GENETIC VARIABILITY FOR GIRTH GROWTH AND RUBBER YIELD IN Hevea brasiliensis
|
|
- Kerrie Powell
- 5 years ago
- Views:
Transcription
1 46 Gonçalvs t al. GENETIC VARIABILITY FOR GIRTH GROWTH AND RUBBER YIELD IN Hva brasilinsis Paulo d Souza Gonçalvs 1 ; Marlo d Almida Silva ; Ligia Rgina Lima Gouvêa 1 ; Erivaldo José Saloppi Junior 3 1 Apta/IAC - Programa Sringuira, Av. Barão d Itapura, 1481, C.P Campinas, SP - Brasil. Apta/DDD - Pólo Rgional Cntro Ost, C.P Jaú, SP - Brasil. 3 Apta/DDD - Pólo Rgional Norost Paulista, C.P , Votuporanga, SP - Brasil. Corrsponding author <paulog@ia.sp.gov.br> ABSTRACT: Basi knowldg of gnti haratristis of populations is nssary to ondut fftiv brding and sltion. Th objtiv of this papr is dsribing th gnti variation of rubbr yild and th orrlation with othr traits, and stimating th gnti paramtrs foirth growth and total numbr of latx vssls. Sixty svn lons of Hva brasilinsis (Willd. x Adr. d Juss.) Mull.-Arg. wr tstd at fiv sits during 10 yars. Charatrs girth growth at panl opning and rubbr yild, showd broad sns hritability on plot man lvl, from 0.3 to 0. and 0.59 to 0.9, rsptivly. Prditd gnti gains qual to 0.73 m and 0.79 g inras rsptivly on girth and yild in th opning panl and matur phass sms ralisti, vn with modrat sltion intnsitis. Gnti orrlations with rubbr yild, bark thiknss and total numbr of latx vssls wr vry larg, and almost no gnotyp-nvironmnt intration was prsnt foirth growth. High gnotyp-nvironmnt intration was prsnt for rubbr yild with gnti and phnotypi orrlations aross th sits, ranging from 0.64 to 0.9 (gnti) and 0.63 to 0.89 (phnotypi). Total numbr of latx vssls rings had a high hritability, ranging from 0.0% to 64.0% in th sits E and B, rsptivly. Ky words: rubbr tr, hritability, gnti orrlations, gnotyp-nvironmnt intration VARIABILIDADE GENÉTICA PARA CRESCIMENTO DO CAULE E PRODUÇÃO DE BORRACHA EM Hva brasilinsis RESUMO: O onhimnto básio das aratrístias prsnts nas populaçõs d plantas é ssnial para a ondução dos trabalhos d slção mlhoramnto. Nst trabalho, objtivou-s dsrvr a variação gnétia da produção d borraha orrlaioná-las om outras aratrístias, assim omo stimar os parâmtros gnétios para prímtro do aul o númro d anéis d vasos latiífros. Um total d 67 lons d sringuira [Hva brasilinsis (Willd. x Adr. Juss.) Mull.-Arg.] foram avaliados m ino loais durant 10 anos. Os aratrs prímtro do aul na abrtura do painl produção d borraha mostraram hrdabilidads no sntido amplo ao nívl d média d parla ntr 0,3 a 0, 0,59 a 0,9, rsptivamnt. Ganhos gnétios prditos d 0,73 m 0,79g d inrmnto d prímtro na fas juvnil parm viávis msmo om uma intnsidad d slção modrada. Corrlaçõs gnétias ntr produção d borraha, spssura d asa númro total d vasos latiífros foram muito altas, pratiamnt não houv intração gnótipo-ambint para prímtro do aul. Alta intração gnótipo-ambint foi dttada para produção d borraha, om orrlaçõs gnétias fnotípias por loais variando ntr 0,64 0,9 (gnétias) 0,63 0,89 (fnotípias). O arátr total d anéis d vasos latiífros aprsntou alta hrdabilidad, variando d 0% até 63% nos loais E B, rsptivamnt. Palavras-hav: sringuira, hrdabilidad, orrlação gnétia, intração gnótipo-ambint INTRODUCTION To improv th produtivity of rubblantations, Hva brding programs xploit gntially variabl populations to obtain suprior trs. A basi knowldg of th gnti haratristis of plant populations is nssary to ondut fftiv brding and sltion. Quantitativ information is rquird about th siz of gnti varians, th typ of gn ation, and th hritability and gnti orrlations for onomially important traits. This nabls th outom of sltion to b prditd, partiularly gnti gains. It also hlps dtrmining diffiultis in sltion and th stratgis to ovrom suh problms. In a broadr ontxt, it broadns knowldg of th gntis and brding bhavior of th spis involvd. Th Instituto Agronômio (IAC) onduts a Brazilian Hva brding program, with mphasis on Si. Agri. (Piraiaba, Braz.), v.63, n.3, p.46-54, May/Jun 006
2 Girth and rubbr yild in rubbr trs 47 improvmnt and sltion of vigour and quality traits, suh as latx vssls rings. Th objtiv of this papr is dsribing th gnti variation of rubbr yild, and its orrlation with othr traits. Gnti paramtrs foirth and total numbr of latx vssls of 67 lons, 13 yars aftr stablishmnt in th fild, wr also studid. MATERIAL AND METHODS Plant matrial and xprimntal loations Thirty on Brazilian, 10 Indonsian, and 6 Malaysian Hva brasilinsis gnotyps (lons) wr usd in this study. Th Brazilian lons Fx, IAC, and IAN wr dvlopd by th Fordland brding program, Instituto Agronômio (IAC), and formr Instituto Agronômio do Nort (IAN), now Embrapa Oidntal. Th Indonsian lons omprisd GT, PR, and AVROS, from Gondang Tapn, Profstation voor Rubbr, and Algmn Vrning Rubbr Plantrs Oostkust Sumatra xprimntal stations, rsptivly. Th Malaysian ultivars onsistd of RRIM and PB, from Rubbr Rsarh Institut of Malaysia, and Prang Bsarivat rubblantation rsptivly. Among th 67 lons, PB 35, GT 1, RRIM 600 and IAN 873 ar rommndd prodution lons, whras RRIM 701, PR 55, PR 61, IAN 873, PB 16, and RO 38, ar usd as parnts in loal rubbr brding programs. Th rubbr lons wr graftd ovr stablishd GT 1 rootstoks at th nursry. On yar-old rootstoks sdlings raisd in nursris wr usd to budgraft lonal matrials. Th sussful budgrafts wr uprootd and plantd in polythyln bags. Aftr th first flush of lavs dvlopd, plants wr stablishd in th fild. Th lons wr grown for tn yars in fiv ontrasting tst nvironmnts (A, B, C, D and E) in th platau rgion of São Paulo Stat, ologial onditions summarizd as: Jaú (A): º17 S, 48º34 W; altitud 580 m; man annual tmpratur 1.6ºC; man annual rainfall 1,344 mm; Kandiudox soil, with good nutrint status and physial strutur. Mooa (B): 1º18 S, 47º01 W; altitud 5 m; man annual tmpratur 4ºC; man annual rainfall 1,500 mm; Eutrustok soil, with good nutrint status and physial strutur. Ribirão Prto (C): º11 S, 47º48 W; altitud 467 m; man annual tmpratur 9ºC; man annual rainfall 1,530 mm; Kandiudox soil, with good nutint status but poohysial strutur. Votuporanga (D): 0º5 S, 49º50 W; altitud 450 m; man tmpratur during growing sason 3ºC; man annual rainfall 1,480 mm; Paludalf soil, with avrag nutrint status and poohysial strutur. Matão (E): 1º18 S, 48º40 W; altitud 551 m; man annual tmpratur 5ºC; man annual rainfall 1,480 mm; Paludox soil typ, with avrag nutrint status and vry good physial strutur. Ths loations rprsnt th most important ontinntal limat, non-traditional rubbrodution aras in Brazil. Exprimntal dsign at ah tst loation was randomizd omplt bloks (n = 3), with tn plants pr on-row plot in all loations. Trs wr spad 8.00 m btwn and.50 m within rows (500 trs ha -1 ). Masurmnts At th nd of th svnth yar, girth, bark thiknss and total latx vssl rings at panl opning for tapping and rubbr yild of ah tr wr masurd. Girth masurmnts wr rordd at 1.0 m from th highst point of th bud union. For annual latx prodution, attmpts wr mad to rord fiv annual yilds aftanl opning. Th latx xtratd from th tapping panl followd a half-spiral, four-daily tapping systm (svn tappings pr month), 11 months pr yar. Aftr tapping, latx was olltd in plasti ups providd for ah rording tr. On th latx flow was stoppd, rubbr was oagulatd in th up by adding % ati aid solution and stirring. Th oagulatd rubbr was prssd into a ylindr, hang-drid for 30 days, and thir wighd for alulation of th dry rubbr ontnt. Statistial analyss within sits Th following linar modl was usd to analyz th data within sits: Y ij = μ + b j + i + ε ij, whr Y ij = prforman of th ramt of i th lon within j th blok; μ = ovrall man, b j = random fft of th j th blok; i = random fft of th i th lon, E( i ) = 0 and Var ( i ) = σ, ε ij = random rror, qual to th intration btwn th i th lon and j th blok, E (ε ij ) = 0 and Var (ε ij ) = σ. Th analysis of varian was prformd using produrs of th softwar Slgn, vrsion 1.0 (Rsnd & Olivira, 1997) to stimat ovarians. Tsts for normal distribution of singl tr data, lon mans data and rsiduals wr mad using th Gns softwar, Windows vrsion, 001 (Cruz, 001). A fw missing masurmnts in th trials wr du to low dvlopmnt of th trs girth, mainly xplaind by th lak of ompatibility btwn rootstoks and sions. Broad sns hritabilitis on plot and lon man lvls wr alulatd. Following Cottrill Si. Agri. (Piraiaba, Braz.), v.63, n.3, p.46-54, May/Jun 006
3 48 Gonçalvs t al. (1987), a distintion was mad btwn diffrnt hritabilitis dpnding on th purpos. Th alulatd broad sns hritability on plot man lvl is, in this as, usd to alulat gnti gains by mass sltion on sits similar to th trials, whr th blok ffts an not b takn into aount. Th broad sns hritability on a lonal man basis is appropriat forditing gnti gains from sltion among th lons in th trials. In this as, th fft of bloks an b aountd forior to sltion. Th plot man broad sns hritability h p was thrfor alulatd as: hp = σ /( σ + σ b + σ ), whr σ = gnti varian or ovarian omponnts btwn lons, σ b is th blok varian, and σ th rror varian omponnts. Th broad sns hritability on lon man lvl h m was alulatd as: hm = σ /( σ + σ / b), whr b is th harmoni man of ramts pr lon in th trial. Approximat standard dviations of hritabilitis wr found using th dlta thniqu (Bulmr, 1980). Th gnti orrlations btwn trait x and y within sits wr alulatd aording to Falonr (1989) as: rg = Cov /( σ x σ y ). Th gnti ovarian Cov was obtaind by using man ross produts from th Gns produr. Approximat standard dviations of th gnti orrlations within sits wr alulatd aording to Falonr (1989). Th phnotypi orrlations r p btwn trait x and wr alulatd as th Parson orrlation using th produrs of th Sanst omputrogram (Zonta & Mahado, 199), sin th phnotypi orrlations in this as inludd all lmnts of ovarians/ varians: th gnti, th blok and th rror ovarian/varian. So, aording to Falonr (1989):, whr Cov is gnti ovarian btwn trait x and y; Covb is blok ovarian btwn trait x and y; Cov is th rror ovarian btwn trait x and y; σ and σ b ar lon and blok varians. σ subsripts rfr to traits x or y. Statistial analyss aross sits Th linar modl for th analysis of varian aross sits had th following omposition: Y ijk = μ + i + b j(i) + k + ik + ε ijk, whr Y ijk is th prforman of th ramt of th k th lon in j th blok within i th sit; μ is th ovrall man; i is th fixd fft of i th sit; b j(i) is th fixd fft of j th blok within i th sits; k is th random fft of k th lon with E( k ) = 0 and Var ( k ) = σ ; ik is th random fft of intration btwn i th sit and k th lon, with E( ik ) 0 and Var( ik ) = σ ; and ε ijk is th random rror du to lon by blok intration within th i th sit with E(ε ijk ) = 0 and Var(ε ijk ) = σ. To b valid, th tst of gnotyp-nvironmnt intration in th modl rquirs: 1) homognous lonal varians aross th diffrnt sits to avoid a gnration of gnotyp-nvironmnt intration du to sal ffts; ) homognous rsidual varian among nvironmnts; and 3) normal distribution of th rsiduals (Burdon, 1977). Ths onditions for th modl wr fulfilld, tsting th gnotyp-nvironmnt intration onrning numbr of latx vssls btwn th four trials. Howvr, som transformation of data from trial D, was nssary in th analyss btwn trial A- D, B-D and C-D. Th transformations implid a rdution of th valus by a fator qual to th ratio of varian of rsiduals from th two sits in th analyss, to assur homognous rsidual varians aross sits. In thos ass, it was latr nssary to us logarithmi valus to gt normal distributions of th rsiduals. Gnti orrlations aross sits for all traits wr alulatd using typ B ovarians (Burdon, 1977), and th gnti varians of th traits within sits, onsidring th sam trait masurd on diffrnt sits as diffrnt traits. Thrfor, th gnti orrlation aross sits aording to th dfinition in Falonr (1989) was: rg = Cov g /( σ ) g σ x g. y Corrlations aross sits for total numbr of latx vssls wr thrfor onsidrd as intra lass orrlations on basis of th varian omponnts in th modl usd for th analyss aross sits. Th intra lass orrlations is altrnativly alulatd as: rg = σ ' /( σ + σ ), whr is th orrlation aross sits; σ is lon varian aross two ' sits; σ is lon-nvironmnt intration, adjustd for sit diffrns in varian, stimatd as: ' σ = σ ( σ x σ y ) /, whr σ x = gnti or lon varian on sit x, and σ y = gnti or lon varian on sit y. Eisn (1994) found this mthod to giv biasd stimats in as of unbaland data, unlss gnti varians and rsidual varians on diffrnt sits ar qual to ah othr. Evn though data wr not fully baland, givn that gnti varians and that rsidual varians on at last thr of th sits (A, B and C) wr similar, th formula dsribd by Frnando t al. (1984) was onsidrd appropriat to stimat th gnti orrlations, alulatd as: y1 l1 y = = y l μ1 Z1 Z1 0 + ug + u I + μ Z Z 0 whr y i is th n j 1 vtor of data for trait i, i -= 1, and n j is th numbr of obsrvations for trait i; μ i is th xptd valu of trait i and l j is an n j 1 vtor of ons; u G is a vtor of avrag gnti-group ffts Si. Agri. (Piraiaba, Braz.), v.63, n.3, p.46-54, May/Jun 006
4 Girth and rubbr yild in rubbr trs 49 of nvironmnts; u I is a vtor of gnotyp x nvironmnt intration ffts; and i is a vtor of rsidual ffts. Diffrns btwn lon mans on on sit and lon mans on anothr sit wr alulatd to invstigat diffrns btwn lons, onrning snsitivity to hangs in th nvironmnt. Th diffrns wr found aftr adjustmnts du to diffrns in varians btwn two sits, x and y. This was don by multiplying th lon man on on of th sits with rgrssion offiints b yx. Th diffrn btwn a lon man on sit x and y, dif was.g. found as: dif = ( byxmx ) m y, whr b yx is rgrssion offiint to adjust for diffrns in varians btwn lon mans on two sits x and y, in this as usd to mak mans on sit x omparabl to mans on sit y; mx is lon man on sit x, and m y is lon man on sit y. Th rgrssion offiint b an b found as: b yx = Cov / Vx = ( r Vx Vy ) / Vx, whr Cov is ovarian btwn lon man on sit x and sit y, assuming zro gnotyp-nvironmnt intration; r is th lonal man orrlations aross sits, qual to 1 sin th gnotyp-nvironmnt intration is assumd to b zro; V x is th lon man varian on sit x; and V y is th lon man varian on sit y. Diffrns wr alulatd onsidring on sit that was both indpndnt and dpndnt in rlation to anothr sit. An analysis of varian of th numri diffrns btwn lon mans on diffrnt sits was thn arrid out to xamin if som lons, in gnral, rat mor snsitivly to nvironmntal hangs than othrs. RESULTS AND DISCUSSION Girth at panl opning Diffrns btwn lons wr highly signifiant in A and B trials, and individual broad sns hritabilitis wr about 0.55 in trials A and B, and lowr ( h i = 0.47) in trial C, whih probably an b attributd to a sampling rror du to missing trs in th trial, and variabl growth onditions within th rpliation (Tabl 1). Th phnotypi standard dviations wr btwn.4 and 3.8 m, and th avrag of girth at panl opning in th trials was about 4.9 m. Compard to othr traits, hritabilitis wr quit low but absolut valus of th phnotypi standard dviations Tabl 1 - Varian omponnts and broad sns hritabilitis on th diffrnt sits. Furthrmor prdit gains (G) by phnotypi sltions with sltion intnsity i= 1.35 and by sltion among th lons in th trial, using th lonal man hritability and with a sltion intnsity of i= Data from sixty svn 10 yars old lons of Hva, tstd at fiv loations in São Paulo Stat, Brazil. 1 Traits Sits 3 Varian omponnts CV% x 4 Hritabiliti s Phnotypi Sltion sltion in trial σ b σ σ σ p h p s.. h x G G% G G% Go A B C ns D ns E ns Yr A B C D Bt A B E Lv A B D ns E ns Go = girth at panl opning, Yr = rubbr yild, Bt = bark thiknss, Lv = total numbr of latx vssl rings. Jaú (A), Mooa (B), Ribirão Prto (C), Votuporanga (D) and Matão (E). 3 σ b = blok varian; σ = gnti varian btwn lons; σ = rror varian; σ p = phnotypi varian. 4 h p = broad sns hritability on plot man lvl; h x = broad sns hritability basd on lon mans. P < 0.01; ns = not signifiant. Si. Agri. (Piraiaba, Braz.), v.63, n.3, p.46-54, May/Jun 006
5 50 Gonçalvs t al. wr high. A modrat sltion intnsity i = 0.8 qual to a sltion of th 43% bst lons will giv a prditd gnti gain about 0. m whil a mass sltion outsid th trials will giv a prditd gain about 0.73 m with a sltion intnsity i = 1.35, qual to a sltd proportion about 14%. Th man girth of about 43 m on panl opning in th trials agrs with formr findings by Gonçalvs t al. (1998). Invstigations of immatur rubbr tr in Amazon rgistrd individual broad sns hritabilitis of about h i = 0.57 (Gonçalvs t al., 1983). Hritabilitis found in this invstigation sm small ompard to that. Mor pris masurmnts.g. on adult trs, would probably hav ld to smallr rsidual varians and hn highr broad sns hritabilitis. Th phnotypi standard dviations wr similar to thos rportd by Gottardi t al. (1995) foirth at panl opning. Rubbr yild, bark thiknss and total numbr of latx vssls rings Clonal diffrns in rubbr yild and bark thiknss wr highly signifiant on all sits (Tabl 1), with modrat to high individual broad sns hritabilitis, ranging from 0.59 to 0.9 for rubbr yild and from 0.68 to 0.87 for bark thiknss at svn yars. Prditd gnti gain for bark thiknss was.41% for a sltion intnsity of 50% basd on lonal mans. Th prditd gain from a mass sltion is about 0.60 to 19.14% for a sltion intnsity of 14% (i = 1.35). Th hritabilitis on lon man lvls and phnotypi standard dviations ar los to thos rportd by Gonçalvs t al. (004) in th sam and othr 10 yar old trials. Hritabilitis for rubbr yild and bark thiknss on sit D wr lowr ompard to th othr sits, probably as a rsult of vry unvn growth onditions. Total numbr of latx vssls rings had a modrat to low broad sns hritability on individual tr lvl at 0.43, and a offiint of varian at 5.46%. Prditd gains ar about 6.70% for a sltion of th bst 50% lons in th trials, and about 5.54% following mass sltion of th 14% bst individuals. Corrlations btwn traits within sits Girth at panl opning showd in gnral vry larg gnti and phnotypi orrlations with bark thiknss (Tabl ). This is in agrmnt with findings of Gonçalvs t al. (1989) for 33 IAC lons, and Gottardi t al. (1995) for 11 lons at th fourth yar of yild. Also Gonçalvs (198) found, in wild mothr trs from 10 sits, pronound diffrns in bark thiknss btwn fast growing and slow growing trs in th Amazon vally basin. Howvr, fast growing trs of Hva hav a tndny to maintain a highr lvl of positiv girth orrlation with bark thiknss. Gonçalvs (198) found largr standard dviations within th groups, whih would suggst a strong gnti influn on bark thiknss. Rsults from Ho (1976), who invstigatd 4 Hva lons from diffrnt trials, showd that th fastst growing trs also had a gratr bark thiknss ompard to th slow growing groups. Howvr ths rsults should b intrprtd with aution givn th rdud numbr of trs in ah group. Th stands wr furthr haratrizd by high sit indis, whih might xplain why th orrlation with growth for th trs in th most fast growing group was apparnt in th bark thiknss. Morti t al. (1994) and Book t al. (1995) working with prognis in juvnil stag, also found that fastst growing plants tnd to maintain high lvl of bark thiknss. Vry high phnotypi and gnti orrlations wr found btwn girths at panl opning and rubbr yild (Tabl ). Th high positiv orrlations found btwn rubbr yild and numbr of latx vssls is in agrmnt with formr rsarh findings (Ho, 1976; Tan, 1987; Narayanan t al., 1973; Gonçalvs t al., 1989; Kalil Filho, 198; Liy & Prmakumari, 1988). Modrat to high positiv phnotypi and gnti orrlations btwn bark thiknss and total numbr of latx vssls wr also found in th trials (Tabl ). Similar rsults hav bn found by Gonçalvs t al. (1998) in four trials. Effts of sits and gnotyp-sit intration Girth at panl opning - Although diffrns of girth at panl opning btwn th sits wr small, thy wr statistially diffrnt, xpt btwn trial A and B (Tabl 3). Vry high gnti orrlations aross sits showd that girth at panl opning has vry littl gnotyp-nvironmnt intration (Tabl 4). Howvr, all hypothsis of gnotyp-nvironmnt intrations qual to zro btwn diffrnt nvironmnts wr rjtd in th analysis of varian aross sits. Th analysis of varian of th diffrns btwn lon mans on diffrnt sits rvald signifiant diffrns among lons onrning snsitivity to hangs in th nvironmnt (Tabl 5). Rubbr yild - Signifiant diffrns btwn th sits wr prsnt Sit A had th highst rubbr yild and sit B th poorst rubbr yild. Gnotypi and phnotypi orrlations for rubbr yild aross sits (Tabl 4) ar vry high, ranging from 0.63 to 0.89 (phnotypi) and from 0.64 to 0.9 (gnotypi), agring with prvious stimats by Gonçalvs t al. (1998). Th analysis of varian btwn lon mans of rubbr yild on diffrnt sits showd that som lons, in gnral, wr mor snsitiv to hangs in th nvironmnts (Tabl 5). Si. Agri. (Piraiaba, Braz.), v.63, n.3, p.46-54, May/Jun 006
6 Girth and rubbr yild in rubbr trs 51 Tabl - Phnotypi ( ) and gnotypi ( ) orrlations within Jaú (A), Mooa (B), Ribirão Prto (C), Votuporanga (D) Matão (E) sits among girth at panl opning (Go), rubbr yild (Yr), bark thiknss (Bt) and numbr latx vssl rings (Lv) of sixty svn 10 yars old lons of Hva, tstd at fiv loations in São Paulo Stat, Brazil. Sit/traits A - Indiana Corrlation Typ Rubbr yild (Yr) P < 0.05; P < 0.01; ns = not signifiant. Traits G irth at panl opning (Go) R ubbr yild (Yr) thiknss (Bt) thiknss (Bt) ns ns Latx vssl rings (Lv) ns B - Mooa Rubbr yild (Yr) ns thiknss (Bt) ns ns Latx vssl rings (Lv) - ns ns C - Ribirão Prto Rubbr yild (Yr) thiknss (Bt) ns ns Latx vssl rings (Lv) 0.033ns D - Votuporanga Rubbr yild (Yr) ns thiknss (Bt) ns ns Latx vssl rings (Lv) ns ns E - Matão thiknss (Bt) Latx vssl rings (Lv) ns ns Corrlations btwn diffrnt traits aross sits Gnti orrlations btwn diffrnt traits aross sits, using th B ovarians btwn lon mans as dsribd by Burdon (1977) wr in gnral smallr and of opposit signs ompard with th orrlations found within sits, although diffrns wr small (Tabl 6). Probably th diffrns asrib to influn of sampling rrors, gnotyp-nvironmnts intrations for th traits, and by th fat that nvironmntal orrlations ar zro aross sits, but ngativ within sits. Th modrat gnti orrlation btwn rubbr yild and bark thiknss in trial C almost disappar btwn rubbr yild in trial C and bark thiknss in trial A, as wll as th strong orrlation btwn girth at panl opning and rubbr yild in trial C disappar btwn girth at panl opning in trial A Si. Agri. (Piraiaba, Braz.), v.63, n.3, p.46-54, May/Jun 006
7 5 Gonçalvs t al. Tabl 3 - Rsults from th analysis of varian aross sits onrning girth at panl opning of sixty svn 10 yars old Hva lons, tstd at fiv loations in São Paulo Stat, Brazil. Trials Sour D.F. A-B A-C Bloks/sits Sits ns x sits 4.60ns 6.999ns 5.439ns ns ns T rials D.F. B-D B-E C-D C-E D-E Sour Man Squars Bloks/sits Sits ns ns C lons sits ns ns ns P < 0.05; P < 0.01; ns = not signifiant. Sits: Jaú (A), Mooa (B), Ribrião Prto (C), Votuporanga (D) and Matão (E). A-D Man Squars Tabl 4 - Phnotypi ( ) and gnotypi ( ) orrlations aross Jaú (A), Mooa (B), Ribirão Prto (C), Votuporanga (D) and Matão (E) sits foirth at panl opning (Go), rubbr yild (Yr), bark thiknss (Bt) and latx vssl rings (Lv) for sixty svn 10-yar old Hva lons in São Paulo Stat, Brazil. A-E B-C Traits GoA YrA BtA LvA GoB YrB BtB LvB GoC YrC GoD YrD LvD GoB ns ns ns ns ns ns YrB ns ns ns ns BtB -48ns 0.30ns rg ns ns ns LvB ns 0.316ns ns ns GoC ns ns ns ns ns ns YrC 0.045ns ns ns rg 0.060ns ns ns ns GoD ns 0.156ns ns ns ns ns ns 0.990ns ns ns ns YrD ns 0.586ns ns ns 0.307ns LvD ns ns ns ns ns 0.513ns 0.333ns ns ns 0.371ns ns GoE ns ns s 0.716ns ns 0.530ns ns ns ns 0.013ns 0.645ns ns ns BtE 0.001ns ns ns ns 0.193ns ns ns 95ns ns 0.049ns rg 0.74ns ns ns 10ns 0.33ns ns ns ns ns 0.056ns ns ns LvE ns ns ns ns ns -6ns ns 0.448ns ns ns ns -0.45ns 1.474ns ns ns ns ns ns P < 0.05; P < 0.01; ns = not signifiant. Si. Agri. (Piraiaba, Braz.), v.63, n.3, p.46-54, May/Jun 006
8 Girth and rubbr yild in rubbr trs 53 Tabl 5 - Rsults of man squars from th analyss of varian on diffrns btwn lon mans on diffrnt sits for girth at panl opning and rubbr yild of sixty svn 10 yars old Hva lons, tstd at fiv loations in São Paulo Stat, Brazil. S our D.F. P < 0.05; P < 0.01 Girth at panl opning MS F valu Clon S our D.F. MS Rubbr yild F valu Clon P> F P > F Tabl 6 - Rsults from th analysis of varian aross sits onrning rubbr yild of sixty svn 10 yars old Hva lons, tstd at fiv loations in São Paulo Stat, Brazil. Trials Sour D.F A-B A-C Man Squars Bloks/sits Sits x sits Trials Sour D. F B-C B-D Man Squars Bloks Sits C lons sits P < 0.05; P < 0.01; ns = not signifiant. Sits: Jaú (A), Mooa (B), Ribirão Prto (C) and Votuporanga (D). A-D C-D and rubbr yild in trial C. Possibly th hang in orrlations aross trials A and C ar ausd by gnotypnvironmnt intration for bark thiknss and rubbr yild, whih liminats th orrlations btwn thos traits and girth at panl opning rubbr yild sn within C. Finally, masurmnts of girth at panl opning at on sit sm to b nough, givn th vry high gnti orrlations aross sits. Considrabl gains in rubbr yild (abov.0%) ar possibl vn with modrat sltion among th lons. Th gnti orrlations aross th sits did not larly indiat any signifiant advantags, using targt nvironmnts. thiknss showd th xptd positiv high orrlation with rubbr yild and th trait must dfinitly b takn into onsidration whn slting for rubbr yild. Hritability and standard dviation for total numbr of latx vssls wr modrat. Th potntial for improving th total numbr of latx vssls is high with modrat hritability and positivly orrlatd with girth at panl opning and rubbr yild. ACKNOWLEDGEMENTS Th authors thank Fundação d Amparo à Psquisa do Estado d São Paulo (FAPESP) and Conslho Naional d Dsnvolvimnto Tnológio (CNPq) for finanial support. REFERENCES BOOCK, M.V.; GONÇALVES, P. d S.; BORTOLETTO, N.; MARTINS, A.L.M. Hrdabilidad, variabilidad gnétia ganhos gnétios para produção aratrs morfológios m progênis jovns d sringuira. Psquisa Agropuária Brasilira, v.30, p , BULMER, M.G. Th mathmatial thory of quantitativ gntis. Oxford: Clarndon Prss, p. Si. Agri. (Piraiaba, Braz.), v.63, n.3, p.46-54, May/Jun 006
9 54 Gonçalvs t al. BURDON, R.D. Gnti orrlation as a onpt for studying gnotypnvironmnt intrations in forst tr brding. Silva Gntia, v.6, p , COTTERILL, P.P. Short not on stimating hritability aording to pratial appliations. Silva Gntia, v.36, p.46-48, CRUZ, C.D. Programa Gns: vrsão Windows. Apliativo omputaional m gnétia statístia. Viçosa: UFV, p. EISEN, E.J. Conpts in quantitativ gntis and annual brding. Hlsinki: Nordi Graduat Cours Compndium, p. FALCONER, D.S. Introdution to quantitativ gntis. Hallow: Longman Sintifi, p. FERNANDO, R.L.; KNIGHTS, S.A.; GIANOLA, D. On a mthod of stimating th gnti orrlation btwn haratrs masurd in diffrnt xprimntal units. Thortial and Applid Gntis, v.67, p , GONÇALVES, P. d S. Colltion of Hva matrials from Rondonia trritory in Brazil: a prliminary study. Psquisa Agropuária Brasilira, v.17, p , 198. GONÇALVES, P. d S.; ROSSETTI, A.R.; VALOIS, A.C.C.; VIEGAS, I.J.M. Cofiint d dtrminação gnotípia stimação d outros parâmtros m lons d sringuira. Psquisa Agropuária Brasilira, v.18, p.57-53, GONÇALVES, P. d S.; CARDOSO, M.; IGUE, T.; MARTINS, A.L.M.; LAVORENTI, C. Corrlations studis btwn plugging indx, yild, girth and bark thiknss in Hva lons. Brazilian Journal of Gntis, v.1, p , GONÇALVES, P. d S.; BATAGLIA, O.C.; SANTOS, W.R. dos; ORTOLANI, A.A.; SEGNINI, J.R.I.; SHIKASHO, E.H. Growth trnds, gnotyp-nvironmnt intration and gnti gains in siar old rubbr tr lons (Hva) in São Paulo Stat, Brazil. Gntis and Molular Biology, v.1, p.115-1, GONÇALVES, P. d S.; MARTINS, A.L.M.; BORTOLETTO, N.; SAES, L.A. Sltion and gnti gains for juvnil traits in prognis of Hva in São Paulo Stat, Brazil. Gntis and Molular Biology, v.7, p.07-14, 004. GOTTARDI, M.V.C.; GONÇALVES, P. d S.; CARDOSO, M.; MENTE, E.M. Corrlaçõs gnotípias fnotípias ntr aratrs d sringuiras adultas. Cintífia, v.3, p.53-64, HO, C.Y. Clonal haratrs dtrmining th yild of Hva brasilinsis. In: INTERNATIONAL RUBBER CONFERENCE, 1., Kuala Lumpur, Prodings. Kuala Lumpur: RRIM, p KALIL FILHO, N.A. Potnial d produtividad stabilidad fnotípia na aratrização d lons d sringuira (Hva spp.). Piraiaba: ESALQ/USP, p. (Ts - Doutorado). LICY, J.; PREMAKUMARI, D. Assoiation of haratrs in hand pollinatd prognis of Hva brasilinsis (Willd. x Adr. d Juss.) Mull-Arg. Indian Journal of Natural Rubbr Rsarh, v.1, p.18-1, MORETI, D.; GONÇALVES, P. d S.; GORGULHO, E.P.; MARTINS, A.L.M.; BORTOLETTO, N. Estimativas d parâmtros gnétios ganhos sprados om a slção d aratrs juvnis m progênis d sringuira. Psquisa Agropuária Brasilira, v.9, p , NARAYANAN, R.; GOMEZ, J.B.; CHEN, K.T. Som strutural fators affting th produtivity of Hva brasilinsis II: orrlation studis btwn strutural fators and yild. Journal of th Rubbr Rsarh Institut of Malaya, v.3, p.85-97, RESENDE, M.D.V.; OLIVEIRA, E.B. Sistma Slgn slção gnétia omputadorizada para mlhoramnto d spéis prns. Psquisa Agropuária Brasilira, v.3, p , TAN, H. Stratgis in rubbr tr brding. In: ABBOTT, A.J.; ATKIM, R.K. (Ed.) Improving vgtativly propagatd rops. London: Aadmi Prss, p.8-6. ZONTA, E.P.; MACHADO, A.A. Sanst - Anális statístia para miroomputadors. Piraiaba: ESALQ/USP, p. Rivd Otobr 04, 005 Aptd Marh 0, 006 Si. Agri. (Piraiaba, Braz.), v.63, n.3, p.46-54, May/Jun 006
Utilizing exact and Monte Carlo methods to investigate properties of the Blume Capel Model applied to a nine site lattice.
Utilizing xat and Mont Carlo mthods to invstigat proprtis of th Blum Capl Modl applid to a nin sit latti Nik Franios Writing various xat and Mont Carlo omputr algorithms in C languag, I usd th Blum Capl
More information22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.
Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th Born-Oppnhimr approximation. Slction ruls for rotational-vibrational transitions. P, R branchs. CHE_P8_M
More informationLecture 14 (Oct. 30, 2017)
Ltur 14 8.31 Quantum Thory I, Fall 017 69 Ltur 14 (Ot. 30, 017) 14.1 Magnti Monopols Last tim, w onsidrd a magnti fild with a magnti monopol onfiguration, and bgan to approah dsribing th quantum mhanis
More informationUncertainty in non-linear long-term behavior and buckling of. shallow concrete-filled steel tubular arches
CCM14 8-3 th July, Cambridg, England Unrtainty in non-linar long-trm bhavior and bukling of shallow onrt-filld stl tubular arhs *X. Shi¹, W. Gao¹, Y.L. Pi¹ 1 Shool of Civil and Environmnt Enginring, Th
More informationEXST Regression Techniques Page 1
EXST704 - Rgrssion Tchniqus Pag 1 Masurmnt rrors in X W hav assumd that all variation is in Y. Masurmnt rror in this variabl will not ffct th rsults, as long as thy ar uncorrlatd and unbiasd, sinc thy
More informationObserver Bias and Reliability By Xunchi Pu
Obsrvr Bias and Rliability By Xunchi Pu Introduction Clarly all masurmnts or obsrvations nd to b mad as accuratly as possibl and invstigators nd to pay carful attntion to chcking th rliability of thir
More informationGRINDING PARAMETERS SELECTION USING TLBO METHOD
INTERNATIONAL JOURNAL OF MANUFACTURING TECHNOLOGY AND INDUSTRIAL ENGINEERING (IJMTIE) Vol. 2, No. 2, July-Dmbr 2011, pp. 91-96 GRINDING PARAMETERS SELECTION USING TLBO METHOD R. V. Rao 1 * & V. D. Kalyankar
More informationWhat are those βs anyway? Understanding Design Matrix & Odds ratios
Ral paramtr stimat WILD 750 - Wildlif Population Analysis of 6 What ar thos βs anyway? Undrsting Dsign Matrix & Odds ratios Rfrncs Hosmr D.W.. Lmshow. 000. Applid logistic rgrssion. John Wily & ons Inc.
More informationMCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17)
MCB37: Physical Biology of th Cll Spring 207 Homwork 6: Ligand binding and th MWC modl of allostry (Du 3/23/7) Hrnan G. Garcia March 2, 207 Simpl rprssion In class, w drivd a mathmatical modl of how simpl
More informationHigher order derivatives
Robrto s Nots on Diffrntial Calculus Chaptr 4: Basic diffrntiation ruls Sction 7 Highr ordr drivativs What you nd to know alrady: Basic diffrntiation ruls. What you can larn hr: How to rpat th procss of
More informationDepartment of Mechanical Engineering, Imperial College, London SW7 2AZ, UK
1 ST Intrnational Confrn on Composit Matrials Xi an, 0 5 th August 017 THE MECHANICS OF INTERFACE FRACTURE IN LAYERED COMPOSITE MATERIALS: (7) ADHESION TOUHNESS OF MULTILAYER RAPHENE MEMRANES NANOSCALE
More informationEstimation of apparent fraction defective: A mathematical approach
Availabl onlin at www.plagiarsarchlibrary.com Plagia Rsarch Library Advancs in Applid Scinc Rsarch, 011, (): 84-89 ISSN: 0976-8610 CODEN (USA): AASRFC Estimation of apparnt fraction dfctiv: A mathmatical
More informationExtraction of Doping Density Distributions from C-V Curves
Extraction of Doping Dnsity Distributions from C-V Curvs Hartmut F.-W. Sadrozinski SCIPP, Univ. California Santa Cruz, Santa Cruz, CA 9564 USA 1. Connction btwn C, N, V Start with Poisson quation d V =
More informationModified Shrinking Core Model for Removal of Hydrogen Sulfide with T Desulfurizer
Modifid Shrinking or Modl for Rmoval of Hydrogn Sulfid with T Dsulfurizr Enguo Wang Dpartmnt of physis Lingnan normal univrsity Zhanjiang, hina -mail: 945948@qq.om Hanxian Guo Institut of oal hmial nginring
More informationFunction Spaces. a x 3. (Letting x = 1 =)) a(0) + b + c (1) = 0. Row reducing the matrix. b 1. e 4 3. e 9. >: (x = 1 =)) a(0) + b + c (1) = 0
unction Spacs Prrquisit: Sction 4.7, Coordinatization n this sction, w apply th tchniqus of Chaptr 4 to vctor spacs whos lmnts ar functions. Th vctor spacs P n and P ar familiar xampls of such spacs. Othr
More informationElectron Transport Properties for Argon and Argon-Hydrogen Plasmas
Chaptr-5 Eltron Transport Proprtis for Argon and Argon-Hydrogn Plasmas Argon and argon-hydrogn plasmas hav important appliations in many thrmal plasma dvis (Patyron t al., 1992; Murphy, 2000; Crssault
More informationBrief Introduction to Statistical Mechanics
Brif Introduction to Statistical Mchanics. Purpos: Ths nots ar intndd to provid a vry quick introduction to Statistical Mchanics. Th fild is of cours far mor vast than could b containd in ths fw pags.
More informationAP Calculus BC Problem Drill 16: Indeterminate Forms, L Hopital s Rule, & Improper Intergals
AP Calulus BC Problm Drill 6: Indtrminat Forms, L Hopital s Rul, & Impropr Intrgals Qustion No. of Instrutions: () Rad th problm and answr hois arfully () Work th problms on papr as ndd () Pik th answr
More informationDetermination of Vibrational and Electronic Parameters From an Electronic Spectrum of I 2 and a Birge-Sponer Plot
5 J. Phys. Chm G Dtrmination of Vibrational and Elctronic Paramtrs From an Elctronic Spctrum of I 2 and a Birg-Sponr Plot 1 15 2 25 3 35 4 45 Dpartmnt of Chmistry, Gustavus Adolphus Collg. 8 Wst Collg
More informationThe pn junction: 2 Current vs Voltage (IV) characteristics
Th pn junction: Currnt vs Voltag (V) charactristics Considr a pn junction in quilibrium with no applid xtrnal voltag: o th V E F E F V p-typ Dpltion rgion n-typ Elctron movmnt across th junction: 1. n
More informationCh. 24 Molecular Reaction Dynamics 1. Collision Theory
Ch. 4 Molcular Raction Dynamics 1. Collision Thory Lctur 16. Diffusion-Controlld Raction 3. Th Matrial Balanc Equation 4. Transition Stat Thory: Th Eyring Equation 5. Transition Stat Thory: Thrmodynamic
More informationWhere k is either given or determined from the data and c is an arbitrary constant.
Exponntial growth and dcay applications W wish to solv an quation that has a drivativ. dy ky k > dx This quation says that th rat of chang of th function is proportional to th function. Th solution is
More informationA Prey-Predator Model with an Alternative Food for the Predator, Harvesting of Both the Species and with A Gestation Period for Interaction
Int. J. Opn Problms Compt. Math., Vol., o., Jun 008 A Pry-Prdator Modl with an Altrnativ Food for th Prdator, Harvsting of Both th Spcis and with A Gstation Priod for Intraction K. L. arayan and. CH. P.
More informationNotes on Vibration Design for Piezoelectric Cooling Fan
World Aadmy of Sin, Enginring and Thnology Intrnational Journal of Mhanial and Mhatronis Enginring Vol:7, No:, 3 Nots on Vibration Dsign for Pizoltri Cooling Fan Thomas Jin-Ch Liu, Yu-Shn Chn, Hsi-Yang
More informationExam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator.
Exam N a m : _ S O L U T I O N P U I D : I n s t r u c t i o n s : It is important that you clarly show your work and mark th final answr clarly, closd book, closd nots, no calculator. T i m : h o u r
More informationData Assimilation 1. Alan O Neill National Centre for Earth Observation UK
Data Assimilation 1 Alan O Nill National Cntr for Earth Obsrvation UK Plan Motivation & basic idas Univariat (scalar) data assimilation Multivariat (vctor) data assimilation 3d-Variational Mthod (& optimal
More informationChapter 13 GMM for Linear Factor Models in Discount Factor form. GMM on the pricing errors gives a crosssectional
Chaptr 13 GMM for Linar Factor Modls in Discount Factor form GMM on th pricing rrors givs a crosssctional rgrssion h cas of xcss rturns Hors rac sting for charactristic sting for pricd factors: lambdas
More informationJournal of Asian Scientific Research CONTROLLING THE PERFORMANCE OF MDPSK IN BAD SCATTERING CHANNELS
Journal of Asian Sintifi Rsarh journal hompag: http://assb.om/journal-dtail.php?id=5003 CONTROLLING THE PERFORMANCE OF MDPSK IN BAD SCATTERING CHANNELS Arafat Zaidan 1 Basim Alsayid 2 ABSTRACT This papr
More informationSolution of Assignment #2
olution of Assignmnt #2 Instructor: Alirza imchi Qustion #: For simplicity, assum that th distribution function of T is continuous. Th distribution function of R is: F R ( r = P( R r = P( log ( T r = P(log
More informationApplied Statistics II - Categorical Data Analysis Data analysis using Genstat - Exercise 2 Logistic regression
Applid Statistics II - Catgorical Data Analysis Data analysis using Gnstat - Exrcis 2 Logistic rgrssion Analysis 2. Logistic rgrssion for a 2 x k tabl. Th tabl blow shows th numbr of aphids aliv and dad
More informationMA 262, Spring 2018, Final exam Version 01 (Green)
MA 262, Spring 218, Final xam Vrsion 1 (Grn) INSTRUCTIONS 1. Switch off your phon upon ntring th xam room. 2. Do not opn th xam booklt until you ar instructd to do so. 3. Bfor you opn th booklt, fill in
More informationph People Grade Level: basic Duration: minutes Setting: classroom or field site
ph Popl Adaptd from: Whr Ar th Frogs? in Projct WET: Curriculum & Activity Guid. Bozman: Th Watrcours and th Council for Environmntal Education, 1995. ph Grad Lvl: basic Duration: 10 15 minuts Stting:
More informationDifferentiation of Exponential Functions
Calculus Modul C Diffrntiation of Eponntial Functions Copyright This publication Th Northrn Albrta Institut of Tchnology 007. All Rights Rsrvd. LAST REVISED March, 009 Introduction to Diffrntiation of
More informationAssignment 4 Biophys 4322/5322
Assignmnt 4 Biophys 4322/5322 Tylr Shndruk Fbruary 28, 202 Problm Phillips 7.3. Part a R-onsidr dimoglobin utilizing th anonial nsmbl maning rdriv Eq. 3 from Phillips Chaptr 7. For a anonial nsmbl p E
More informationMath 34A. Final Review
Math A Final Rviw 1) Us th graph of y10 to find approimat valus: a) 50 0. b) y (0.65) solution for part a) first writ an quation: 50 0. now tak th logarithm of both sids: log() log(50 0. ) pand th right
More informationWhy is a E&M nature of light not sufficient to explain experiments?
1 Th wird world of photons Why is a E&M natur of light not sufficint to xplain xprimnts? Do photons xist? Som quantum proprtis of photons 2 Black body radiation Stfan s law: Enrgy/ ara/ tim = Win s displacmnt
More informationAS 5850 Finite Element Analysis
AS 5850 Finit Elmnt Analysis Two-Dimnsional Linar Elasticity Instructor Prof. IIT Madras Equations of Plan Elasticity - 1 displacmnt fild strain- displacmnt rlations (infinitsimal strain) in matrix form
More informationThe van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012
Th van dr Waals intraction D. E. Sopr 2 Univrsity of Orgon 20 pril 202 Th van dr Waals intraction is discussd in Chaptr 5 of J. J. Sakurai, Modrn Quantum Mchanics. Hr I tak a look at it in a littl mor
More informationPrinciples of Humidity Dalton s law
Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid
More informationLecture 20. Calorimetry
Ltur 0 Calorimtry CLORIMTRY In nular and partil physis alorimtry rfrs to th dttion of partils through total absorption in a blok of mattr Th masurmnt pross is dstrutiv for almost all partil Th xption ar
More informationAnswer Homework 5 PHA5127 Fall 1999 Jeff Stark
Answr omwork 5 PA527 Fall 999 Jff Stark A patint is bing tratd with Drug X in a clinical stting. Upon admiion, an IV bolus dos of 000mg was givn which yildd an initial concntration of 5.56 µg/ml. A fw
More informationElements of Statistical Thermodynamics
24 Elmnts of Statistical Thrmodynamics Statistical thrmodynamics is a branch of knowldg that has its own postulats and tchniqus. W do not attmpt to giv hr vn an introduction to th fild. In this chaptr,
More informationTitle: Vibrational structure of electronic transition
Titl: Vibrational structur of lctronic transition Pag- Th band spctrum sn in th Ultra-Violt (UV) and visibl (VIS) rgions of th lctromagntic spctrum can not intrprtd as vibrational and rotational spctrum
More informationSearch sequence databases 3 10/25/2016
Sarch squnc databass 3 10/25/2016 Etrm valu distribution Ø Suppos X is a random variabl with probability dnsity function p(, w sampl a larg numbr S of indpndnt valus of X from this distribution for an
More information2008 AP Calculus BC Multiple Choice Exam
008 AP Multipl Choic Eam Nam 008 AP Calculus BC Multipl Choic Eam Sction No Calculator Activ AP Calculus 008 BC Multipl Choic. At tim t 0, a particl moving in th -plan is th acclration vctor of th particl
More informationSeptember 23, Honors Chem Atomic structure.notebook. Atomic Structure
Atomic Structur Topics covrd Atomic structur Subatomic particls Atomic numbr Mass numbr Charg Cations Anions Isotops Avrag atomic mass Practic qustions atomic structur Sp 27 8:16 PM 1 Powr Standards/ Larning
More informationClassical Magnetic Dipole
Lctur 18 1 Classical Magntic Dipol In gnral, a particl of mass m and charg q (not ncssarily a point charg), w hav q g L m whr g is calld th gyromagntic ratio, which accounts for th ffcts of non-point charg
More informationu x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula
7. Intgration by Parts Each drivativ formula givs ris to a corrsponding intgral formula, as w v sn many tims. Th drivativ product rul yilds a vry usful intgration tchniqu calld intgration by parts. Starting
More informationLecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields
Lctur 37 (Schrödingr Equation) Physics 6-01 Spring 018 Douglas Filds Rducd Mass OK, so th Bohr modl of th atom givs nrgy lvls: E n 1 k m n 4 But, this has on problm it was dvlopd assuming th acclration
More informationPipe flow friction, small vs. big pipes
Friction actor (t/0 t o pip) Friction small vs larg pips J. Chaurtt May 016 It is an intrsting act that riction is highr in small pips than largr pips or th sam vlocity o low and th sam lngth. Friction
More informationQuasi-Classical States of the Simple Harmonic Oscillator
Quasi-Classical Stats of th Simpl Harmonic Oscillator (Draft Vrsion) Introduction: Why Look for Eignstats of th Annihilation Oprator? Excpt for th ground stat, th corrspondnc btwn th quantum nrgy ignstats
More informationEFFECTIVENESS AND OPTIMIZATION OF FIBER BRAGG GRATING SENSOR AS EMBEDDED STRAIN SENSOR
EFFECTIVENESS AND OPTIMIZATION OF FIBE BAGG GATING SENSO AS EMBEDDED STAIN SENSO Xiaoming Tao, Liqun Tang,, Chung-Loong Choy Institut of Txtils and Clothing, Matrials sarh Cntr, Th Hong Kong Polythni Univrsity
More informationA novel ice-pressure sensor based on dual FBGs
Confrn: Snsors and Smart Struturs Thnologis for Civil, Mhanial, and Arospa Systms, SPIE, San Digo, USA, 25 A novl i-prssur snsor basd on dual FBGs Zhi Zhou, Chunguang Lan, Taiming Lin, Jinping Ou Shool
More informationThat is, we start with a general matrix: And end with a simpler matrix:
DIAGON ALIZATION OF THE STR ESS TEN SOR INTRO DUCTIO N By th us of Cauchy s thorm w ar abl to rduc th numbr of strss componnts in th strss tnsor to only nin valus. An additional simplification of th strss
More informationSimulated Analysis of Tooth Profile Error of Cycloid Steel Ball Planetary Transmission
07 4th Intrnational Matrials, Machinry and Civil Enginring Confrnc(MATMCE 07) Simulatd Analysis of Tooth Profil Error of Cycloid Stl Ball Plantary Transmission Ruixu Hu,a, Yuquan Zhang,b,*, Zhanliang Zhao,c,
More informationSCALING OF SYNCHROTRON RADIATION WITH MULTIPOLE ORDER. J. C. Sprott
SCALING OF SYNCHROTRON RADIATION WITH MULTIPOLE ORDER J. C. Sprott PLP 821 Novmbr 1979 Plasma Studis Univrsity of Wisconsin Ths PLP Rports ar informal and prliminary and as such may contain rrors not yt
More informationDIFFERENTIAL EQUATION
MD DIFFERENTIAL EQUATION Sllabus : Ordinar diffrntial quations, thir ordr and dgr. Formation of diffrntial quations. Solution of diffrntial quations b th mthod of sparation of variabls, solution of homognous
More information( ) Differential Equations. Unit-7. Exact Differential Equations: M d x + N d y = 0. Verify the condition
Diffrntial Equations Unit-7 Eat Diffrntial Equations: M d N d 0 Vrif th ondition M N Thn intgrat M d with rspt to as if wr onstants, thn intgrat th trms in N d whih do not ontain trms in and quat sum of
More informationSelf-interaction mass formula that relates all leptons and quarks to the electron
Slf-intraction mass formula that rlats all lptons and quarks to th lctron GERALD ROSEN (a) Dpartmnt of Physics, Drxl Univrsity Philadlphia, PA 19104, USA PACS. 12.15. Ff Quark and lpton modls spcific thoris
More informationEinstein Equations for Tetrad Fields
Apiron, Vol 13, No, Octobr 006 6 Einstin Equations for Ttrad Filds Ali Rıza ŞAHİN, R T L Istanbul (Turky) Evry mtric tnsor can b xprssd by th innr product of ttrad filds W prov that Einstin quations for
More informationFirst derivative analysis
Robrto s Nots on Dirntial Calculus Chaptr 8: Graphical analysis Sction First drivativ analysis What you nd to know alrady: How to us drivativs to idntiy th critical valus o a unction and its trm points
More informationSundials and Linear Algebra
Sundials and Linar Algbra M. Scot Swan July 2, 25 Most txts on crating sundials ar dirctd towards thos who ar solly intrstd in making and using sundials and usually assums minimal mathmatical background.
More informationA Propagating Wave Packet Group Velocity Dispersion
Lctur 8 Phys 375 A Propagating Wav Packt Group Vlocity Disprsion Ovrviw and Motivation: In th last lctur w lookd at a localizd solution t) to th 1D fr-particl Schrödingr quation (SE) that corrsponds to
More informationMor Tutorial at www.dumblittldoctor.com Work th problms without a calculator, but us a calculator to chck rsults. And try diffrntiating your answrs in part III as a usful chck. I. Applications of Intgration
More informationVTU NOTES QUESTION PAPERS NEWS RESULTS FORUMS
Diffrntial Equations Unit-7 Eat Diffrntial Equations: M d N d 0 Vrif th ondition M N Thn intgrat M d with rspt to as if wr onstants, thn intgrat th trms in N d whih do not ontain trms in and quat sum of
More information0 +1e Radionuclides - can spontaneously emit particles and radiation which can be expressed by a nuclear equation.
Radioactivity Radionuclids - can spontanously mit particls and radiation which can b xprssd by a nuclar quation. Spontanous Emission: Mass and charg ar consrvd. 4 2α -β Alpha mission Bta mission 238 92U
More informationMultivariable Fuzzy Control of CFB Boiler Combustion System
Prodings of th World Congrss on Enginring and Computr Sin 3 Vol II WCECS 3, 3-5 Otobr, 3, San Franiso, USA Multivariabl Fuzzy Control of CFB Boilr Combustion Systm Yu-Fi Zhang, Li-Wi Xu, Pi Chn, Xiao-Chn
More informationTheoretical study of quantization of magnetic flux in a superconducting ring
Thortial study of quantization of magnti flux in a supronduting ring DaHyon Kang Bagunmyon offi, Jinan 567-880, Kora -mail : samplmoon@hanmail.nt W rfind th onpts of ltri urrnt and fluxoid, and London
More informationNote If the candidate believes that e x = 0 solves to x = 0 or gives an extra solution of x = 0, then withhold the final accuracy mark.
. (a) Eithr y = or ( 0, ) (b) Whn =, y = ( 0 + ) = 0 = 0 ( + ) = 0 ( )( ) = 0 Eithr = (for possibly abov) or = A 3. Not If th candidat blivs that = 0 solvs to = 0 or givs an tra solution of = 0, thn withhold
More informationCalculus II (MAC )
Calculus II (MAC232-2) Tst 2 (25/6/25) Nam (PRINT): Plas show your work. An answr with no work rcivs no crdit. You may us th back of a pag if you nd mor spac for a problm. You may not us any calculators.
More informationcycle that does not cross any edges (including its own), then it has at least
W prov th following thorm: Thorm If a K n is drawn in th plan in such a way that it has a hamiltonian cycl that dos not cross any dgs (including its own, thn it has at last n ( 4 48 π + O(n crossings Th
More informationSara Godoy del Olmo Calculation of contaminated soil volumes : Geostatistics applied to a hydrocarbons spill Lac Megantic Case
wwwnvisol-canadaca Sara Godoy dl Olmo Calculation of contaminatd soil volums : Gostatistics applid to a hydrocarbons spill Lac Mgantic Cas Gostatistics: study of a PH contamination CONTEXT OF THE STUDY
More informationMath-3. Lesson 5-6 Euler s Number e Logarithmic and Exponential Modeling (Newton s Law of Cooling)
Math-3 Lsson 5-6 Eulr s Numbr Logarithmic and Eponntial Modling (Nwton s Law of Cooling) f ( ) What is th numbr? is th horizontal asymptot of th function: 1 1 ~ 2.718... On my 3rd submarin (USS Springfild,
More informationHomotopy perturbation technique
Comput. Mthods Appl. Mch. Engrg. 178 (1999) 257±262 www.lsvir.com/locat/cma Homotopy prturbation tchniqu Ji-Huan H 1 Shanghai Univrsity, Shanghai Institut of Applid Mathmatics and Mchanics, Shanghai 272,
More informationForces. Quantum ElectroDynamics. α = = We have now:
W hav now: Forcs Considrd th gnral proprtis of forcs mdiatd by xchang (Yukawa potntial); Examind consrvation laws which ar obyd by (som) forcs. W will nxt look at thr forcs in mor dtail: Elctromagntic
More information(Upside-Down o Direct Rotation) β - Numbers
Amrican Journal of Mathmatics and Statistics 014, 4(): 58-64 DOI: 10593/jajms0140400 (Upsid-Down o Dirct Rotation) β - Numbrs Ammar Sddiq Mahmood 1, Shukriyah Sabir Ali,* 1 Dpartmnt of Mathmatics, Collg
More informationChapter 37 The Quantum Revolution
Chaptr 37 Th Quantum Rvolution Max Plank Th Nobl Priz in Physis 1918 "in rognition of th srvis h rndrd to th advanmnt of Physis by his disovry of nrgy quanta" Albrt Einstin Th Nobl Priz in Physis 191 "for
More informationSec 2.3 Modeling with First Order Equations
Sc.3 Modling with First Ordr Equations Mathmatical modls charactriz physical systms, oftn using diffrntial quations. Modl Construction: Translating physical situation into mathmatical trms. Clarly stat
More informationOptimal environmental policies in a heterogeneous product market under research and development competition and cooperation
Optimal nvironmntal poliis in a htrognous produt markt undr rsarh and dvlopmnt omptition and oopration By Olusgun Oladunjoy Univrsity of Gulph, Ontario, Canada Sptmbr 0, 005 Introdution Pollution xtrnality
More informationOn-Line PI Controller Tuning Using Closed-Loop Setpoint Responses for Stable and Integrating Processes*
On-Lin PI Controllr Tuning Using Closd-Loop Stpoint Rsponss for Stabl and Intgrating Prosss* Mohammad Shamsuzzoha a, Sigurd Skogstad a, Ivar J. Halvorsn b a Norwgian Univrsity of Sin and Thnology (NTNU),
More informationMEASURING HEAT FLUX FROM A COMPONENT ON A PCB
MEASURING HEAT FLUX FROM A COMPONENT ON A PCB INTRODUCTION Elctronic circuit boards consist of componnts which gnrats substantial amounts of hat during thir opration. A clar knowldg of th lvl of hat dissipation
More informationLinear Non-Gaussian Structural Equation Models
IMPS 8, Durham, NH Linar Non-Gaussian Structural Equation Modls Shohi Shimizu, Patrik Hoyr and Aapo Hyvarinn Osaka Univrsity, Japan Univrsity of Hlsinki, Finland Abstract Linar Structural Equation Modling
More informationStudies of Turbulence and Transport in Alcator C-Mod Ohmic Plasmas with Phase Contrast Imaging and Comparisons with GYRO*
Studis of Turbulnc and Transport in Ohmic Plasmas with Phas Contrast Imaging and Comparisons with GYRO* L. Lin 1, M. Porkolab 1, E.M. Edlund 1, J.C. Rost 1, M. Grnwald 1, D.R. Mikklsn 2, N. Tsujii 1 1
More informationCALCULATION OF SHRINKAGE STRAIN IN EARLY-AGE CONCRETE STRUCTURES---AN EXAMPLE WITH CONCRETE PAVEMENTS
Cmntitious Composits, 11-13 April 212, Amstrdam, Th Nthrlands CALCULATION OF SHRINKAGE STRAIN IN EARLY-AGE CONCRETE STRUCTURES---AN EXAMPLE WITH CONCRETE PAVEMENTS Jun Zhang, Dongwi Hou and Yuan Gao Dpartmnt
More informationSupplementary Materials
6 Supplmntary Matrials APPENDIX A PHYSICAL INTERPRETATION OF FUEL-RATE-SPEED FUNCTION A truck running on a road with grad/slop θ positiv if moving up and ngativ if moving down facs thr rsistancs: arodynamic
More informationThermodynamical insight on the role of additives in shifting the equilibrium between white and grey tin
hrmodynamical insight on th rol of additivs in shifting th quilibrium btwn whit and gry tin Nikolay Dmntv Dpartmnt of Chmistry, mpl Univrsity, Philadlphia, PA 19122 Abstract In this study mthods of statistical
More information5.80 Small-Molecule Spectroscopy and Dynamics
MIT OpnCoursWar http://ocw.mit.du 5.80 Small-Molcul Spctroscopy and Dynamics Fall 008 For information about citing ths matrials or our Trms of Us, visit: http://ocw.mit.du/trms. Lctur # 3 Supplmnt Contnts
More informationSUMMER 17 EXAMINATION
(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr jct Cod: Important Instructions to aminrs: ) Th answrs should b amind by ky words and not as word-to-word as givn in th modl answr schm. ) Th modl answr
More information4 x 4, and. where x is Town Square
Accumulation and Population Dnsity E. A city locatd along a straight highway has a population whos dnsity can b approimatd by th function p 5 4 th distanc from th town squar, masurd in mils, whr 4 4, and
More informationRecursive Estimation of Dynamic Time-Varying Demand Models
Intrnational Confrnc on Computr Systms and chnologis - CompSysch 06 Rcursiv Estimation of Dynamic im-varying Dmand Modls Alxandr Efrmov Abstract: h papr prsnts an implmntation of a st of rcursiv algorithms
More informationAddition of angular momentum
Addition of angular momntum April, 0 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat th
More informationOPTIMIZATION OF WAVELENGTHS FOR QUADRI-SPECTRAL PYROMETER IN VISIBLE AND NEAR INFRARED RADIATION RANGE USED FOR HEAT TREATMENTS OF STEELS
Vol- Issu-5 08 IJARIIE-ISS(O)-95-96 OPIMIZAIO OF WAVELEGHS FOR QUADRI-SPERAL PYROMEER I VISIBLE AD EAR IFRARED RADIAIO RAGE USED FOR HEA REAMES OF SEELS RAIAARIVO Paul Ezkl, RASEFAO Elisé, RAKOOMIRAHO
More informationProperties of Quarks ( ) Isospin. π = 1, 1
Proprtis of Quarks Isospin So far, w hav discussd thr familis of lptons but principally concntratd on on doublt of quarks, th u and d. W will now introduc othr typs of quarks, along with th nw quantum
More informationMCE503: Modeling and Simulation of Mechatronic Systems Discussion on Bond Graph Sign Conventions for Electrical Systems
MCE503: Modling and Simulation o Mchatronic Systms Discussion on Bond Graph Sign Convntions or Elctrical Systms Hanz ichtr, PhD Clvland Stat Univrsity, Dpt o Mchanical Enginring 1 Basic Assumption In a
More informationProblem Set 6 Solutions
6.04/18.06J Mathmatics for Computr Scinc March 15, 005 Srini Dvadas and Eric Lhman Problm St 6 Solutions Du: Monday, March 8 at 9 PM in Room 3-044 Problm 1. Sammy th Shark is a financial srvic providr
More informationErrata. Items with asterisks will still be in the Second Printing
Errata Itms with astrisks will still b in th Scond Printing Author wbsit URL: http://chs.unl.du/edpsych/rjsit/hom. P7. Th squar root of rfrrd to σ E (i.., σ E is rfrrd to not Th squar root of σ E (i..,
More informationChemical Physics II. More Stat. Thermo Kinetics Protein Folding...
Chmical Physics II Mor Stat. Thrmo Kintics Protin Folding... http://www.nmc.ctc.com/imags/projct/proj15thumb.jpg http://nuclarwaponarchiv.org/usa/tsts/ukgrabl2.jpg http://www.photolib.noaa.gov/corps/imags/big/corp1417.jpg
More information4.2 Design of Sections for Flexure
4. Dsign of Sctions for Flxur This sction covrs th following topics Prliminary Dsign Final Dsign for Typ 1 Mmbrs Spcial Cas Calculation of Momnt Dmand For simply supportd prstrssd bams, th maximum momnt
More informationReview Statistics review 14: Logistic regression Viv Bewick 1, Liz Cheek 1 and Jonathan Ball 2
Critical Car Fbruary 2005 Vol 9 No 1 Bwick t al. Rviw Statistics rviw 14: Logistic rgrssion Viv Bwick 1, Liz Chk 1 and Jonathan Ball 2 1 Snior Lcturr, School of Computing, Mathmatical and Information Scincs,
More informationBackground: We have discussed the PIB, HO, and the energy of the RR model. In this chapter, the H-atom, and atomic orbitals.
Chaptr 7 Th Hydrogn Atom Background: W hav discussd th PIB HO and th nrgy of th RR modl. In this chaptr th H-atom and atomic orbitals. * A singl particl moving undr a cntral forc adoptd from Scott Kirby
More information