Then
ad x= i∈I[ad x i,ad y i].(2.5) Then for any D∈Der(Der g),we have
D(ad x)= i∈I D([ad x i,ad y i])
= i∈I([D(ad x i),ad y i]+[ad x i,D(ad y i)]).(2.6)
Let d i=D(ad x
i ),e i=D(ad y
i
)∈Der g.Then by(2.2),we have
D(ad x)= i∈I(ad d i(y i)?ad e i(x i))
=ad
i∈I
(d i(y i)?e i(x i))
∈ad g.
(2.7)
This means that D(ad x)=ad y for some y∈g.Since C(g)=0,such y is unique.Thus d:x→y de?nes a linear transformation of g such that
D(ad x)=ad d(x).(2.8)
For x,y∈g,we have
ad d([x,y])=D(ad[x,y])
=D([ad x,ad y])
=[D(ad x),ad y]+[ad x,D(ad y)]
=[ad d(x),ad y]+[ad x,ad d(y)]
=ad[d(x),y]+[x,d(y)].
(2.9)
This and the fact that C(g)=0mean that d([x,y])=[d(x),y]+[x,d(y)],i.e.,d∈Der g.Then (2.8)gives that D(ad x)=ad d(x)=[d,ad x]for all x∈g,i.e.,
(D?ad d)(ad g)=0.(2.10) By Claim I,we have D?ad d=0,i.e.,D=ad d is an inner derivation on Der g.This together with(2.1)proves Theorem1.1(i).
Proof of Theorem1.1(ii).“?=”:First we prove the su?ciency.So suppose C(Der g/ad g)= 0.We want to prove that h(g)is complete.
First we prove C(h(g))=0.Suppose h=x+d∈C(h(g))for some x∈g,d∈Der g. Letting y=0in(1.2),we obtain[d,e]=0for all e∈Der g,i.e.,d∈C(Der g)=0.Then h=x∈C(h(g))∩g?C(g)=0,i.e.,h=0.Thus C(h(g))=0.Then as in the proof of(2.1), we have
C(Der(h(g)))=0.(2.11) Now let D∈Der(h(g)).For any x∈g?h(g)written in the form(2.4),since g is an ideal of h(g),we have
D(x)= i∈I([D(x i),y i]+[x i,D(y i)])∈g.(2.12)
Thus d′=D|g:g→g is a derivation of g,i.e.,d′∈Der g?h(g).Let D1=D?ad d′∈Der(h(g)).Then D1(x)=D(x)?[d′,x]=D(x)?d′(x)=0,i.e.,
D1|g=0.(2.13) For any d∈Der g?h(g),by(1.3),we can write D1(d)∈h(g)as
D1(d)=x d+d1for some x d∈g,d1∈Der g.(2.14)
Then in h(g),by(1.2),for any y∈g,we have
[x d,y]+d1(y)=[x d+d1,y]
=[D1(d),x d]
=D1([d,x d])?[d,D1(x d)]
=D1(d(x d))?[d,D1(x d)]
=0,
(2.15)
where the last equality follows from(2.13).This means that d1=?ad x
d
and so D1(d)= x d?ad x
d
.For d,e∈Der g,we have
x[d,e]?ad x
[d,e]
=D1([d,e])
=[D1(d),e]+[d,D1(e)]
=(?e(x d)+d(x e))+([?ad x
d ,e]+[d,?ad x
e
]),
(2.16)
where the last equality follows from(1.2)and the fact that D1(d)=x d?ad x
d
.So
ad x
[d,e]=[ad x
d
,e]+[d,ad x
e
],(2.17)
i.e.,the linear transformation D:Der g→Der g de?ned by
D(d)=ad x
d
for d∈Der g,(2.18) is a derivation of Der g.Since Der g is complete,there exists d′′∈Der g such that
D=ad d′′.(2.19) For any d∈Der g,we have
[d′′,d]=D(d)=ad x
d
∈ad g,(2.20) i.e.,d′′+ad g∈C(Der g/ad g)=0.Thus d′′∈ad g.Therefore there exists y∈g such that
d′′=ad y.(2.21)
Note that y?ad y∈h(g).Let D2=D1?ad y?ad
y
.Then for any x∈g?h(g),we have
D2(x)=D1(x)?[y?ad y,x]
=?[y,x]+ad y(x)
=?[y,x]+[y,x]
=0,
(2.22)
where the second equality follows from(2.13)and(1.2),and for any d∈Der g?h(g),
D2(d)=D1(d)?[y?ad y,d]
=(x d?ad x
d
)?(?d(y)?[ad y,d])
=(x d+d(y))?(ad x
d
?[ad y,d])
=0,
(2.23)
because?ad d(y)=[ad y,d]=[d′′,d]=ad x
d
by(2.20)and(2.21),and x d=?d(y)(since g has zero center).Thus(2.22)and(2.23)show that D2=0and so D is inner.This and(2.11)prove that h(g)is complete.
“=?”:Now we prove the necessity.So assume that h(g)is complete.Suppose conversely C(Der g/ad g)=0.Then there exists D∈Der g such that
D/∈ad g but[D,Der g]?ad g.(2..24)
Then for any d∈Der g,there exists x d∈g such that[D,d]=ad x
d
.Such x d is unique since C(g)=https://www.doczj.com/doc/6e18042497.html,ing the fact that[D,[d,e]]=[[D,d],e]+[d,[D,e]],we obtain
x[d,e]=?e(x d)+x d(e)for d,e∈Der g.(2.25) We de?ne a linear transformation D:h(g)→h(g)as follows:D|g=0,and for d∈Der g?h(g), we de?ne
D(d)=x d?ad x
d
∈g×|Der g=h(g).(2.26) From this de?nition,we have
[D(d),x]=0for x∈g?h(g),d∈Der g?h(g).(2.27) Then for any h=x+d,h′=y+e∈h(g),by(1.2)and the fact that D g=0,we have
D([h,h′])=D([d,e])
=x[d,e]?ad x
[d,e]
=(?e(x d)+d(x e))?([ad x
d ,e]+[d,ad x
e
])
=(?e(x d)?[ad x
d ,e])+(d(x e)+[d,ad x
e
])
=[D(d),e]+[d,D(e)]
=[D(h),h′]+[h,D(h′)].
(2.28)
Thus D is a derivation of h(g).Since h(g)is complete,D is inner,therefore,there exists h=y+e∈h(g)such that D=ad h.For any x∈g,since D|g=0,we have
0=D(x)
=[h,x]
(2.29)
=[y,x]+e(x),
i.e.,e=?ad y.Then by(2.26),
=D(d)
x d?ad x
d
=[h,d]
(2.30)
=?d(y)?[ad y,d]
=?d(y)+ad d(y).
=?ad d(y).Then for any d∈Der g,
Hence ad x
d
[D,d]=ad x
d
(2.31)
=?ad d(y)
=[ad y,d].
Since Der g has zero center,(2.31)implies that D=ad y∈ad g,a contradiction with(2.24). Thus C(Der g/ad g)=0,and the proof of Theorem1.1(ii)is complete.
§3.Some Examples
Example3.1.An n×n matrix q=(q ij)over a?eld F of characteristic0such that
q ii=1and q ji=q?1ij,(3.1) is called a quantum matrix.The quantum torus
F q=F q[t±1,···,t±n],(3.2) determined by a quantum matrix q is de?ned as the associative algebra over F with2n generators t±1,···,t±n,and relations
t i t?1i=t?1i t i=1and t j t i=q ij t i t j,(3.3) for all1≤i,j≤n.
For any a=(a1,···,a n)∈Z n,we denote t a=t a11···t a n n.For any a,b∈Z n,we de?ne
σ(a,b)= 1≤i,j≤n q a j b i j,i and f(a,b)=n i,j=1q a j b i j,i.(3.4)
Then we have
t a t b=σ(a,b)t a+b,t a t b=f(a,b)t b t a and f(a,b)=σ(a,b)σ(b,a)?1.(3.5) Note that the commutator of monomials in F q satis?es
[t a,t b]=(σ(a,b)?σ(b,a))t a+b=σ(b,a)(f(a,b)?1)t a+b,(3.6) for all a,b∈Z n.De?ne the radical of f,denoted by rad(f),by
rad(f)={a∈Z n|f(a,b)=1for all b∈Z n}.(3.7) It is clear from(3.4)that rad(f)is a subgroup of Z n.The center of F q is C(F q)= a∈rad(f)F t a and the Lie algebra F q has the Lie ideals decomposition
F q=C(F q)⊕[F q,F q].(3.8) By(3.8),we obtain that the Lie algebra[F q,F q]～=F q/C(F q)is perfect and has zero center. From Theorem1.1,we obtain the following result.
Corollary 3.2.Let F q be a quantum torus as above.Then the derivation algebra Der([F q,F q])of[F q,F q]is complete.
Example3.3.A Lie algebra g is called a symmetric self-dual Lie algebra if g is endowed with a nondegenerate invariant symmetric bilinear form B.For any subspace V of g,we de?ne V⊥={x∈g|B(x,y)=0,?y∈V}.Then we can easily check that[g,g]⊥=C(g),where C(g) is the center of g.Then we have
Corollary3.4.Assume that g is a symmetric self-dual Lie algebra with zero center.Then the Lie algebra Der g is complete.
Remark3.5.By[18],we know that the structure of a perfect symmetric self-dual Lie algebra is not clear even in the?nite dimension case.
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语言学名词解释 Define the following terms: 1. design feature:are features that define our human languages,such as arbitrariness,duality,creativity,displacement,cultural transmission,etc. 2. function: the use of language tocommunicate,to think ,https://www.doczj.com/doc/6e18042497.html,nguage functions inclucle imformative function,interpersonal function,performative function,interpersonal function,performative function,emotive function,phatic communion,recreational function and metalingual function. 3. etic: a term in contrast with emic which originates from American linguist Pike’s distinction of phonetics and phonemics.Being etic mans making far too many, as well as behaviously inconsequential,differentiations,just as was ofter the case with phonetic vx.phonemic analysis in linguistics proper. 4. emic: a term in contrast with etic which originates from American linguist Pike’s distinction of phonetics and phonemics.An emic set of speech acts and events must be one that is validated as meaningful via final resource to the native members of a speech communith rather than via qppeal to the investigator’s ingenuith or intuition alone. 5. synchronic: a kind of description which takes a fixed instant(usually,but not necessarily,the present),as its point of observation.Most grammars are of this kind. 6. diachronic:study of a language is carried through the course of its history. 7. prescriptive: the study of a language is carried through the course of its history. 8. prescriptive: a kind of linguistic study in which things are prescribed how ought to be,https://www.doczj.com/doc/6e18042497.html,ying down rules for language use. 9. descriptive: a kind of linguistic study in which things are just described. 10. arbitrariness: one design feature of human language,which refers to the face that the forms of linguistic signs bear no natural relationship to their meaning. 11. duality: one design feature of human language,which refers to the property of having two levels of are composed of elements of the secondary.level and each of the two levels has its own principles of organization. 12. displacement: one design feature of human language,which means human language enable their users to symbolize objects,events and concepts which are not present c in time and space,at the moment of communication. 13. phatic communion: one function of human language,which refers to the social interaction of language. 14. metalanguage: certain kinds of linguistic signs or terms for the analysis and description of particular studies. 15. macrolinguistics: he interacting study between language and language-related disciplines such as psychology,sociology,ethnograph,science of law and artificial intelligence etc.Branches of macrolinguistics include
Fill in the blanks: 1.An i_________ is pronounced letter by letter, while an a________ is pronounced as a word. 2.Lexicon, in most cases, is synonymous with v_______. 3.All words may be said to contain a root m________. 4.A small set of conjunctions, prepositions and pronouns belongs to c_______ class, while the largest part of nouns, verbs, adjectives and adverbs belongs to o_____ class. 5.B______ is a reverse process of derivation, and therefore is a process of shortening. 6.Words are divided into simple, compound and derived words on the m_______ level. 7.A word formed by derivation is called a d_______, and a word formed by compounding is called a c________. 8.The poor is an example of p______ conversion. 9.The m________ is the smallest linguistic unit that carries meaning. 10. M________ studies the internal structure of words and the rules by which words are formed. 11. C__________ is the combination of two or sometimes more than two words to create new words. 答案： 1. initialism; acronym 2. vocabulary 3. morpheme
Comparison of inflection and derivation Inflection is variation in the form of a word, typically by means of an affix, that expresses a grammatical contrast which is obligatory for the stem’s word class in some given grammatical context. Derivation may be exactly defined as a process of forming new words by the addition of a word element, such as a prefix, suffix or combining form, to an already existing word. The basic distinction between inflection and derivation is mainly morphological. Inflection results in the formation of alternative grammatical forms of the same word, while derivation creates new vocabulary items. Such as the verb work becomes worker if we add the derivational morpheme –er. The adjective poor becomes poorer if we add the inflectional morpheme –er. So, the suffix form –er can be an inflectional morpheme as part of an adjective and also a derivational morpheme as part of the noun. Inflectional operations create forms that are fully grounded and able to be integrated into discourse, whereas derivational operations create stems that are not necessarily fully grounded and which may still require inflectional operations before they can be integrated into discourse. Following is the comparison of inflection and derivation. First in lexical category inflection don’t change the lexical category of the word. But the derivation often change it. In location, inflection tend to occur outside derivational affixes while the derivation tend to occur next to the root. At the type of meaning, inflection contribute syntactically conditioned information, such as number, gender, or aspect while derivation contribute lexical meaning. At affixes used, inflection occur with all or most members of a class of stems, but the derivation are restricted to some, not all members of a class of stems. About productivity and grounding, inflection may be used to coin new words of the same type and create forms that are fully-grounded and able be integrated into discourse, while derivation create forms that are not necessarily fully grounded and may require inflectional operations before they can be integrated into discourse. As mentioned by Finegan and Besnier, English today has only eight remaining inflectional morphemes, two on nouns, four on verbs, and two on adjectives, as shown in the following : Noun include plural(like cars) and possessive(like car’s). Verb include third person(like swims), past tense(like showed), past participle(like shown) and present participle(like showing). Adjective include comparative(like taller) and superlative(like tallest). Word sets like child/children, ox/oxen, and who/whom/when reflect earlier productive inflectional morphemes. The system of English pronouns also gives some hint of an earlier inflectional morphology. In contrast to inflection, derivation is not obligatory and typically produces a greater change of meaning from the original form, and is more likely to result in a form which has a somewhat idiosyncratic meaning, it often changes the grammatical category of a root. Derivation or affixation may be exactly defined as a process of forming new words by the addition of a word element, such as a prefix, suffix or combining form, to an already existing word. For example: re + cover
a r X i v :16 5 . 6 1 2 7 v 1 [ m a t h . R A ] 1 9 M a y 2 1 6 Conjugacy of Cartan Subalgebras in Solvable Leibniz Algebras and Real Leibniz Algebras Ernie Stitzinger and Ashley White May 23,2016ABSTRACT.We extend conjugacy results from Lie algebras to their Leibniz algebra gen-eralizations.The proofs in the Lie case depend on anti-commutativity.Thus it is necessary to ?nd other paths in the Leibniz case.Some of these results involve Cartan subalgebras.Our results can be used to extend other results on Cartan subalgebras.We show an ex-ample here and others will be shown in future work.Keywords:Leibniz algebras,Conjugacy,Cartan subalgebras,maximal subalgebras MSC 2010:17A32A self-centralizing minimal ideal in a solvable Lie algebra is complemented and all com-plements are conjugate [1].Such an algebra is called primitive.If the minimal ideal is not self-centralizing,then there is a bijection which assigns complements to their intersec-tion with the centralizer [7].Such an intersection is the core of the complement.Towers extended this result to show that maximal subalgebras are conjugate exactly when their cores coincide,with the additional condition at characteristic p that L 2has nilpotency class less than p .Under this same condition,Cartan subalgebras are conjugate.We show these results hold for Leibniz algebras.The antisymmetry is used in the Lie algebra case,and so we amend the arguments in the Leibniz algebra case.We also show consequences for the conjugacy of Cartan subalgebras in solvable Lie algebras.We also consider conjugacy of Cartan subalgebras for real Leibniz algebras,obtaining an extension of a result of Barnes [1]in the Lie case.Omirov [6]treated conjugacy of Cartan subalgebras in complex Leibniz algebras.For an introduction to Leibniz algebras,see [5] Let A be an ideal in a solvable Leibniz algebra L .Also assume that at characteristic p ,A has nilpotency class p .As usual,for a ∈A ,let exp(L a )= ∞01
1.Lexicology is a branch of linguistics concerned with the vocabulary of the English language in respect to words and word equivalents. 2.A word may be defined as a fundamental unit of speech and a minimum free form; with a unity of sound and meaning, capable of performing a given syntactic function. 3.The morpheme is the smallest meanings linguistics unit of language, not divisible or analyzable into small forms. 4.Word-formation rules refer to the scope and methods whereby speakers of a language may create new words. https://www.doczj.com/doc/6e18042497.html,pounding or composition is a word-formation process consisting of joining two or more bases to form a new unit, a compound word. 6. Derivation may be defined as a process of forming new words by the addition of a word element, such as a prefix,suffix or combining form, to an already existing word. 7.Conversion is a word-formation process whereby a word of a certain word-class is shifted into a word of another word-class without the addition of an affix. 8.Motivation refers to the connection between word-symbol and its sense. 9.Metaphor is a figure of speech containing an implied comparison based on association of similarity, in which a word or a phrase ordinary and primarily used for one thing is applied to another, a process which often results in semantic change or figurative extension of meaning.
Compounding or Derivation After learning the word-formation, I think that I have had a general understanding about the various ways of forming words. By and large, the various processes can be classified on the basis of frequency of usage, into major and minor processes. Referring to the three major processes, namely, compounding, derivation and conversion, I think the conversion is relatively independent; however the compounding and derivation have some relationship to a certain extent. As we know, compounding is a common device which has been productive at every period of the English Language; it is a word-formation process consisting of joining two or more bases to form a new unit, a compound word. Compounds can be formed from various parts of speech. Some of the commonest ones consist of noun + noun, adjective +noun, adverb + noun, and noun + -ing form. In a word, actually the compounds can be divided into three kinds, noun compounds, adjective compounds, and the verb compounds. As for derivation, it is generally a word-formation process by which new words are created by adding a prefix, or suffix, or both, to the base. To be more exact, derivation may be defined as a process of forming new words by the addition of a word element, such as a prefix, suffix or combining form, to an already existing word. When it comes to the topic” which comes first, the compound or derivation”, may different people hold different opinions. As far as I am concerned, I think it is difficult to come up a exact answer. So I think that it depends, which one comes first should depend on the particular facts. There are many examples that we can take into consideration. Take the word “two sided”for example, whether the “two side “comes first or the “sided” comes first. “two side” just put more emphasis on the amount “two”, but “sided” pay more attention to the “side”. It stands to reason that the “sided” comes first, because that the amount “two” is certainly on the basis of the root “sided”. So in this word, derivation comes first, compound comes later. There are some similar examples else. Such as weather-beaten, thunder-struck, suntanned and so on. Take the word “hardworking” for instance, “hard work” comes first or “working” comes first? The “working” just comes from the “work” itself, however the word “hard work” grow out of the basis of “work”. So in this word, derivation still comes first, compound comes later. There are many other similar examples, such as daydreaming, window shopping, everlasting, ocean-going,
Key Points of “English Lexicology” Chapter 4 Word Formation (1) The expansion of vocabulary in modern English depends chiefly on word-formation. The most productive means of word formation are affixation, compounding and conversion. Affixation: 30%-40%, compounding: 28%-30%, conversion: 26%, shortening (clipping and acronymy): 8%-10%, blending and others 1%-5%. Rules themselves are not fixed but undergo changes. There are always exceptions to rules of word-formation. 4.1 Affixation Affixation is defined as the formation of words by adding word forming or derivational affixes to bases. According to their position, affixation falls into prefixation and suffixation. 1. Prefixation Prefixation is the formation of new words by adding prefixes to bases. Prefixes do not change the word-class of the base but only change its meaning.
第一章 词word, lexis 词汇vocabulary，lexicon 本族词native words 外来词borrowed words 词汇学lexicology 形态学morphology 语义学semantics 词汇语义学lexical semantics 认知语义学cognitive semantics 词源学etymology 词典学lexicography 认知词典学cognitive lexicography 语料库语言学corpus linguistics 纵聚合关系paradigmatic relation 新词coinage 时髦词语buzzwords 第二章 词素morpheme 自由词素free form 粘着词素bound form\morpheme 变体allomorph 词根root 自由词根free root 粘着词根bound root 组合词素combining form 词缀affix 前缀prefix 后缀suffix 词缀法affixation 派生法derivation 派生词derivative 构词能力productivity 复合法compounding，composition 复合词compound 转化法conversion 或功能转化法functional shift 或转移法transmutation 零位后缀派生法derivation by zero suffix 或零位派生法zero derivation 第三章 拼缀法blending 截短法clipping 首字母拼写法acronmy 逆生法back formation 由专有名词而来words from proper names 拟声法onomatopoeia
1、英语词汇概述：（8%） （1）英语词汇的谱系关系及其历史发展：英语的谱系关系；英语的三个发展阶段。 （2）英语词汇的构成：基本词汇与专用词汇；英语词汇中的本族词与外来词。 （3）英语词汇的三大特点：数量大、来源广、变化多。 ‘Indo-European’印欧语系 With Vikings’ invasion, many Scandinavian words at least 900 words of Scandinavian origin have survived in modern English. Old English has a vocabulary of about 50,000 to 60,000 words. It was a highly inflected language just like modern German. 1. Word词--- A word is a minimal free form of a language that has a given sound and meaning and syntactic function. 2．Vocabulary词汇——Vocabulary is most commonly used to refer to the sum total of all the words of a language. It can also refer to all the words of a given dialect，a given book，a given subject and all the words possessed by an individual person as well as all the words current in a particular period of time in history. 3. basic word stock 基本词汇i s the foundation of the vocabulary accumulated over centuries and forms the common core of the language. Though words of the basic word stock constitute a small percentage of the English vocabulary, yet it is the most important part of it. These words have obvious characteristics. （1）All national character全民性. Words of the basic word stock denote the
Derivation of Space Charge limited Currents with a Distribution of Traps in Trap Depth Top Hat Distribution The trapped charge is in the top-hat trap distribution shown below. The amount of charge for every cubic metre (m3) that resides in the conduction band at ?= 0 (i.e. this is the charge that is free to move) is given by eN c exp (-(?min/kT)) Here: N c is the concentration of states in the band (number per cubic metre) exp (-?min/kT) is the probability that a state has an electron in it (This comes from the Fermi probability function, which is Probability of occupancy of a state at Energy E = [exp {(E- E fermi)/kT} +1]-1 ((E- E fermi)= ?min, when E is the conduction band energy) and e is the charge on the electron. So we have to find ?min for a given voltage V. We do this by finding the amount of trapped charge in the material for every cubic metre and using it to fill the trap states up to ?min. It is assumed that almost all the charge is trapped, so the total amount of trapped charge = the total amount of charge. The total amount of charge is given by the Capacitance multiplied by the voltage. The charge per m3 is given by the Capacitance x Voltage/volume = (Capacitance/Surface Area)Voltage/thickness = CV/d The number of trapped electrons per m3 is thus CV/de. This is used to fill the trap states. The total number of electrons per m3 in the trap states between ?max and ?min is given by:
Chapter1 Derivation by Phase Noam Chomsky What follows extends and revises an earlier paper(``Minimalist Inquiries,'' MI),1which outlines a framework for pursuit of the so-called Minimalist Program,one of a number of alternatives that are currently being explored. The shared goal is to formulate in a clear and useful wayDand to the extent possible to answerDa fundamental question of the study of lan-guage,which until recently could hardly be considered seriously and may still be premature:to what extent is the human faculty of language FL an optimal solution to minimal design speci?cations,conditions that must be satis?ed for language to be usable at all?We may think of these speci?-cations as``legibility conditions'':for each language L(a state of FL),the expressions generated by L must be``legible''to systems that access these objects at the interface between FL and external systemsDexternal to FL, internal to the person. The strongest minimalist thesis SMT would hold that language is an optimal solution to such conditions.The SMT,or a weaker version, becomes an empirical thesis insofar as we are able to determine interface conditions and to clarify notions of``good design.''While the SMT cannot be seriously entertained,there is by now reason to believe that in non-trivial respects some such thesis holds,a surprising conclusion insofar as it is true,with broad implications for the study of language,and well beyond. Note the inde?nite article:an optimal solution.``Good design''condi-tions are in part a matter of empirical discovery,though within general guidelines of an a prioristic character,a familiar feature of rational in-quiry.In the early days of the modern scienti?c revolution,for example, there was much concern about the interplay of experiment and mathe-matical reasoning in determining the nature of the world.Even the most extreme proponents of deductive reasoning from?rst principles,Descartes