Pelargonidina Extraída Del Rábano Como Sustituto de Indicadores de PH Ácido-Base de Origen Sintético

 

Wh`irjbdoeodi hxtriëei eh` récidb abkb sustotutb eh odeoaiebrhs eh pM éaoeb-cish eh brojhd sodtïtoab  Iderhi Airb`odi Cirei`hs Cirei`hs Kirtëdhz 9  Orki Ei`o`i Vhdturi 3 

SHQXKHD   @i ph`irjbdoeodi hxtriëei eh` récidb hs udi idtbaoidodi quh cinb `i odf`uhdaoi eh `i iaoehz b cisoaoeie eh` kheob hd quh sh hdauhdtri, prbpbraobdi eofhrhdths ab`briaobdhs, bfrhaohdeb isë `i airiathrëstoai eh ud odeoaiebr eh pM. H` bcnhtovb eh` hstueob fuh oehdtofoair `bs odeoaiebrhs eh pM éaoeb-cish eh brojhd sodtïtoab, hkp`hiebs hd `i Xdovhrsoeie Diaobdi` Iutñdbki eh Mbdeuris hd h` Vi``h eh Qu`i, quh pueohrid shr sustotuoebs pbr `i ph`irjbdoeodi hxtriëei eh` récidb. H` eoshùb eh hsti odvhstojiaoñd fuh eh topb hxphrokhdti` eh aikpb, `i rhab`haaoñd eh eitbs fuh ``hviei i aicb hxtriyhdeb `i idtbaoidodi eh` récidb y ehthrkodideb `bs pudtbs eh vorinh prhshdtiebs pbr hsti. Qucshauhdthkhdth, sh rhi`ozñ udi shroh eh totu`iaobdhs hkp`hideb h` hxtriatb eh` récidb y `bs odeoaiebrhs eh pM eh brojhd sodtïtoab quh abodaoeohrbd abd h` odthrvi`b eh vorinh prhshdtieb pbr `i ph`irjbdoeodi. @bs rhsu`tiebs fuhrbd eosautoebs y hvi`uiebs i trivïs eh mhrrikohdtis hstieëstoais. H` 66.6: % eh `bs odeoaiebrhs eh pM eh brojhd sodtïtoab prhshdtñ udi ehsvoiaoñd hstédeir kiybr quh `i ph`irjbdoeodi hd `is totu`iaobdhs rhi`ozieis. @is ehthrkodiaobdhs eh pM piri sustidaois eh pruhci hd préatoais eh `icbritbrob eh quëkoai jhdhri` eh `i Xdovhrsoeie Diaobdi` Iutñdbki eh Mbdeuris hd h` Vi``h eh Qu`i, crodeirbd rhsu`tiebs soko`irhs tidtb abd odeoaiebr eh pM eh brojhd sodtïtoab abkb abd `i idtbaoidodi hxtriëei eh` récidb. H` 977 % eh `bs odeoaiebrhs eh pM hvi`uiebs hd `i odvhstojiaoñd puhehd shr féao`khdth sustotuoebs pbr `i ph`irjbdoeodi hxtriëei eh` récidb. Wi`icris a`ivh> odeoaiebrhs eh pM, idtbaoidodis, hxtriatb eh récidb, totu`iaobdhs éaoeb-cish, ph`irjbdoeodi 9 3

  Hstueoidth, Airrhri eh Yuëkoai Yuëkoai Odeustroi`, XDIM-VQ> iderhiamhkostry?3Gjkio`.abk iderhiamhkostry?3Gjkio`.abk   Ishsbri, Wrbfhsbri Airrhri eh Yuëkoai Yuëkoai Odeustroi`, XDIM-VQ> ei`o`ivhdturiGyimbb.abk ei`o`ivhdturiGyimbb.abk ?1

 

Shvosti Wbrti` eh `i Aohdaoi, Db. 97, nudob 3796

ICQUSIAU   Odtrbeuatobd> Wh`irjbdoeod, i rieosm‟s hxtriat os id idtmbayidod wmoam ehphdeodj bd tmh iaoeoty br i`li`odoty bf tmh kheouk eosp`iys eoffhrhdt ab`brs, iatodj is i amiriathrostoa pM odeoaitbr. Umh purpbsh bf tmh stuey wis tb oehdtofy tmh sydtmhtoa pM odeoaitbrs tmit abu`e ch sucstotuthe fbr tmh ph`irjbdoeod hxtriathe frbk rieosm, is ushe od tmh Ditobdi` Iutbdbkbus Xdovhrsoty bf Mbdeuris od tmh aikpus `baithe it Qu`i Vi``hy. Khtmbe> Umh ehsojd tilhd od tmos rhshiram wis id hxphrokhdti` foh`e< tmh eiti ab``hatobd wis airrohe but cy hxtriatodj idtmbayidod frbk rieosm ide ehthrkododj tmh ab`br turdodj pbodts prhshdthe cy tmos hxtriat. Qucshquhdt`y i dukchr bf totritobds whrh phrfbrkhe usodj tmh rieosm hxtriat ide sydtmhtoa pM odeoaitbrs wotm soko`ir ab`br turdodj pbodts prhshdthe cy tmh ph`irjbdoeod. Umh rhsu`ts whrh eosausshe ide hvi`uithe cy stitostoai` tbb`s. Shsu`ts> 66.6:% bf sydtmhtoa pM odeoaitbrs smbwhe i stideire ehvoitobd mojmhr tmid tmh ph`irjbdoeod od tmh totritobds kieh. WM ehthrkoditobds fbr thst sucstidahs ushe od jhdhri` amhkostry‟s `icbritbry od tmh XDIM-VQ aikpus jivh soko`ir fbr cbtm pM odeoaitbr ide tmhaid idtmbayidod hxtriathe rieosm. rhsu`ts Abda`usobd> tmh sydtmhtoa rieosm‟s hxtriat, ph`irjbdoeod, hiso`y rhp`iah 977%frbk pM odeoaitbrs isshsshe od tmh odvhstojitobd. Lhywbres> Odeoaitbrs bf pM, idtmbayidods, rieosm hxtriat, iaoe-cish totritobds, ph`irjbdoeod

?5

 

Wh`irjbdoeodi hxtriëei eh` récidb abkb sustotutb eh odeoaiebrhs eh pM éaoeb-cish...

ODUSBEXAAOÑD   @bs odeoaiebrhs eh pM bcthdoebs eh `i sëdthsos eh sustidaois brjédoais sbd hd h` kudeb iatui` `bs kés hkp`hiebs hd eostodtbs `icbritbrobs eh idé`osos quëkoab, hstb sh ehch i su i`ti abdfoico`oeie auideb h` idi`osti quëkoab pbshh `is abkphthdaois dhahsirois piri uto`ozir`bs. Hsth topb eh sustidaois brjédoais sodthtozieis pbr `i odeustroi quëkoai db sbd `is þdoais aipiahs eh kheor h` pM eh sustidaois odbrjédoais iaoeis y césoais< tikcoïd `is idtbaoidodis, kb`ïau`is prhshdths hd `i kiybrëi eh frutbs y mbnis, rhspbdsic`hs eh `i pojkhdtiaoñd eh hstbs, sbd aipiahs eh aikcoir su ab`briaoñd cinb h` hfhatb eh ud iukhdtb b eoskoduaoñd hd h` pM eh` kheob iaubsb hd quh sh hdauhdtrhd. (@`iki Jirki, Wojkhdtbs f`ivbdboehs, Idtbaoidodis, Hstruaturi, 9?6=).  I`okhdtbs abkb `i ab` `bkcirei b rhpb``b kbrieb, aþrauki, irédeidb, frhsi, chrhd nhdi, récidb pïti`bs ehpbshh rbsi, pbshhd hd su hstruaturi hstrua turi fosob`ñjoaipojkhdtb i `is idtbaoidodis. H` récidb, hdypirtoau`ir, hd su aésairi i `i ph`irjbdoeodi, i` quh sh `h itrocuyh h` ab`br fuasoi. (Juirdozb Fridab & Kirtëdhz _hphs, Idtbaoidodis, 377?).  I`judbs eh `bs i`okhdtbs khdaobdiebs mid soeb hstueoiebs pbr udovhrsoeiehs i`rhehebr eh` kudeb, cusaideb udi i`thrditovi hfhatovi hd `i sustotuaoñd eh `bs odeoaiebrhs eh pM eh brojhd sodtïtoab, yi quh hstb okp`oairëi khdbr abstb kbdhtirob eh iequosoaoñd, féao` iaahsb eh` pojkhdtb, `hvh rohsjb i `i si`ue pbr sbcrhhxpbsoaoñd y féao` kidhnb eh `bs ehshambs. H` pM b, prbpoikhdth eoamb, `i abdahdtriaoñd eh obd moerbdob hs udi kheoei kuy okpbrtidth i dovh` cob`ñjoab h odeustroi`. Wrbahsbs cobquëkoabs ti`hs abkb `i bxojhdiaoñd eh `i sidjrh, `i aité`osos eh rhiaaobdhs hdzokétoais y h` ehsirrb``b eh hdhrjëi khticñ`oai euridth `i rhsporiaoñd b `i fbtbsëdthsos eh brjidoskbs vovbs, sbd ifhatiebs pbr `i abdahdtriaoñd eh` obd moerbdob. (Mbrtbd, I, Whrry, Whrry, & Siwd N, 377=).  I dovh` odeustroi`, odeustroi`, `i okpbrtidaoi eh` pM pM rieoai rieoai hd rucrbs abkb h` eh i`okhdtbs, abskïabskïtoabs, firkiaïutoai y ip`oaiaobdhs abkb h` tritikohdtb eh ijuis piri ai`ehris y ijuis rhsoeui`hs, prbahsbs eh fhrkhdtiaoñd y iatoviaoñd eh hdzokis y ciathrois piri `i prbeuaaoñd eh cobprbeuatbs. @i kheoaoñd eh` pM sh miah pbr kïtbebs pbthdaobkïtroabs b ab`brokïtroabs. Hstbs þ`tokbs, abdsosthd hd h` hkp`hb (eh sb`uaobdhs b piph` okprhjdieb) eh sustidaois ?8

 

Shvosti Wbrti` eh `i Aohdaoi, Db. 97, nudob 3796

quh prbvhhd ud ab`br hsphaëfoab hd prhshdaoi eh udi abdahdtriaoñd ehthrkodiei eh obdhs moerbdob< hstis sustidaois sh abdbahd abkb odeoaiebrhs eh pM.   @i rizñd eh ud aikcob eh ab`br pbr pirth eh` odeoaiebr eh pM sh ehch i udi tridsfbrkiaoñd hstruaturi` quh sufrh `i kb`ïau`i eh` odeoaiebr prbvbaiei pbr udi prbtbdiaoñd b ehsprbtbdiaoñd. (Jbkhz Qbsi, 3797). @bs odeoaiebrhs eh pM eh brojhd sodtïtoab y dituri` ehchd su fiau`tie i udi sustidaoi hsphaëfoai, sohdeb hd `i kiybrëi eh `bs aisbs ud abkpuhstb brjédoab. Qod hkcirjb, hxosthd odeoaiebrhs eh pM quh puhehd oda`uor udi shroh eh abkpuhstbs brjédoabs, i hsth topb eh odeoaiebrhs sh `hs abdbah abkb udovhrsi`hs. Hd `i tic`i 9 sh puhehd iprhaoir `is airiathrëstoais eh i`judbs eh `bs odeoaiebrhs eh pM eh brojhd sodtïtoab, su dbkcrh abkþd y su abkpbdhdth iatovb.

Uic`i 9. Odeoaiebrhs eh pM eh brojhd sodtïtoab  

 

 

Dbkcrh abkþd

Dbkcrh quëkoab

Vorinh eh ab`br  Odthrvi`b eh pM 

Izu` eh tokb` 

Uokb`sufbdfti`hodi  

Sbnb- ikiro``b  9.3-3.= 

Diridni eh khto`b 

Éaoeb p-eokhtoo`ikodbizbchdahdbsu`fbdoab 

Sbnb- ikiro``b  1.9-5.5 

Sbnb eh khto`b 

Éaoeb eokhto`ikodbizbchdahdb-aircbxo`oab  

Sbnb-ikiro``b 

5.3-6.3 

Izu` eh crbkbtokb` 

Eorcrbkbtokb`sufbdfti`hodi  

Ikiro``b-izu` 

6.7-:.6 

Fhdb`fti`hëdi  

Fhdb`fti`hëdi 

Odab`brb-rbsi  

=.7-?.= 

Uokb`fti`hëdi 

Uokb`fti`hëdi 

Odab`brb- izu` 

?.1-97.8 

Fuhdth> (@iotodhd & Mirros, 9?=3)

Auideb sh triti eh ud odeoaiebr eh pM eh brojhd dituri`, `i sustidaoi hdairjiei eh prbpbraobdir eoami fiau`tie sh abdbah abkb idtbaoidodis< `i ab`briaoñd prhshdtiei pbr hstis vi udoei i` dþkhrb eh jrupbs moerbxo`b y khtbxo`b hd `bs ido``bs eh` hsquh`htb césoab eh `bs f`ivbdboehs, `i prhshdaoi eh éaoebs irbkétoabs hsthrofoaieb hd h` ido``b prodaopi` y pM ebdeh sh i`kiahdi h` pojkhdtb. Xd hstueob rhi`ozieb hd Kïxoab (Yuodthrb Mhrdidehz, 3795) rhvh`ñ quh `i idtbaoidodi prhshdth hd `i aisairi eh` récidb rbnb hs `i ph`irjbdoeodi-1-sbfbrbsoeb-8-j`uabsoeb. @i ph`irjbdoeodi, i` ojui` quh h` rhstb eh idtbaoidodis, hs ud abkpuhstb moerbsb`uc`h quh crodei udi ab`briaoñd rbnb-diridni i `is hsphaohs quh `b abdtohdhd. ?6

 

Wh`irjbdoeodi hxtriëei eh` récidb abkb sustotutb eh odeoaiebrhs eh pM éaoeb-cish...

KHUBEB@BJËI H` kïtbeb hkp`hieb piri `i hxtriaaoñd eh `i idtbaoidodi eh` récidb hs udi kbeofoaiaoñd eh` kïtbeb Jousto & Zrb`stie (9?6=). Qh rhi`ozirbd auitrb kiahriaobdhs, i fod eh hstic`hahr ud kïtbeb p`iusoc`h piri ``hvir i aicb i dovh` eh `icbritbrob. Hd `i tic`i 3 sh kuhstri `is abdeoaobdhs cinb `is aui`hs sh rhi`ozirbd 5 hxtriaaobdhs abdsoehrideb eofhrhdths viroic`hs piri `i bcthdaoñd eh` kiybr abdthdoeb eh idtbaoidodi. H` kïtbeb hkp`hieb sujohrh `i abdahdtriaoñd eh` hxtriatb pbr kheob eh ud rbtivipbr,, piri `b aui` udi eh `is kiahriaobdhs sh tritñ abd ehsto`iaoñd pbr kheob eh rbtivipbr ciùb Kirëi y i udi thkphrituri eh :7 ·A i prhsoñd itkbsfïroai.

Uic`i 3. Uïrkodbs cinb `bs aui`hs sh ``hvirbd i aicb `is kiahriaobdhs   Db. eh kiahriaoñd

 

 

 

 

 

9

3

1

5

  93.8 jr 

  93.8 jr 

  53.3 jr 

  53.3 jr 

Abdeoaobdhs

Kisi eh `i aésairi eh récidb uto`oziei   Qb`vhdth hkp`hieb

Khtidb` 7.79 % Khtidb` 7.79 % Khtidb` 7.79 % Khtidb` 7.79 % éaoeb iaïtoab éaoeb iaïtoab éaoeb iaïtoab éaoeb iaïtoab

Vb`ukhd eh sb`vhdth hkp`hieb

387 k`

Fo`triaoñd piph` Air` Q&Q Ab Db. 8?8 Ehsto`iaoñd

 

  387 k`

387 k`

 

387 k`

 

  Qh rhi`ozñ

  Qh rhi`ozñ

  Qh rhi`ozñ

Qh rhi`ozñ

Db sh rhi`ozñ

Qh rhi`ozñ

Db sh rhi`ozñ

Db sh rhi`ozñ

Fuhdth> h`icbriaoñd prbpoi.

?:

 

Shvosti Wbrti` eh `i Aohdaoi, Db. 97, nudob 3796

Wiri rhi`ozir `i airiathroziaoñd eh` ab`br eh` odeoaiebr eh ph`irjbdoeodi sh prhpirñ udi shroh eh sb`uaobdhs cuffhr b tikpñd, iciraideb ud ridjb eh pM eh 9-93.=. I aiei sb`uaoñd cuffhr sh ijrhjñ ud tbti` eh 8 jbtis eh odeoaiebr eh ph`irjbdoeodi pbr aiei 8k` eh sb`uaoñd tikpñd y sh tbkñ dbti eh `i ab`briaoñd prhshdtiei, isë abkb fbtbjrifëis. Wbsthrobrkhdth, sh rhi`ozñ `i sh`haaoñd eh `bs odeoaiebrhs eh pM eh brojhd sodtïtoab quh abodaoeohrbd abd `bs pudtbs eh vorinh prhshdtieb pbr `i ph`irjbdoeodi. @i sh`haaoñd sh fudeikhdtñ hd `bs vorinhs eh pM piri odeoaiebrhs sodtïtoabs prhshdtieb pbr Ebdi` C. Qukkhrs (9?=1).   Wiri ehthrkodir `i prhaosoñd eh `i ph`irjbdoeodi y pbdhr`i hd abdtristh abd `i prhaosoñd eh `bs odeoaiebrhs eh pM eh brojhd sodtïtoab, sh rhi`ozirbd udi shroh eh totu`iaobdhs éaoeb-cish< hstis sh ``hvirbd i aicb hd rïp`oais eh aodab, uto`ozideb MA` 7.38 K, DiBM 7.9K y DiMAB1 7.9K. Qh hkp`hñ abkb odeoaiebr eh ph`irjbdoeodi `i kiahriaoñd 5. Abd h` fod eh ishjurir h` hkp`hb eh `i ph`irjbdoeodi hd `i kheoaoñd eh` pM eh sustidaois abkp`hnis, hd auidtb i su abdthdoeb eh hdtoeiehs quëkoais y db sb`b hd sb`uaobdhs eh udi sb`i hdtoeie, sh ``hvirbd i aicb kheoaobdhs eh pM hd `is sojuohdths sustidaois> `hamh, nujb eh diridni, sbei (chcoei aircbditiei), si`ovi, brodi, sb`uaoñd  nicbdbsi, jh` idtociathroi` y pb`vb piri mbrdhir mbrdhir.. @is kheoaobdhs sh rhi`ozirbd pbr eup`oaieb, tbkideb 8 k` eh aiei sustidaoi y ijrhjideb ud tbti` eh 97 jbtis eh ph`irjbdoeodi misti bcshrvir `i fbrkiaoñd eh` ab`br odeoaitovb eh pM< hsth hd aiei sustidaoi sh vhrofoañ pbr kheobs pbthdaobkïtroabs.  Isokoskb, `is kheoaobdhs eh eoamis eoamis sustidaois sustidaois abkp`hnis sh rhi`ozirbd rhi`ozirbd abd abd h` odeoaiebr eh Lb`tmbff, abdsoehrideb quh hsth þ`tokb hs hkp`hieb piri `i préatoai> kheoaoñd eh pM okpirtoei hd `bs `icbritbrobs eh quëkoai jhdhri` hd `i Xdovhrsoeie Diaobdi`  Iutñdbki eh Mbdeuris Mbdeuris hd h` Vi``h Vi``h eh Qu`i.Ehspuïs eh rhi`ozir `bs hdsiybs, miaohdeb usb eh mhrrikohdtis hstieëstoais, sh ehthrkodñ `i ehsvoiaoñd hstédeir eh aiei shroh eh totu`iaobdhs y sh rhi`ozñ udi eosausoñd eh `bs vi`brhs bcthdoebs.

SHQX@UIEBQ @bs rhsu`tiebs eh `i khtbeb`bjëi eh hxtriaaoñd eh ph`irjbdoeodi (idtbaoidodi) eh` récidb sh prhshdtid hd `i tic`i 1. ?=

 

Wh`irjbdoeodi hxtriëei eh` récidb abkb sustotutb eh odeoaiebrhs eh pM éaoeb-cish...

Uic`i 1. Qhjuokohdtb eh` prbahsb eh hxtriaaoñd eh `i idtbaoidodi eh` récidb   Db.

  Odoaob kiahriaoñd

  Euridth kiahriaoñd

 

Fodi` eh kiahriaoñd @ëquoeb fo`trieb

9

3

1

5

Fuhdth> h`icbriaoñd prbpoi.

@i airiathroziaoñd eh` ab`br eh `i ph`irjbdoeodi hd sb`uaoñd i`abmñ`oai sh rhi`ozñ piri aiei hxtriaaoñd abd h` fod eh ehthrkodir, vosui`khdth, aué` eh `is kiahriaobdhs prbpbraobdirëi `is tbdi`oeiehs khnbr ehfodoeis y abd kiybr odthdsoeie eh ab`br. @bs khnbrhs tic`i 5). rhsu`tiebs fuhrbd crodeiebs pbr `i kiahriaoñd b hxtriaaoñd dþkhrb 5 (vhr ??

 

Shvosti Wbrti` eh `i Aohdaoi, Db. 97, nudob 3796

Uic`i 5. Airiathroziaoñd eh` ab`br eh `i ph`irjbdoeodi, kiahriaoñd 5 pM

9.3

9.=

1.7

5.7

8.7

6.7

:.7

=.7

?.9

97.7

99.7

93.7

93.=

Ab`br 

Fuhdth> h`icbriaoñd prbpoi.

Eh iauhreb i `bs rhsu`tiebs bcthdoebs abd `i airiathroziaoñd eh` ab`br eh `i ph`irjbdoeodi, `bs odeoaiebrhs sh`haaobdiebs piri hsth hstueob sh kuhstrid hd `i tic`i 8.

Uic`i 8. Odeoaiebrhs eh pM eh brojhd sodtïtoab pbsoc`hkhdth rhhkp`izic`hs pbr `i ph`irjbdoeodi   Odeoaiebr éaoeb-cish

Aikcob eh ab`br (I-4 C)

 

Izu` eh crbkbfhdb`

Ikiro``b-4 izu`

1.7-5.6

Fhdb`fti`hëdi

Odab`brb-4 rbsi

=.1-97.7

Uokb` fti`hëdi

Odab`brb-4 izu`

?.1-97.8

Odthrvi`b eh pM

 

Fuhdth> h`icbriaoñd prbpoi.

Hstic`haoebs `bs odeoaiebrhs eh pM sodtïtoabs, pbsoc`hs eh shr rhhkp`iziebs pbr `i ph`irjbdoeodi, sh ``hvirbd i aicb `is totu`iaobdhs éaoeb-cish abrrhspbdeohdth i` odthrvi`b eh pM hsphaëfoab piri aiei odeoaiebr sh`haaobdieb.   Wiri `i totu`iaoñd éaoeb-cish hd h` odthrvi`b eh pM fodi` 1.7-5.6, `bs rhsu`tiebs eh `i ehsvoiaoñd hstédeir sh puhehd vhr hd `i tic`i 6.

977

 

Wh`irjbdoeodi hxtriëei eh` récidb abkb sustotutb eh odeoaiebrhs eh pM éaoeb-cish...

Uic`i 6. Wrhaosoñd eh ikcbs odeoaiebrhs, odeo aiebrhs, pM fodi` 1.7-5.6   Odeoaiebr 

  Wrbkheob Ehsvoiaoñd Wrhaosoñd (x)   (x) hstédeir (ρ)  ( x + ρ )  )  

Ub`hridaoi (x+3ρ) 

Izu` eh crbkbfhdb` Wh`irjbdoeodi

5.76 1.?1

5.76¹7.97= 1.?1¹ 7.7==

7.785 7.755

5.76¹ 7.785 1.?1¹7.755

Fuhdth> h`icbriaoñd prbpoi.

Wiri `i totu`iaoñd éaoeb-cish hd h` odthrvi`b eh pM fodi` =.1-97.7, `bs rhsu`tiebs eh `i ehsvoiaoñd hstédeir sh kuhstrid hd `i tic`i :.

Uic`i :. Wrhaosoñd eh ikcbs odeoaiebrhs, pM fodi` =.1-97.7 Odeoaiebr  

Wrbkheob Ehsvoiaoñd Wrhaosoñd  (x)   (x) hstédeir (ρ)  ( x + ρ )  )  

Ub`hridaoi (x+3ρ) 

Fhdb`fti`hëdi

1.=

7.38=

5.76¹ 7.38=

5.76¹7.896

Wh`irjbdoeodi

1.:

7.7=3

11.:¹7.7=3

1.?1¹ 7.965

Fuhdth> h`icbriaoñd prbpoi.

Wiri `i totu`iaoñd éaoeb-cish hd h` odthrvi`b eh pM fodi` ?.1-97.8, `bs rhsu`tiebs eh `i ehsvoiaoñd hstédeir sh iprhaoid hd `i tic`i =.

Uic`i =. Wrhaosoñd eh ikcbs odeoaiebrhs, pM fodi` ?.1-97.8.1-97.7   Odeoaiebr 

  Wrbkheob Ehsvoiaoñd Wrhaosoñd (x)   (x) hstédeir (ρ)  ( x + ρ )  )  

Ub`hridaoi (x+3ρ) 

Uokb`fti`hëdi

7.93

7.73:

7.93¹ 7.73:

7.93¹7.785

Wh`irjbdoeodi

7.91

7.73:

7.91¹7.73:

7.91¹ 7.785

Fuhdth> h`icbriaoñd prbpoi.

979

 

Shvosti Wbrti` eh `i Aohdaoi, Db. 97, nudob 3796

Hd `i kheoaoñd eh` pM eh sustidaois abkp`hnis, hkp`hideb ph`irjbdoeodi h odeoaiebr eh Lb`tmbff, `bs rhsu`tiebs bcthdoebs hstéd hd `i tic`i ?.

Uic`i ?. Shsu`tiebs eh `is kheoaobdhs eh pM, odeoaiebr Lb`tmbff y ph`irjbdoeodi  

Kheoaoñd eh pM

Qustidaoi

Lb`tmbff

Wh`irjbdoeodi

pMkhtrb 

Qbei 

  5,7

  5,7

  5,7

Nujb eh diridni 

5,7

  1,7

  5,3

@hamh eh kijdhsoi 

  ?,7

  ?,7

  ?,7

Jh` idtociathroi` 

  8,7

  6,7

  6,3

Brodi 

  =,7

  6,7

  6,?

Wb`vb eh mbrdhir  

  ?,7

  ?,7

  :,?

Iahoth vhjhti` 

  8,7

  8,7

  8,5

@hamh 

  6,7

  6,7

  6,9

Qi`ovi 

  :,7

  6,7

  6,:

Nicñd 

6,7 

5,7 

6,6 

Fuhdth> h`icbriaoñd prbpoi.

IDI@OQOQ Eh `bs rhsu`tiebs bcthdoebs piri aiei kiahriaoñd, ehspuïs eh su fo`triaoñd ticu`iebs hd `i tic`i 1, sh bcshrvi quh `i kiahriaoñd 5 prhshdti kiybr ab`briaoñd quh h` rhstb, pbr `b aui` sh abdsoehri quh su abdthdoeb eh idtbaoidodi hs kiybr kiybr..

973

 

Wh`irjbdoeodi hxtriëei eh` récidb abkb sustotutb eh odeoaiebrhs eh pM éaoeb-cish...

Abdsoehrideb `bs rhsu`tiebs fodi`hs eh `is auitrb kiahriaobdhs rhi`ozieis, `is abdeoaobdhs ñptokis piri `i hxtriaaoñd eh ph`irjbdoeodi eh` récidb sbd `is ``hvieis i aicb hd `i kiahriaoñd 5, phrb eieb quh h` sb`vhdth pbshh ud `hvh jrieb eh tbxoaoeie, su vi`br hd h` abkhraob hs habdñkoab y db hs dhahsiroi udi abdahdtriaoñd eh` hxtriatb pbr kheob eh ehsto`iaoñd b h` hkp`hb eh i`tis thkphrituris piri i`aidzir ud cuhd rhdeokohdtb eh hxtriaaoñd. Eh iauhreb abd `i tic`i 5, `bs rhsu`tiebs bcthdoebs hd `i airiathroziaoñd eh` ab`br eh `i ph`irjbdoeodi rhspi`eid abkb khnbr kïtbeb eh hxtriaaoñd h` ``hvieb i aicb piri `i kiahriaoñd 5. Qhjþd `i tic`i 6, idth udi khdbr ehsvoiaoñd hstédeir prhshdtiei pbr `i ph`irjbdoeodi, sh abdsoehri quh hsti crodei udi kiybr prhaosoñd hd abkpiriaoñd i `i prhaosoñd eh` odeoaiebr izu` eh crbkbfhdb`. Eh iauhreb abd `i tic`i :, idth udi khdbr ehsvoiaoñd hstédeir prhshdtiei pbr `i ph`irjbdoeodi, sh abdsoehri quh hsti crodei udi kiybr prhaosoñd hd abkpiriaoñd i `i eh` odeoaiebr eh fhdb`fti`hëdi. Hd `i tic`i =, idth udi ehsvoiaoñd hstédeir prhshdtiei pbr `i ph`irjbdoeodi ojui` i` odeoaiebr eh tokb`fti`hëdi, sh abdsoehri quh ikcbs odeoaiebrhs pbshhd udi prhaosoñd soko`ir. soko`ir. Wbr þ`tokb, hd `i tic`i ?, idth `bs rhsu`tiebs bcthdoebs, `i ph`irjbdoeodi hs ud fiatoc`h sustotuyhdth eh` odeoaiebr eh Lb`tmbff piri `is sustidaois prbpuhstis.

ABDA@XQOBDHQ @bs odeoaiebrhs eh pM sodtïtoabs piri sustidaois odbrjédoais iaoeis y césoais hkp`hiebs hd `bshd `icbritbrobs quëkoai eh `i Xdovhrsoeie Iutñdbki eh Mbdeuris h` Vi``h ehehQu`i, quh jhdhri` pberéd shr sustotuoebs pbrDiaobdi` `i ph`irjbdoeodi hxtriëei eh` récidb y quh sh oehdtofoairbd, fuhrbd `bs sojuohdths> h` odeoaiebr eh Lb`tmbff, izu` eh crbkbfhdb`, fhdb`fti`hëdi y tokb`fti`hëdi. Hd abdshauhdaoi, eh iauhreb abd `bs rhsu`tiebs bcthdoebs y `i eosausoñd rhi`oziei, sh hstic`hah quh hs `i ph`irjbdoeodi ud ñptokb odeoaiebr eh pM quh puheh sustotuor i `bs odeoaiebrhs eh pM eh brojhd sodtïtoab oehdtofoaiebs< db sb`b pbr prhshdtir udi hxah`hdth prhaosoñd, sodb pbrquh rhsu`ti ud itriatovb sustotuyhdth pbr su fiao`oeie eh bcthdaoñd y su `hvh jrieb eh tbxoaoeie.

971

 

Shvosti Wbrti` eh `i Aohdaoi, Db. 97, nudob 3796

IJSIEHAOKOHDUBQ  I Nbrjh @uos @uos Whrhori, pbr `i trieuaaoñd i` hspiùb` hspiùb` eh kithroi` y fuhdths eh odfbrkiaoñd hdabdtriebs hd odj`ïs. Isokoskb, i Orki Vhdturi, pbr `i abrrhaaoñd y hvi`uiaoñd eh` tricinb eh odvhstojiaoñd rhi`ozieb.

COC@OBJSIFËI Ciaaid, D.< Iderieh, N.< Jbeodmb, B. H. y Cirbdh, N. Q. (9?:?). Yuëkoai Idi`ëtoai Auidtotitovi H`hkhdti`. 3ei he . Aikpodis> Xdoaikp. 56 @`iki Jirki, H. (9?=6). Wojkhdtbs f`ivbdboehs, Idtbaoidodis, Hstruaturi, Wrbpoheiehs. Yuëkoai y Cobquëkoai eh `is Frutis y Vhjhti`hs  Vhjhti`hs  @i Micidi, Auci> Wuhc`b y Heuaiaoñd. 5:-89 Jousto, & Zrb`stie,Nburdi` S. (9?6=). Sieosm Idtmbayid Idtmbayidod od Hxtriat is 133-136. Dituri` She Ab`bridt fbrK. Kirisamodb. bf Fbbe Qaohdah ide Dutrotobd, Dutrotobd , 69, Jñkhz Qbsi, J. (3797). Odeoaiebrhs eh pM . Kïxoab> Fiau`tie eh Yuëkoai, XDIK. Juirdozb Fridab, I. y Kirtëdhz _hphs, W. D. (377?). Hxphrokhdtbs eh quëkoai brjédoai.. Ab`bkcoi> H`ozabk. ai Mbrtbd, M. S.< Kbrid, @. I.< Whrry, K. E. y Siwd, N. (377=). Wrodaopobs eh cobquëkoai. cobquëkoai. Kïxoab> Whirsbd Heuaiaoñd. Qukkhrs, E. C. (9?=1). Kidui` eh Yuëkoai. Yuëkoai. Kïxoab> Ochrbikïroai. _ufhri, H. W. W. (9??8). Yuëkoai brjédoai césoai y ip`oaiei> eh `i kb`ïau`i i `i odeustroi. odeustroi. Hspiùi> Shvhrth.

975