• 検索結果がありません。

Use of of in "Noun of Noun" Trigrams by Japanese Learners of English

N/A
N/A
Protected

Academic year: 2021

シェア "Use of of in "Noun of Noun" Trigrams by Japanese Learners of English"

Copied!
13
0
0

読み込み中.... (全文を見る)

全文

(1)

BackgroundoftheStudy

Thereareseveralstudieswhich show thatprepositionsaresignificantly underused in

non-nativewrittenlanguagecorporacomparedtonativecorpora.S.GrangerandP.Rayson

(1998)show thedistribution oftheninemajorwordcategoriestaking non-nativeadvanced

levelFrenchuniversitystudentscorporafrom theInternationalCorpusofLearnerEnglish

(ICLE)databaseaswellasnativecontrolcorpusfrom theLouvainCorpusofNativeEnglish

Essays(LOCNESS)database.They statethatarticles,adjectivesand verbsproveto have

similar frequencies in native and non-native corpora,while non-native speaker writers

overused determiners,pronounsand adverbsbutunderused conjunctions,prepositionsand

nouns.Nevertheless,itisreportedthattheprepositionofisoverusedingeneral.・Overuse・

isdefinedbythefactthatthelearnersinquestionusecertainlinguisticfeaturessignificantly

moreoften,while・underuse・isdefinedbythefactthatthelearnersusethem significantly

lessoften(Leech,1998).

Asforthefrequencyofprepositionsasawhole,Japaneselearnersarenotexceptions.

Farfrom it,Uchida(2007)analyzedtheJapaneseEnglish asaForeign LanguageLearner

(JEFLL)corpuscollected from 10,000 high schoolstudentsand heshowsthatthemost

frequentlyusedprepositionisinandthesecondisofinthecorpus,buttheorderisreversed

in theBritish NationalCorpus(BNC).Thefrequency ofofin JEFLL islessthan halfof

thatusedbythenativespeakersintheBNC.

Table1showsan overview description aswellasoftokensanditsratioin thewhole

tokens from ICLE French subcorpus (ICLE-F), German subcorpus (ICLE-G), Italian

― 2 ― 学苑英語コミュニケーション紀要 No.882 2~14(20144)

Useofofi

n・NounofNoun・Tri

grams

byJapaneseLearnersofEngl

i

sh

TomokoKaneko

Abstract

Useofofin・N ofN・trigramsbylearnerswithdifferentlanguagebackgroundsaswell asbynativespeakersofEnglishwasexaminedandcomparedusingwrittenlanguagecorpora. Japaneseuniversity studentsarefound to havea specialtendency in using thetrigrams, which arein somecasescommon toalllearnersandin theothercasesdifferentfrom other groupsoflearnersornativespeakersofEnglish.Theeducationalcontextin Japanesehigh schools,the learners・focus in learning English,mother tongue transfer,and cognitive complexity ofthe meanings ofofare discussed as some ofthe reasons for their special tendencyinusingofinwrittenEnglish.

(2)

subcorpus(ICLE-I),Japanesesubcorpus(ICLE-J)andLOCNESS.Thechartshowsthatofis

underusedbyJapanesestudentswhileitisoverusedbyItalianstudents.

InTable1,・Type・meansalldifferentwordsinthecorpus.Forexample,ifatexthas

ten words,butallofthem arethesameword,thetexthasonly onetype.On theother

hand,ifalloftheten wordsaredifferentfrom oneanother,ithasten types.・Tokens・

meanallwordsofthetext.Thismeansthataten-wordtexthastentokens.・TTR・stands

for・Type-Token Ratio.・TTR isobtainedby dividing thetypecountby thetoken count.

However,asthetextgetsbigger,thenumberofnew wordtypesbeing countednaturally

fallsanditisdifficulttocomparetheTTR ofsmallertextsagainstlargerones.In order

toremedythis,a・StandardizedTTR・calculatesevery1,000wordsandproduceanaverage

TTR ofthewholetext.

Standardized TTR showsthatthevariety ofvocabulary used by Japaneseuniversity

studentsismuch narrowerthan studentsofotherlanguagebackgrounds.Thechartalso

showsthatJapanesestudentsunderuseofin written English.Why they underuseofisa

ratherinteresting phenomena becausewealso havea particlewhich expressesoneofthe

meaningsofof,possession,inJapanese.Itisthecase-markingparticleNO andisoftenused

justin the same way as of.For example,fragranceofcoffeeis KOHINO KAORIin

Japanese,althoughthepositionsofthetwonounsareopposite.However,whenexpressing

possessionsin English,ofisnotalwaysexpressed,forexample,theJapaneseTARO NO

HON iseitherTaro・sbookorabookofTaro.Wecouldask,then,how thisdifferenceinthe

structureofthetwolanguagesworkintheuseofofbyJapaneselearners.J.AartsandS.

Granger(1998)analyzedthetop-tenratingtrigrams(three-wordphrases)inLOCNESSand

checkediftheywereoverusedorunderused.Theresultsshow thatthe・N prepositionN・

trigram isunderused in someEuropean ICLE subcorpora.Then,do Japaneseuniversity

students also use fewer ・N ofN・ trigrams compared to students with other language

background?

Thusin thepresentpaper,asthefirststep to find outtheuseofofby Japanese

Englishlearners,theuseofofin・N ofN・trigramswillbethefocus.Thepurposeofthe

presentstudy istofindoutifthereareany gapsin theuseofofin ・N ofN・trigrams

― 3 ―

Table1.Overview ofFrench,German,ItalianandJapaneseSubcorporaandLOCNESS Corpora

Features French German Italian Japanese LOCNESS

TotalTokens 513,115 233,792 230,032 239,288 388,033

TotalTypes 51,826 14,951 11,616 10,300 19,414

StandardizedTTR 34.51 40.66 30.58 12.69 37.12

OfTokens 10,266 6,735 7,989 4,758 10,919

(3)

betweenJapanesestudentsandstudentswithotherlanguagebackgroundsaswellasnative

speakersofEnglish.Biberetal.(1994)explain somemajorcausesoflearners・underuseof

prepositionalpatternsbasedontheirstudyonpostnominalmodifiers.Onemajorcause,they

state,isthatEFL/ESL grammartextbooksgiveprepositionalpostnominalmodifiers(ex.

mapsofManhattan)theleastattention among theseven typesofpostnominalmodifiers.

Furthermore,they provethatprepositionalpostnominalmodifiersaremuch m orecommon

thanrelativeorparticipialclauses(ex.thelinesrepresentingneighboringstreets)inactual

use,eveninwrittenlanguage.

Method

Materials

Thedataarefrom ICLE-F,ICLE-G,ICLE-I,andICLE-J,inadditiontoLOCNESS.The

British NationalCorpus (BNC),which has a 100 m illion word collection ofsamples of

writtenandspokenlanguagefromawiderangeofsourceswillalsobeusedasareference.

Each ICLE corpuscontainsover2,000,000wordsofcompositions(500wordseach)mainly

writtenby3rdand4thgradeuniversitystudents.Theaim oftheICLE projectistocompare

thefeaturesamong theEnglish interlanguageused by studentswith differentlanguage

backgrounds.Alongside these non-native varieties of English,a comparable corpus of

written English compiledby nativespeakersofEnglish,LOCNESS,willalsobeusedasa

controldatabase. Procedures

Sincethefocusofthispaperison・N ofN・trigrams,allthetrigramscenteringonof

wereselectedfrom thecorporafirst.Ann-gram isacontiguoussequenceofnitemsfrom

agivensequenceoftextandthe・trigram・isaspecialcasewherenequalsthree.Thetop

ten trigramslisted atthisstageareattached in Appendix 1.Then among thetrigrams

centeringonoflisted,only・N ofN・trigramswereselected(cf.Appendix2).Someofthe

trigramsinAppendix2canalsobeseenintheBNCtop50・N ofN・trigrams(cf.Appendix

3),butmostofthem aredifferentbecauseofthedifferenceofthetopicson which ICLE

subcorporaaretargetedon.

Inordertofindthedistributionofofindifferentmeanings,alltheexamplesofofin

・N ofN・trigramswerecategorizedbasedon themeaningsdescribedin Oxford Advanced

Learner・sDictionary ofCurrentEnglish (OALD)(2010).TheOALD isused by 30million

peopleallovertheworldandmany studentsincluding Japaneseuniversity studentsuseit

inlearningEnglish.Thisfactsuggeststheappropriatenessinusingthemeaningcategories

described in this dictionary as a basic reference,along with the fact that the m any

dictionariesusedbyJapanesestudentsareoftenbasedontheBNC research.

Table2showsninemeaningsbasedontheOALD (2010)exceptforfourmeaningsinthe

orderoffrequencyinuse.ThefourmeaningswhichwerenotincludedinTable2are:①used

(4)

aftersomeverbsbeforementioningsomebody(sb)/something(sth)involvedintheaction(ex.

Hewasclearedofallblame.),②usedaftersomeadjectivesbeforementioningsb/sththata

feelingrelatesto(ex.tobeproudofsth),③usedtogiveanopinionofsb・sbehaviour(ex.Itwas

kindofyoutooffer.)and,④usedwhenonenoundescribesasecondone(ex.Where・sthat

idiotofaboy?).Theywerenotincludedinthetablebecausethefirsttwodoesnotfollow

・N ofN・structureandthelasttwowerenotfoundinthetargetcorpora.Examplesshown

afterthedefinitionofeachmeaninginTable2arealsofrom thesamedictionary.

Asthelaststep,thefrequency ofofin ・N ofN・trigramsin differentmeaningsby

Japaneseuniversity studentswillbecompared to thoseby learnerswith otherlanguage

backgroundsto find outthespecialfeaturesoftheuseofofin ・N ofN・trigramsby

Japaneseuniversitystudents.

Results

Inordertoanswertheresearchquestion,thematerialsarecomparedinthreedifferent

perspectives.

Frequencyof・N ofN・Trigrams

Frequencyof・N ofN・trigramsisshowninTable3.Inthetable,thethird,fourthand

fifthrowsareaddedfrom Table1tocomparetheuseofofand・N ofN・trigrams.Thelast

threerowsshow thedataabout・N ofN・trigrams;the・N ofN・tokens,theratioof・N

― 5 ―

Table2.NineMeaningsofOfBasedonOxfordAdvancedLearner・sDictionary ofCurrentEnglish

Meanings Definition Examples

1 belongingtosb;relatingtosb afriendofmine,theroleoftheteacher 2 belonging to sth; being part of sth;

relatingtosth thelidofthebox,amemberoftheteam

3 concerningorshowingsb/sth astoryofpassion,aphotoofmydog 4 usedwithmeasurementsandexpressions

oftime,age,etc. agirlof12,2kilosofpotatoes

5 usedtoshow sb/sthbelongstoagroup,

oftenaftersome,afew,etc. some of hiproblems s friends, a few of the 6 usedtosay whatsb/sth is,consistsof,

orcontains thecityofDublin,aglassofmilk

7 usedafternounsformedfrom verbs.The noun after・of・can beeithertheobject orthesubjectoftheaction

thearrivalofthepolice,criticism ofthe police

8 used to show theposition orsth/sb in

spaceortime jrevolustnorthofDetroiution t,atthetimeofthe 9 comingfrom aparticularbackgroundor

(5)

ofN・tokenscomparedtothewholecorpustokens,andtheratioof・N ofN・tokensamong

theoftokens.When counting theraw ・N ofN・trigramsin thecorpora,thefrequencies

lower than five were notcounted by referring to Dunning・s (1993)proposalaboutthe

reliabilityofvaluesinunbalancedsamplesizes.

Japaneseuniversitystudentsusedfewer・N ofN・trigramscomparedtotheotherlearner

groupsandnativespeakersofEnglish in thetotaltokens.However,French andJapanese

studentsoverused・N ofN・trigramsintheoftokenscomparedtotheothercorpora.

Frequenciesof・N ofN・PhrasesUsedinEachMeaning

Table4comparestheraw frequenciesof・N ofN・trigramsaswellasthenormalized

valuesintheninemeaningslistedinTable2.Normalizedvaluesareshownwithunderlines.

Inthiscase,thetokensofeachcorpusaresetto100,000wordsinordertomakethecomparison

easier.Thenumberofthedatacoded by theresearcherwas3,172in total,among which

10% wasdoublecodedbythesecondcoder.Theinter-coderreliabilityofthecodingofthe

― 6 ―

Table3.FrequencyofOfand・N ofN・TrigramsintheFiveCorpora Corpora

French German Italian Japanese LOCNESS

TotalTokens 513,115 233,792 230,032 239,288 388,033 OfTokens 10,266 6,735 7,989 4,758 10,919 % inTotalTokens 2.001 2.881 3.473 1.988 2.814 ・N ofN・Tokens 1,002 428 681 430 801 % inTotalTokens 0.195 0.183 0.296 0.180 0.206 % inofTokens 9.760 6.355 8.524 9.037 7.336

Table4.FrequenciesofNineMeaningsofOfin・N ofN・TrigramsinFiveCorpora Normalizedin100,000OfTokens

Corpora

French German Italian Japanese LOCNESS

OfTokens 10,266 6,735 7,989 4,758 10,919 100,000 100,000 100,000 100,000 100,000 Meanings 1 0 0 36 535 20 250 19 399 162 1384 2 28 237 94 1396 51 638 78 1639 120 1099 3 0 0 0 0 0 0 0 0 41 375 4 509 4958 107 1589 341 4268 135 2837 159 1456 5 26 235 0 0 0 0 0 0 20 183 6 12 117 62 921 0 0 11 231 61 559 7 192 1870 103 1529 194 2428 180 3783 69 1548 8 0 0 7 104 0 0 0 0 8 73 9 235 2289 19 282 5 939 7 147 61 559 Total 1002 9706 428 6356 611 8523 430 9036 701 7236

(6)

meaningsofofreachedtoagreementrateof0.78.When therewasadisagreementon the

coding,thetwocodersdiscussedituntilagreementwasreachedbetweenthem.A chi-square

testinvestigatingtherelationshipofbackgroundlanguagesandfrequencyofninemeanings

foundthesetwovariableswerecloselyrelated(χ2=0.138Ex+4,df=32,p=.000).

Graph 1isdrawn to makecomparisonsvisually cleareramong thefivecorpora.For

example,itisclearfrom Graph 1that,excepttheGerman corpus,allthelearnersused

more・N ofN・trigramsasawholeandoverusedmeaningNo.4comparedtoLOCNESS.On

the other hand,Japanese and French leaners ofEnglish used manymore examples of

meaningNo.7andNo.9respectivelythananyothergroups.

TheGraph showsthatalthough allthelearnersusedmeaning No.2moreoften than

meaningNo.1,nativespeakersofEnglishusedmeaningNo.1moreoftenthanmeaningNo.2.

Another difference between the learners and native speakers ofEnglish is that native

speakersusedofin・N ofN・trigramsinalltheninemeaningswhilenoneofthelearner

groupsdidso.

SimilaritiesandDissimilaritiesamongtheFiveCorpora

TofindoutthetypicalfeaturesintheuseofofbyJapaneseuniversitystudents,cluster

analysisisutilized.Clusteranalysisisastatisticalclassificationtechniqueinwhichdatais

sub-dividedintoclusters.Theclustersin Graph 2show iftheitemsin aclusterarevery

similartooneanotherordifferentfrom theitemsin otherclusters.Thegraph makesit

possibletoclusterthefivedifferentgroupsofstudentsfrom differentlanguagebackground

and nativespeakersofEnglish into a branching diagram depending on theuseofofin

・N ofN・trigrams.

The graph also shows that the students with Japanese and Italian language

backgroundsaretheclosestto each otherin theuseofofin ・N ofN・trigrams,while

studentswithaGermanlanguagebackgroundareinthesecondmostsimilarpairingwith

LOCNESS.The students with a French language background behave differently from

studentswithJapaneseandItalianlanguagebackgroundsbutthesethreegroupsoflearners

― 7 ―

(7)

aremoresimilartoeachotherthanstudentswithaGermanlanguagebackgroundornative

speakersofEnglish.

Thus,itisshownthatbasicallythefivegroupsaredividedintotwolargegroups.One

groupconsistoflearnerswithaGermanlanguagebackground,whoseuseofmeaningsofofin

・N ofN・trigramsaretheclosesttonativespeakers,andtheothergroupconsistofallthe

otherlearnersgroups.

Discussions

Theresearchquestionofthepresentstudyiswhetherthereareanygapsintheuseof

ofin ・N ofN・trigrams between Japanese students and students with other language

backgroundsaswellasnativespeakersofEnglish.Table3 showsthatthe・N ofN・

frequencypercentageintotaltokensoftheJapanesesubcorpusisthelowest(0.180)among

thefivecorpora.TheItalian subcorpus,on theotherhand,showsthehighestpercentage,

0.296,which ismorethan 1.6timesasfrequentasin theJapanesesubcorpus.Thisfact

showsthatthelearners・useof・N ofN・trigramsinallthetokensshowsalargevariance.

However,ifwelook atthepercentageof・N ofN・in theoftokens,learners,including

Japanese students,show somewhat different results.Compared to native speakers,the

learnersusedmore・N ofN・trigramsexceptGerman students.Itisinteresting toknow

thatJapanesestudentsaswellasFrench studentsused many more・N ofN・trigrams

amongthevarioususeofofthanotherlearnergroupsandnativespeakersofEnglish.Thus

theanswertotheresearch question isthattherearegapsin theuseofofin ・N ofN・

phrasesbetweenJapanesestudentsandstudentswithotherlanguagebackgroundsaswellas

nativespeakersofEnglish.

TherearealsotwootherthingstobenoticedasspecialfeaturesofJapanesestudents・

use ofofin ・N ofN・trigrams.Table 3 shows that Japanese students underuse the

prepositionof,anditalsoshowsthattheyusefewer・N ofN・trigramsthanstudentswith

― 8 ―

Graph2.ClusterAnalysis

(8)

otherlanguagebackgroundsand nativespeakersofEnglish in thetotaltokens.On the

otherhand,amongtheoftokensinthecorpus,theyuse・N ofN・trigramsmostfrequently

compared to theothergroupsofstudentsand nativespeakersofEnglish.Furthermore,

Table4showsthattheyusemeaningNo.7themostfrequentlyamongtheninemeanings,

likenativespeakersofEnglishdo,whilealltheotherstudentsusedmeaningNo.4themost.

Why aretherethesegaps,then? In thefollowing section,why Japaneseuniversity

studentsuseofin・N ofN・trigramsinthemannerstatedabovewillbeexploredfrom four

different perspectives.In addition,why allthe learners use more meaning No.2 than

meaningNo.1willalsobediscussed.

・N ofN・inJapaneseHighSchoolEnglishTextbooks

MostEnglishinputsforJapaneseuniversitystudentsbeforetheygetintouniversityare

from highschoolEnglishclasses.Andwhathighschoolstudentsrelyonasthemainsource

forlearningEnglisharetheirtextbooks.Table5showsthefrequencyofofand・N ofN・

trigramsfrom thesix first,second,andthirdgradejuniorhigh schoolEnglish textbooks

(Columbus,EverydayEnglish,New Crown,New Horizon,OneWorld,andSunshine)andfive

levelIandIIseniorhighschoolEnglishtextbooks(Crown,Mainstream,Polestar,Pro-Vision,

andUnicorn).Allthetextbookswerepublishedin2007.

Thepercentageofofamong thetotaltokensin juniorand seniorEnglish textbooks

(1.19% and2.25% respectively)shownabovedoesnotindicatemuchdifferencefrom thatof

LOCNESS(2.81%)showninTable1.However,intheoftokensinthetextbooks,・N ofN・

areintroducedmoreoftenthaninLOCNESS.Thepercentageofofis58.77% injuniorhigh

schooland20.00% in seniorhigh schooltextbooks,which isfrom threetoeighttimesas

high asthatin LOCNESS (7.34%)shown in Table3.Thisfactmay explain why Japanese

universitystudentsuselotsofofin・N ofN・trigrams.Inadditiontothefactthatthere

aremany examplesof・N ofN・ trigramsin theirtextbooks,theuseisoften carefully

explainedbyteachersinclassrooms.Thismightbeoneofthereasonsforthefrequentuse

ofthetrigrams.TeachersinJapanesehighschoolsusetheirclasshoursmostlytoexplain

― 9 ―

Table5.Ofand・N ofN・inJapaneseHighSchoolEnglishTextbooks Corpora

JuniorHighSchool SeniorHighSchool

TotalTokens 39,913 89,605 Types 3,324 7,075 StandardizedTTR 37.33 40.48 OfTokens 473 2,020 % inTotalTokens 1.185 2.254 ・N ofN・Tokens 278 404 % inTotalTokens 0.697 0.451 % inofTokens 58.77 20.00

(9)

aboutthelanguage,particularly on grammar.Itisoften thecasethatthestructureof ・N ofN・isgrammatically explainedin detailby teachersespecially meaning No.7,which

isusedonly in averagefrequenciesby nativespeakersofEnglish.However,although this

data showsoneofthereasonsfor Japaneseuniversity students・abundantuseofofin

・N ofN・trigrams,itdoesnotexplainthefeweruseofofbythem comparedtostudents

withotherlanguagebackgrounds.

OfandtheapostropheinJapanese

InJapanese,theEnlgishofandapostropheareoftentranslatedi

ntoNO.TheJapanesecase-markingparticleNO hasvariousmeaningsandevenJapaneselanguagegrammarbookstell

thatitisnotpossibletoanalyzeallthemeaningsNO has(Fei,2013).Fei(2013)statesthat

the Japanese language also has many ・N NO N・ structures,where NO indicates six

differentrelationshipsbetweenthefirstN (N1)andthesecondN (N2).Amongthosesix,the

mostfrequently used NO signifiesa meanig ・N2which N1does・(ex.KAERU NO KOE

=croaksoffrogs),whereN1and N2arereversed in Enlgish.ThisNO showsthesame

meaningasindicatedinmeaningNo.2inTable2.Thisfactsuggeststhattheremaybean

L1(mothertongue)influenceinthefrequentuseofofbyJapaneseuniversitystudents.

Althoughitisnotinthescopeofthispaper,thereasonfortheoveruseofofin・N of

N・bystudentswithaFrenchlanguagebackgroundisplausiblythatintheFrenchlanguage,

thereareno・N ofN・sturucturesexceptforafew examples.Thesamephenomenacanbe

seen in theItalian language.Oneoftheoften seen casuesofoveruseisthatbecausethe

learnersdonothavethesametargetphrasestructureintheirL1asinthetargetlanguage,

theyaretooconsciousaboutthestructure.

SincethefocusofthepresentpaperisontheuseofJapanesestudents・ofin・N ofN・

trigrams,other findings centering on the use of of by learners with other language

backgroundswillhopefullybestudiedinthefutureindetail.

Phrase-frames

AnotherreasonthatJapanesestudentsunderuseofseemstobethattheylearnofasa

rule,notasan item.Schmitt(2004)suggeststhattheacquisition oflexicalphrasesmight

depend tosomeextenton whetherthelearnersare・system・learnersor・item・learners.

System learners rely on rules in learning a new language and item learners rely on

formulaic sequences.Japanese students learn English mostly based on grammar,which

meanstheyarerulelearners.OfisoneofthefunctionwordsinEnglishandfunctionwords

areoftenusedasapartofsetphrases.Kaneko(2011)showsthatrulelearnersarenotgood

atusing function wordsasapartofphrasesbasedon theanalysisofboundprepositions

andfreeprepositionsinICLE-J.

Phrase-framesaresetsofvariantsofann-gram identicalexceptforoneword.Theidea

ofphrase-framesorlexicalbundleswillcertainlyworkineducationalsettings.Thistrendis

plausiblebecausethesamephrase-framesarerepeatedly usedalthough thesame・N ofN・

(10)

phrasewillnotbeusedsofrequently.Forexample,numberframeslikelotsof~,oneof~,

manyof~,allof~,someof~,orpossessionframeslike,pleasureof~,titleof~,sense

of~ aresomeoftheexamplesofphrase-framesseen in thecorpora.Ashasbeen stated

before,inEnglishclassroomsinJapan,teachersoftenputfocusonthelexico-grammatical

featuresofofandnotonthephrasesaspatternsorframes.Thelearnersneedtoputmore

focusnoton theindividualmeaning ofthepreposition ofbuton thecommon featuresof

phrase-frames,sothattheywillrecognizecertainpatternsofthosephrasesincludingofin

Englishfrom awiderview.

CognitiveComplexity

Lastly,Iwouldliketodiscussthefrequencydifferencebetweenthenativespeakers・and

thelearners・useofofregarding meaning No.1and No.2.Asstated in theBackground

section,Tyler and Evans (2003)explain the degree ofcognitive complexity between the

trajectory andlandmark.Theirideasuggeststhattherelationshipbetween trajectory and

landmark isoneofthekey factorstoexplain learners・difficulty in learning prepositions.

They pointoutthatthe simpler relationship between the trajectory and landmark,the

easierforthelearnersto understand therelationship.In meaning No.1,ifwetakethe

example・theroleoftheteacher,・thetrajectory ・role・isnotclearly separated from the

landmark・teacher.・Itisbecausethelandmarkisnotathingbutaperson.Ontheother

hand,in theexample・thelidofthebox・in meaning No.2,thetrajectory ・lid・isclearly

standing outfrom thelandmark ・box.・In thisway,theirtheory on cognitivecomplexity

supportsthatalthoughthemostfrequentuseofthemeaningsofofbynativespeakersof

English ismeaning No.1,in thecaseoflearners,meaning No.2 isthemostfrequent.

However,adetailedstudy willbeneededon thesemanticdifferencesin theninemeanings

showninTable2todemonstrateexactlyhow theirtheoryexplainsthecognitivedifferences

intheproductionoftheuseofofin・N ofN・trigrams.

Conclusion

In concluding thispaper,thefollowing twopointswillsummarizethisstudy.Firstly, various factors-the educationalcontexts,how the similar function is expressed in the

JapaneselanguageandthewaythelearnerslearnEnglishexpressions,seem toaffecthow

welltheprepositionofin・N ofN・trigramsislearnedinaJapanesecontext.Inaddition,

althoughthisseemscommontoalllearners,thecognitivecomplexityofthetargetmeaning

ofofin・N ofN・trigramsalsoseemstobeakeyfactor.Secondly,thedistinctionofthe

usagein theninemeaningsofofshown in thefourlearners-groups・corporaisdifferent

from each otherand alsofrom thenativespeakers・corpus.However,asawhole,allthe

learnershaveatendency touseofdifferently from thenativespeakers;they underuseor

overuseofin certain meaningsand they donotuseofin asvariousmeaningsasnative

speakers.

(11)

Thedesignation ofthemeaning ofofshould berefined in any futurestudies.For

example,itmightbepossibletocategorizethemeaningsofofaccording tothecognitive

complexity explained by Tylorand Evans(2003).Itwillalso beinsightfulto discussthe

abundantuseof・N ofN・phrasesby studentswith aFrench languagebackground,who

seldom usethesamestructureintheirL1.Bylearningabouttherelationshipbetweenthe

learners・L1 and theuseofofin ・N ofN・ trigrams,moreinsightfulfindingswillbe

expected.Thepresentpapershedslightonlyontheuseofofin・N ofN・trigramsbuta

moredetailedandwideranging study aroundtheuseofofwillsurely bring much more

fruitfulresultsanditwillbeabletoofferlotsofexpansiveideasonlanguageteaching,too.

References

Aarts,J.,andGranger,S.(1998).Tagsequencesinlearnercorpora:akeytointerlanguagegrammar anddiscourse.InGranger,S.(ed.)LearnerEnglishonComputer(pp.13241).London& New York: AddisonWesleyLongman.

Biber,D.,S.Conrad,andRappen,R.(1994).Corpus-basedapproachestoissuesin appliedlinguistics. AppliedLinguistics15(2):16989.

Dunning,T.(1993).Accuratemethodsforthestatisticsofsurpriseand coincidence.Computational Linguistics19(1):6174.

Fei,Yu.NihongoJoshi・NO・toChugokugoJoshi・TEKI・noHikakuTaishouKennkyu(A Comparative StudyofJapanese・NO・andChinese・TEKI・).Retrieved8/20/2013from http://human.kanagawa -u.ac.jp/gakkai/publ/pdf/no172/17206.pdf

Granger,S.,andRayson,P.(1998).Automaticprofiling oflearnertexts.In Granger,S.(ed.)Learner EnglishonComputer(pp.11931).London& New York:AddisonWesleyLongman.

Hornby,A.S.(2010).Oxford Advanced Learner・s Dictionary ofCurrent English (8th ed.).(p.1051).

OxfordUniversityPress.

Kaneko,T.(2011).UseofEnglishbyJapaneseLearners:StudyofErrors.Tokyo:Sanshusha.

Leech,G.(1998).Preface.InGranger,S.(ed.)LearnerEnglishonComputer(pp.xivxx).London& New York:AddisonWesleyLongman.

Schmitt,N.(ed.).(2004).FormulaicSequences:Acquisition,Processing,and Use.Amsterdam:John Benjamins.

Tyler,A.,and Evans,V.(2003).The Semantics ofEnglish Prepositions:SpatialScenes,Embodied MeaningandCognition.Cambridge:CambridgeUniversityPress.

Uchida,T.(2007).Zenchi-shinohattatsu(Developmentofprepositions.)InTono,Y.(ed.)Nihonji nChu-kou-sei10,000-nin noEigoKoopasu (English LanguageCorpusCompiled from 10,000Juniorand SeniorHighSchoolStudents)(pp.10916).Tokyo:Shogakukan

(12)

Appendices

― 13―

Appendix 1.Top10TrigramsCenteringonof

FR GE IT

N Cluster Freq. Mg. N Cluster Freq. Mg. N Cluster Freq. Mg. 1 BIRTH OF A 160 1 ONE OF THE 107 1 ONE OF THE 148 2 ONE OF THE 140 2 BECAUSE OF THE 49 2 POINT OF VIEW 105 4 3 POINT OF VIEW 119 4 3 OUT OF THE 48 3 FIRST OF ALL 66 7 4 PART OF THE 109 4 MOST OF THE 44 4 PART OF THE 54 5 LOSSOF IDENTITY 106 9 5 FRONT OF THE 36 5 BECAUSE OF THE 53 6 FIRST OF ALL 76 7 6 AWARE OF THE 32 6 MATTER OF FACT 39 4 7 END OF THE 76 7 PART OF THE 32 7 MOST OF THE 39 8 MOST OF THE 62 8 FIRST OF ALL 28 6 8 AND OF THE 31 9 BECAUSE OF THE 57 9 POINT OF VIEW 26 4 9 END OF THE 30 10 WAY OF LIFE 53 4 10 MEMBER OF THE 22 10 VICTIMSOF THEIR 28

JP LOC

N Cluster Freq. Mg. N Cluster Freq. Mg. 1 ONE OF THE 150 1 ONE OF THE 148 2 INVENTION OF THE 64 2 END OF THE 70 3 BECAUSE OF THE 50 3 PART OF THE 68 4 FIRST OF ALL 35 7 4 OUT OF THE 52 5 POINT OF VIEW 27 4 5 AWARE OF THE 49 6 SOME OF THEM 25 7 6 INVENTION OF THE 47 7 LOT OF PEOPLE 21 7 7 ALL OF THE 47 8 MOST OF THEM 21 2 8 MANY OF THE 43 9 NAME OF THE 19 9 SOME OF THE 42 10 ALL OF THE 17 10 MOST OF THE 41

Appendix 3.Reference:BNC Top50

N Cluster Freq. N Cluster Freq. N Cluster Freq. 1 SECRETARY OF STATE 5004 11 WAY OF LIFE 1029 21 WORKSOF ART 624 2 POINT OF VIEW 2865 12 PERIOD OF TIME 864 22 QUALITY OF LIFE 612 3 SORT OF THING 2100 13 COUPLE OF YEARS856 23 YEARSOF AGE 605 4 COURT OF APPEAL 1855 14 COUNCILOFMINISTERS841 24 COUPLE OF WEEKS580 5 HOUSE OF COMMONS1854 15 LOT OF MONEY 835 25 NUMBER OF YEARS579 6 HOUSE OF LORDS1677 16 CHRUCH OF ENGLNAD 700 26 SENSE OF HUMOUR 572 7 LOT OF PEOPLE 1290 17 MINISTER OF STATE 691 27 PIECE OF PAPER 562 8 CUP OF TEA 1270 18 KIND OF THING 690 28 STATE OF AFFAIRS541 9 MEMBER OF PEOPLE 1165 19 COUPLE OF DAYS 635 29 MINISTRY OF DEFENCE 533 10 BANK OF ENGLAND 1057 20 PRINCE OF WALES 634 30 BALANCEOFPAYMENTS 526 N Cluster Freq. N Cluster Freq.

31 LENGTH OF TIME 523 41 WASTE OF TIME 451 32 DIVISION OF LABOUR 518 42 HEAD OF STATE 449 33 RATE OF INTEREST 516 43 AMOUNT OF TIME 435 34 LOT OF TIME 512 44 COUPLE OF HOURS429 35 AMOUNT OF MONEY 504 45 HOUSEOFREPRESENTATIVES 424 36 DEPARTMENTOFHEALTH 499 46 TIME OF YEAR 421 37 CITY OF LONDON 482 47 GROUP OF PEOPLE 419 38 CUP OF COFFEE 470 48 RATE OF INFLATION 418 39 DEPARTMENTOFTRADE 462 49 COURSE OF ACTION 414 40 MEMBER OF STAFF 451 50 MEMBERSOF STAFF 397

Appendix 2.Top10・N ofN・

FR GE IT

N Cluster Freq. Mg. N Cluster Freq. Mg. N Cluster Freq. Mg. 1 POINT OF VIEW 119 4 1 FIRST OF ALL 28 6 1 POINT OF VIEW 105 4 2 LOSSOF IDENTITY 106 9 2 POINT OF VIEW 26 4 2 FIRST OF ALL 66 7 3 FIRST OF ALL 76 7 3 ONE OF THEM 20 2 3 MATTER OF FACT 39 4 4 WAY OF LIFE 53 4 4 ONE OF THOSE 19 2 4 SOME OF THEM 22 7 5 MATTER OF FACT 43 4 5 FRIEND OF MINE 19 1 5 ONE OF THESE 20 7 6 WAY OF THINKING 32 4 6 MATTER OF FACT 15 4 6 CAUSE OF CRIME 18 4 7 POINTSOF VIEW 24 4 7 ONE OF THESE 14 2 7 CAUSESOF CRIME 15 9 8 SOME OF THEM 23 7 8 PLEASURESOFCYCLING 13 4 8 LOT OF PEOPLE 15 7 9 WAY OF LIVING 21 4 9 NUMBER OF PEOPLE 13 2 9 ONE OF THEM 15 7 10 DESTRUCTION OFDRESDEN 20 9 10 MOST OF THEM 13 7 10 AMOUNT OF MONEY 15 7

JP LOC

N Cluster Freq. Mg. N Cluster Freq. Mg. 1 FIRST OF ALL 35 7 1 LOSSOF SOVEREIGNTY 40 9 2 POINT OF VIEW 27 4 2 WAY OF LIFE 29 4 3 SOME OF THEM 25 7 3 PEOPLE OF ARGOS28 3 4 LOT OF PEOPLE 21 7 4 ABSURDITY OF LIFE 26 1 5 MOST OF THEM 21 2 5 EXAMPLE OF THIS 24 2 6 ALL OF THEM 15 2 6 AMOUNT OF MONEY 24 7 7 WAY OF THINKING 13 4 7 ALL OF THESE 20 2 8 LOT OF THINGS12 7 8 NUMBER OF PEOPLE 20 4 9 LOT OF INFORMATION 12 7 9 FUTILITY OF LIFE 19 1 10 INTRODUCTIONOFENGLISH 11 4 10 FIRST OF ALL 18 6

Notes)Freq.=frequency Mg.=meaning

(13)

(金子 朝子 英語コミュニケーション学科) ― 14―

Appendix 4.TokensandTypesofN ofN Categorizedby9Meaningsinthe5Corpora

FR GE IT JP LOC

N Cluster Freq.Mg.N Cluster Freq.Mg.N Cluster Freq.Mg.N Cluster Freq.Mg.N Cluster Freq.Mg. 1 PART OF LIFE 8 2 1 FRIEND OF MINE 19 1 1 RIGHT OF SELF 10 1 1 PROCESSOF CHILD 8 1 1 ABSURDITY OF LIFE 26 1 2 ROOT OF ALL 8 2 2 WORLD OF SPORTS 7 1 2 KIND OF CRIME 10 1 2 WAY OFCOMMUNICATION 6 1 2 FUTILITY OF LIFE 19 1 3 ALL OF US 7 2 3 POWER OF MUSIC 5 1 3 PERIOD OF TIME 8 2 3 MATTER OF COURSE 5 1 3 THEORY OF OPTIMISM 13 1 4 PART OF EUROPE 5 2 4 SYSTEM OF EDUCATION 5 1 4 PART OF IT 8 2 4 MOST OF THEM 21 2 4 THEMESOF GUILT 10 1 5 POINT OF VIEW 119 4 5 ONE OF THEM 20 2 5 ALL OF THEM 7 2 5 ALL OF THEM 15 2 5 FREEDOM OF SPEECH 8 1 6 WAY OF LIFE 53 4 6 ONE OF THOSE 19 2 6 PROBLEM OF CRIME 7 2 6 ALL OF US 10 2 6 THEME OF GUILT 8 1 7 MATTER OF FACT 43 4 7 ONE OF THESE 14 2 7 WORK OF ART 6 2 7 NUMBER OF PEOPLE 8 2 7 CHURCH OF ENGLAND 8 1 8 WAY OF THINKING 32 4 8 NUMBER OF PEOPLE 13 2 8 ALL OF US 5 2 8 ALL OF JAPANESE 8 2 8 COURT OF JUSTICE 8 1 9 POINTSOF VIEW 24 4 9 PERIOD OF TIME 10 2 9 EACH OF US 5 2 9 ROOT OF ALL 6 2 9 HOUSE OF COMMONS 8 1 10WAY OF LIVING 21 4 10WORST OF ALL 7 2 10 BOTH OF THEM 5 2 10MEMBER OF SOCIETY 5 2 10 CHARACTEROFPANGLOSS 6 1 11 STANDARD OF LIVING 12 4 11 ALL OF THEM 6 2 11 POINT OF VIEW 105 4 11 EMPEROR OF JAPAN 5 2 11 DEATH OF DRUSILLA 6 1 12 LACK OF INTEREST 12 4 12 ALL OF US 5 2 12 MATTER OF FACT 39 4 12 POINT OF VIEW 27 4 12 GUILT OF MANKIND 6 1 13 IDENTITY OF EACH 11 4 13 POINT OF VIEW 26 4 13 CAUSE OF CRIME 18 4 13 WAY OF THINKING 13 4 13 FORM OF PUNISHMENT 6 1 14 PERIOD OF TIME 10 4 14 MATTER OF FACT 15 4 14 LACK OFCOMMUNICATION 12 4 14 INTRODUCTION OFENGLISH 11 4 14 ACTSOF BAD 5 1 15 HISTORY OF EUROPE 9 4 15 PLEASURESOF CYCLING 13 4 15 WAY OF THINKING 12 4 15 STUDY OF ENGLISH 10 4 15 BOARD OF EDUCATION 5 1 16 MEANSOFCOMMUNICATION 9 4 16 JOYSOF LIFE 12 4 16 WAY OF LIVING 12 4 16 TREATY OF WAITANGI 10 4 16 PRACTICEOFEUTHANASIA 5 1 17 AWARE OF THAT 9 4 17 WAY OF LIVING 11 4 17 POINTSOF VIEW 11 4 17 FREEDOM OFEXPRESSION 8 4 17 STATE OF NATURE 5 1 18 POINT OF VIEWS 8 4 18 WAY OF LIFE 8 4 18 ACT OF LOVE 11 4 18 MATTER OF FACT 7 4 18 FORMSOF GAMBLING 5 1 19 HISTORY OF CROME 8 4 19 STATE OF MIND 8 4 19 STATE OF MIND 11 4 19 CARE OF THEM 7 4 19 EQUALITY OFOPPORTUNITY 5 1 20 STATE OF MIND 8 4 20 CREATURE OF HABIT 7 4 20 MEANSOFCOMMUNICATION 9 4 20 LACK OFRESPONSIBILITY 6 4 20 EXAMPLE OF THIS 24 2 21 FUTURE OF EUROPE 8 4 21 ATTITUDEOFTOLERANCE 7 4 21 DENSITY OFPOPULATION 9 4 21 WAY OF LIFE 6 4 21 ALL OF THESE 20 2 22 REALITY OF LIFE 8 4 22 FIRST OF ALL 28 6 22 RATE OF CRIME 7 4 22 ABILITY OF ENGLISH 5 4 22 ROOT OF ALL 16 2 23 HISTORY OF SUFFERING 7 4 23 KIND OF PUNISHMENT 10 6 23 OWNERSHIP OF GUNS 7 4 23 ABILITY OF JAPANESE 5 4 23 ALL OF THIS 14 2 24 WORLDOFTECHNOLOGY 7 4 24 KINDSOF DRUGS 7 6 24 SUM OF MONEY 6 4 24 WAY OF TEACHING 5 4 24 COUNCIL OF MINISTERS 7 2 25 ASPECT OF LIFE 7 4 25 HUNDREDSOF YEARS 7 6 25 DISINTEGRATION OFFAMILY 6 4 25 NUMBER OF JAPANESE 5 4 25 WORKSOF LITERATURE 6 2 26 VIEW OF LIFE 7 4 26 COUPLE OF YEARS 5 6 26 WORLD OF WORK 6 4 26 NUMBER OF CRIMES 5 4 26 ALL OF THEM 6 2 27 PIECESOFINFORMATION 6 4 27 SHEET OF PAPER 5 6 27 WAY OF LIFE 5 4 27 CIRCUMSTANCESOFAPPLICATION 5 4 27 HOUSESOFPARLIAMENT 6 2 28 TITLE OF THIS 6 4 28 MOST OF THEM 13 7 28 WAY OF BEING 5 4 28 MILLIONSOF PIECES 6 6 28 OPPONENTSOF SUICIDE 6 2 29 CASE OF WAR 6 4 29 LOT OF MONEY 12 7 29 INSTITUTIONSOF LAW 5 4 29 KIND OF STORIES 5 6 29 MEMBERSOF SOCIETY 5 2 30WAYSOF LIVING 6 4 30MILLIONSOF PEOPLE 11 7 30 FREEDOM OF SPEECH 5 4 30 FIRST OF ALL 35 7 30 TYPE OF EUTHANASIA 5 2 31 WAY OF LOOKING 6 4 31 CUP OF COFFEE 11 7 31 IDEA OF SOCIETY 5 4 31 SOME OF THEM 25 7 31 PEOPLE OF AMERICA 5 2 32 WORK OF ART 6 4 32 LOT OF PEOPLE 10 7 32 MEANSOF TRANSPORT 5 4 32 LOT OF PEOPLE 21 7 32 PEOPLE OF ARGOS 28 3 33 CONDITION OF WOMEN 6 4 33 THOUSANDSOF PEOPLE 9 7 33 ASPECT OF LIFE 5 4 33 LOT OF THINGS 12 7 33 CITIZENSOF ARGOS 13 3 34 STUPIDITY OF WAR 5 4 34 MOST OF US 8 7 34 ASPECTSOF LIFE 5 4 34 LOT OF INFORMATION 12 7 34 WAY OF LIFE 29 4 35 STANDARDSOF LIVING 5 4 35 GROUP OF PEOPLE 7 7 35 CONCEPTION OF LIFE 5 4 35 LOT OF TIME 11 7 35 NUMBER OF PEOPLE 20 4 36 DIFFERENCE OF AGE 5 4 36 GLASSOF WINE 6 7 36 PROBLEM OF JUVENILE 5 4 36 ONE OF THEM 10 7 36 QUESTION OF WEATHER 12 4 37 SENSE OF PATRIOTISM 5 4 37 CUP OF TEA 6 7 37 PLEASURE OF READING 5 4 37 MOST OF JAPANESE 9 7 37 TREATY OF ROME 11 4 38 RIGHT OF MAN 5 4 38 HUNDREDSOF CATTLES 5 7 38 STATE OF AFFAIRS 5 4 38 NUMBER OF FILES 7 7 38 LEGALIZATION OFMARIJUANA 10 4 39 RIGHTSOF MAN 5 4 39 LOTSOF PEOPLE 5 7 39 FIRST OF ALL 66 7 39 MOST OF US 6 7 39 DOCTRINE OF OPTIMISM 10 4 40ART OF LITERATURE 5 4 40 CENTRE OF AUGSBURG 7 8 40 SOME OF THEM 22 7 40 LOT OF ENGLISH 6 7 40ACT OF BAD 9 4 41 TOWN OF SULACO 15 5 41 LACK OF TOLERANCE 7 9 41 ONE OF THESE 20 7 41 LOT OF JAPANESE 6 7 41 SUMSOF MONEY 7 4 42 COMMUNITY OFPEOPLE 6 5 42 WASTE OF TIME 7 9 42 LOT OF PEOPLE 15 7 42 BOTH OF THEM 5 7 42 SENSE OF SYMPATHY 6 4 43 ABSURDITY OF WAR 5 5 43 SEARCH OFPERFECTION 5 9 43 ONE OF THEM 15 7 43 LOT OF MONEY 5 7 43 QUALITY OF LIFE 6 4 44 EUROPE OF 1992 12 6 Total 428 44 AMOUNT OF MONEY 15 7 44 LOTSOF PEOPLE 5 7 44 PROBLEM OFHOMELESSNESS 6 4 45 FIRST OF ALL 76 7 45 MOST OF THEM 13 7 45 MANY OF THEM 5 7 45 NUMBER OF CASES 6 4 46 SOME OF THEM 23 7 46 MOST OF ALL 9 7 46 WASTE OF TIME 7 9 46 LOVE OF MONEY 5 4

47 EACH OF THEM 18 7 47 LOT OF MONEY 9 7 Total 430 47 IDEA OF OPTIMISM 5 4

48 MOST OF THEM 18 7 48 NUMBER OF CHILDREN 5 7 48 CRIME OF PASSION 5 4

49 ONE OF THEM 10 7 49 NUMBER OF WEAPONS 5 7 49 POINT OF VIEW 12 4

50 EACH OF US 9 7 50 CAUSESOF CRIME 15 9 50 CITY OF CLEVELAND 9 5

51 LOTSOF PEOPLE 8 7 51 LACK OF MORAL 9 9 51 BOOK OF VALUES 6 5

52 MILLIONSOF PEOPLE 7 7 52 USE OF GUNS 8 9 52 SPORT OF BOXING 5 5

53 MAJORITY OF PEOPLE 7 7 53 LACK OF EDUCATION 6 9 53 FIRST OF ALL 18 6

54 ALL OF THEM 6 7 54 USE OF ARMS 6 9 54 MILLIONSOF POUNDS 10 6

55 SOME OF US 5 7 55 USE OF DRUGS 6 9 55 THOUSANDSOF PEOPLE 9 6

56 EVERYONE OF US 5 7 56 CARE OF THEM 5 9 56 1OF 31 6 6

57 LOSSOF IDENTITY 106 9 57 PRESENCE OF BOTH 5 9 57 AMOUNTOFKNOWLEDGE 6 6

58 DESTRUCTION OFDRESDEN 20 9 58 PASSING OF TIME 5 9 58 BILLIONSOF DOLLARS 6 6

59 LACK OFCOMMUNICATION 17 9 59 POSSESSION OFFIREARMS 5 9 59 GROUPSOF PEOPLE 6 6

60 UNIFICATION OFEUROPE 15 9 60 PERCEPTION OFREALITY 5 9 60AMOUNT OF MONEY 24 7

61 ABSENCE OF GOD 8 9 Total 681 61 SOME OF THESE 14 7

62 LOSSOF SOVEREIGNTY 7 9 62 MILLIONSOF PEOPLE 14 7

63 MOVEMENT OF PEOPLE 7 9 63 ONE OF THESE 13 7

64 TREATY OFMAASTRICHT 7 9 64 BEST OF ALL 13 7

65 LACK OF TIME 7 9 65 MANY OF THESE 12 7

66 INFLUENCEOFTELEVISION 7 9 66 NUMBER OF CARS 12 7

67 CHANGEOFMENTALITY 7 9 67 GROUP OF PEOPLE 8 7

68 WASTE OF TIME 6 9 68 MOST OF THEM 7 7

69 EXISTENCE OF GOD 6 9 69 SOME OF THEM 6 7

70 TEACHINGOFLANGUAGES 5 9 70 BOTH OF THESE 6 7

71 PROTECTION OFNATURE 5 9 71 EACH OF THESE 6 7

72 BOMBING OF DRESDEN 5 9 72 NONE OF THESE 6 7

Total 1002 73 LOT OF PEOPLE 6 7

74 MAJORITY OF PEOPLE 6 7 75 MANY OF THEM 6 7 76 NUMBER OF STUDENTS 5 7 77 MOST OF THESE 5 7 78 REST OF EUROPE 8 8 79 LOSSOF SOVEREIGNTY 40 9 80ACT OF PARLIAMENT 9 9 81 SEPARATION OFCHURCH 5 9 82 MURDER OF EGISTHE 7 9 Total 801 Notes)Freq.=frequency Mg.=meaning

Tabl e1.Overvi ew ofFrench,German,Ital i anandJapaneseSubcorporaandLOCNESS Corpora
Tabl e2.Ni neMeani ngsofOfBasedonOxfordAdvancedLearner・ sDictionary ofCurrentEnglish
Tabl e3.FrequencyofOf and・N ofN・Tri gramsi ntheFi veCorpora Corpora
Tabl e5.Ofand・N ofN・i nJapaneseHi ghSchoolEngl i shTextbooks Corpora

参照

関連したドキュメント

This conjecture is not solved yet, and a good direction to solve it should be to build first a Quillen model structure on the category of weak ω-groupoids in the sense of

Kwak, J.H., Kwon, Y.S.: Classification of reflexible regular embeddings and self-Petrie dual regular embeddings of complete bipartite graphs. Kwon, Y.S., Nedela, R.: Non-existence

Key words: Interacting Brownian motions, Brownian intersection local times, large deviations, occupation measure, Gross-Pitaevskii formula.. AMS 2000 Subject Classification:

Then Catino [15] generalized the previous result concerning the classification of complete gradient shrinking Ricci solitons to the case when Ricci tensor is nonnegative and a

Note that various authors use variants of Batanin’s definition in which a choice of n-globular operad is not specified, and instead a weak n-category is defined either to be an

More precisely, the category of bicategories and weak functors is equivalent to the category whose objects are weak 2-categories and whose morphisms are those maps of opetopic

Given T and G as in Theorem 1.5, the authors of [2] first prepared T and G as follows: T is folded such that it looks like a bi-polar tree, namely, a tree having two vertices

Since we need information about the D-th derivative of f it will be convenient for us that an asymptotic formula for an analytic function in the form of a sum of analytic