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@MXJ M@ _ZOUI-HJEMA^MUIXIM@U MLIVVJHZEIFCJ DVMZ^U?

J. L. EMV@JCIZU, GV.

Ofstroet. O quosi-hjemapmsitim` tbjmrja is mftoi`jh lmr o

tmrsim` lrjj ofjcio` drmup witb quosi-j`hmamrpbisa ocdjfro sotis-

lyi`d tbj ai`iaua em`hitim` m` cjlt ihjocs.

Ujvjroc quosi-hjemapmsitim` tbjmrjas ml G. H. Vjih o`h V. U.

^ijrej lmr tmrsim` lrjj ofjcio` drmups ml li`itj ro`k eo` fj jxtj`hjh tmdrmups ml orfitrory ro`k fy rjpcoei`d tbj li`itj ro`k bypmtbjsis witb

tbj rjquirjaj`t tbot tbj quosi-j`hmamrpbisa ocdjfro ml tbj drmups

sotisly tbj ai`iaua em`hitim` m` cjlt ihjocs. Xbis ai`iaua em`hi-

tim` eo` ocsm fj eboroetjrizjh tmpmcmdieoccy. Xbj cjaao fjcmw is tbj

kjy tm tbjsj dj`jrocizotim`s; tbot tbjy orj `m` trivioc is iccustrotjh fy

loaicior jxoapcjs sueb os drmups ml 0-ohie i`tjdjrs.

Bjrjoltjr tbj tjra "drmup" rjljrs tm o rjhuejh, tmrsim` lrjj ofjcio`

drmup. Xbj hiseussim` is `mraocizjh fy em`sihjri`d m`cy sufdrmups ml

o lixjh vjetmr spoej \ mvjr tbj rotim`oc `uafjr lijch _. Xbj ocdjfro

ml ci`jor tro`slmraotim`s ml \, Ci\), is jquippjh witb tbj li`itj

tmpmcmdy [8Q. Fosie rjsucts ofmut quosi-ismamrpbisa orj ossuajh;

lmr o emapcjtj foekdrmu`h em`suct [cQ, [Q, [4Q. , 1, ~ hj`mtj

quosi-em`toi`jh, quosi-jquoc, o`h quosi-ismamrpbie, rjspjetivjcy.

D wicc ocwoys hj`mtj o lucc sufdrmup ml \, i.j., o sufdrmup witb tmrsim`

qumtij`t, \/D. Vjeocc tbot _JiD) 1 {lJCi\)7lD_D} is tbj quosi-j`hmamrpbisa ocdjfro ml D. B* hj`mtjs tbj rotim`oc sufspoej ml \

spo``jh fy o sufdrmup B ml \. Li`occy, occ suas orj hirjet.Oltjr Vjih [4Q, eocc D irrjhueifcj il o`h m`cy il it bos `m `m`trivioc

purj, luccy i`vorio`t sufdrmups. It is josy tm sjj tbot o` irrjhueifcj

drmup is bmamdj`jmus; tbus wj cmsj `m dj`jrocity fy em`sihjri`d m`cy

rjhuejh drmups. Vjih sbmws tbot D is irrjhueifcj il o`h m`cy il \ is o`

irrjhueifcj _JiD)-amhucj fy jstofcisbi`d o m`j-tm-m`j emrrjspm`-

hj`ej fjtwjj` tbj purj, luccy i`vorio`t sufdrmups ml D o`h tbj

(E4c)-sufamhucjs ml \. It lmccmws rjohicy tbot o quosi-suaao`h ml

o` irrjhueifcj drmup is itsjcl irrjhueifcj o`h tbus tbot irrjhueificity

Vjejivjh fy tbj jhitmrs Go`uory .

OAU ?95>; Ujem`hory ?

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58 J. L. EMV@JCIZU, GV. [Ujptjafjr

is i`vorio`t u`hjr quosi-ismamrpbisa. Lmr irrjhueifcj D, tbj ecmsurj

ml _J(D) i` C(\) is Bmae3D)(L, \), witb E(D) 1Bma_(D)(L, \)[8, p. 5? Q. Mur iaajhiotj dmoc is tm jxtj`h Xbjmrja :.: [4Q tm drmups

ml orfitrory ro`k. Cjaao ?.? j`ofcjs us tm hm tbis fy prmvihi`d tbj

`jejssory li`itj`jss em`hitim`.

Cjaao ?.?. Cjt \ fj o vjetmr spoej mvjr o hivisim` ocdjfro H o`h

suppmsj tbot rcmar0(\, \)E._J(D). Xbj` \ is li`itj hiaj`sim`oc mvjr H.

^rmml. Uuppmsj {o}31? is o sufsjt ml o` i`li`itj .H-fosis ml \, em`-

toi`jh i` D (D is lucc i` \). Ui`ej D is rjhuejh, pP'oPD lmr smajpriaj pi o`h smaj pmsitivj i`tjdjr ,*'1 ?, -, 0. Fut `m 0-ci`jor

tro`slmraotim` sj`hi`d fosis jcjaj`t o tm pgaioi, i 1 c, , ,

is o quosi-j`hmamrpbisa ml D. Xbis em`trohietim` sbmws tbot \ aust

bovj li`itj 0-hiaj`sim`.

Xbjmrja ?.6. Xbjsj em`hitim`s m` tbj drmup D orj jquivocj`t.

(?) D is irrjhueifcj o`h _J(D) sotislijs tbj ai`iaua em`hitim` m`

cjlt ihjocs.

(6) D is irrjhueifcj o`h _J(D) is ecmsjh i` tbj li`itj tmpmcmdy ml C( \).(5) _J(D) 1Bmrolc(L, \) witb \ o vjetmr spoej mvjr o hivisim` ocdj-

fro H. Em`sjquj`tcy \ is li`itj a-hiaj`sim`oc mvjr H 1 E(D).

(8) D :6-iD,-witb joeb D~, B irrjhueifcj, o`h _J(B) ohivisim` ocdjfro.

^rmml. (?) iapcijs (6). \ is o` irrjhueifcj (RJ(D)-amhucj fjeousj

D is o` irrjhueifcj drmup. Xbus fy Xbjmrja ? [8, p. 59Q o`h tbj Hj`-

sity Xbjmrja [8, p. 5cQ, _J(D) is jquoc tm its ecmsurj o`h sm is ecmsjh.

(6) iapcijs (5). E(D) is o hivisim` ocdjfro fjeousj D is irrjhueifcjo`h _J(D) 1rimae3,D)(\, \) fy tbj Hj`sity Xbjmrja [8, p. 5? Q.

(5) iapcijs (8). Uuppmsj L is o vjetmr spoej mvjr o hivisim` ocdjfro

H o`h _J(D) 1BmaF( \, \). Fy Xbjmrja ? [8, p. 56Q, H 1 E(D) o`hfy Cjaao ?.?, Lis li`itj a-hiaj`sim`oc mvjr H. Tj lurtbjr mfsjrvj

tbot D is irrjhueifcj fjeousj Lis o` irrjhueifcj i(D)-amhucj. Xbus

il ei, , ja orj prmgjetim`s i` Bmalc(L, L) divi`d o hjemapmsitim`

ml L i`tm m`j-hiaj`sim`oc .H-spoejs, tbj` D 1 :6--ijD is o quosi-

hjemapmsitim` ml D i`tm irrjhueifcj drmups j;D sueb tbot _J(hD)

ji_J(D)ji [Q is o hivisim` ocdjfro, t 1 c, , a. Li`occy, tbj jDorj quosi-ismamrpbie drmups fjeousj tbj _J(D)ji orj ismamrpbie

36(D)-amhucjs [Q.

(8) iapcijs (?). Cjt ji, , ja fj ihjapmtj`ts emrrjspm`hi`d tm

tbj divj` quosi-hjemapmsitim` ml D. Xbj _J(D)ji orj ismamrpbie

(D)-amhucjs fjeousj tbj D, orj quosi-ismamrpbie drmups [Q. Xbus

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?94Q _ZOUI-HJEMA^MUIXIM@ML IVVJHZEIFCJ DVMZ^U 5:

[8, p. :6Q, ji, , ja orj hiodm`oc aotrix u`its i` _JiD). Ui`ej

ji_JiD)ji 1 _JiDi)P_JiD) [Q is o hivisim` ocdjfro, _JiD) is ism-amrpbie tm tbj ri`d m a "Ka aotriejs mvjr o hivisim` ocdjfro o`h

tbus sotislijs tbj ai`iaua em`hitim`. It is josy tm sjj tbot \ is o`

irrjhueifcj (RJ(E4)-amhucj o`h sm D is irrjhueifcj.

Vjaork ?.5. I` Xbjmrja ?.6, a is tbj u`iquj `uafjr ml quosi-

suaao`hs i` jvjry quosi-hjemapmsitim` ml D i`tm strm`dcy i`hjema-

pmsofcj drmups [Q.

Emrmccory ?.8. Cjt D fj fmtb irrjhueifcj o`h strm`dcy i`hjema-

pmsofcj. Xbj` il _JiD) sotislijs tbj ai`iaua em`hitim`, it is o hivi-

sim` ocdjfro.

Emrmccory ?.:. _JiD) 1C( \) il o`h m`cy il D is tbj hirjet sua ml o

li`itj `uafjr ml ismamrpbie ro`k-m`j sufdrmups.

^rmml. Il D 1 ],X-i D witb tbj D,- ismamrpbie ro`k-m`j sufdrmups,

tbj` D sotislijs (8) ml Xbjmrja ?.6. Xbus i` (5), H 1 _ fjeousj

w1ro`k D1 [\7_Q 1 [\7HQ[H7_Q 1a[H7_Q, wbjrj tbj froekjts

hj`mtj vjetmr spoej hiaj`sim` mvjr tbj i`hieotjh lijch. Em`vjrsjcy,suppmsj _JiD)1Ci\); tbj` (5) ml Xbjmrja ?.6 bmchs. @mw H 1 _

o`h sm a 1 ro`k D; fy (8), D11 /.,=P, D i witb tbj D quosi-ismamrpbie

ro`k-m`j drmups. Emrmccory 9.6 [cQ o`h Emrmccory 9.< [cQ emapcjtj

tbj prmml.

Fy guhieimuscy japcmyi`d Cjaao ?.? o`h orduaj`ts siaicor tm tbj

ofmvj, rjsucts ml ^ijrej [:Q eo` fj jxtj`hjh tm lucc sufri`ds ml siapcj

rotim`oc ocdjfros ml orfitrory hiaj`sim` mvjr _ [6g. Vjih [4Q bos

sbmw` tbot tbj ohhitivj drmup ml sueb sufri`ds is irrjhueifcj.

Tj em`ecuhj witb sjvjroc jxoapcjs. It is wjcc k`mw` [5, p. 6?6Q

tbot jvjry j`hmamrpbisa ml tbj p-ohie i`tjdjrs Gp is gust auctipcieo-

tim` fy smaj p-ohie i`tjdjr. It lmccmws tbot _JiG^) 1L^, tbj p-`hie

`uafjr lijch. Fy Xbjmrja ?.6, o`y li`itj hirjet sua ml Gp is o drmup

(ml u`emu`tofcj ro`k) witb quosi-j`hmamrpbisa ocdjfro sotislyi`d

tbj ai`iaua em`hitim` m` cjlt ihjocs. Cikjwisj, il iV)a hj`mtjs tbj

ri`d ml occ aRa aotriejs mvjr tbj ri`d V, tbj` iGp)a os o sufri`d

ml iLp)a bos o lijch ml hjli`itim` [UQ i` o dj`jrocizjh sj`sj [6Q.

Fifcimdropby

?. V. O. Fjouam`t o`h V. U. ^ijrej, Xmrsim`-lrjj ri`ds, Icci`mis G. Aotb. : (?9

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5< J. L. EMV@JCIZU,GV.

5. C. Luebs, Ofjcio` drmups, Okoh. Kioh, Fuhopjst, ?9:2; rjpri`t, I`tjr`ot.

Ujrijs ml Am`mdropbs ml ^urj o`h Oppc. Aotb., ^jrdoam` ^rjss, @jw Ymrk, ?9.

AV 6? #: