Genetic parameter estimates and response to selection for weight and testicular traits in Nelore cattle

Size: px
Start display at page:

Download "Genetic parameter estimates and response to selection for weight and testicular traits in Nelore cattle"

Transcription

1 Gntic prmtr stimts n rspons to slction for wight n tsticulr trits in Nlor cttl F.R. Arujo Nto 1, R.B. Lôbo 2, M.D.S. Mot 3 n H.N. Olivir 1 1 Dprtmnto Gnétic Mlhormnto Animl, Fcul Ciêncis Agráris Vtrináris, Univrsi Estul Pulist Julio Msquit Filho, Jboticbl, SP, Brsil 2 Dprtmnto Gnétic, Fcul Micin Ribirão Prto, Univrsi São Pulo, Ribirão Prto, SP, Brsil 3 Dprtmnto Nutrição Mlhormnto Animl, Fcul Micin Vtrinári Zootcni, Univrsi Estul Pulist Julio Msquit Filho, Botuctu, SP, Brsil Corrsponing uthor: F.R. Arujo Nto E-mil: ntozoo@hotmil.com Gnt. Mol. Rs. 10 (4): (2011) Rciv Jnury 4, 2011 Accpt Jun 3, 2011 Publish Dcmbr 19, 2011 DOI ABSTRACT. W stimt gntic prmtrs for vrious phss of boy n tsticulr growth until 550 ys of g in Nlor cttl, using Bysin infrnc, incluing corrltion vlus n rror stimts. Wight n scrotl rcors of 54,182 Nlor nimls originting from 18 frms prticipting in th Brzilin Nlor Bring Progrm (PMGRN) wr inclu. Th following trits wr msur: wight t stnr gs of 120 (W120), 210 (W210), 365 (W365), 450 (W450), n 550 (W550) ys; wight gin btwn 120/210 (WG1), 210/365 (WG2), 365/450 (WG3), 450/550 (WG4), 120/365 (WG5), 120/450 (WG6), 120/550 (WG7), 210/450 (WG8), 210/550 (WG9), n 365/550 (WG10) Gntics n Molculr Rsrch 10 (4): (2011) FUNPEC-RP

2 F.R. Arujo Nto t l ys of g; scrotl circumfrnc t 365 (SC365), 450 (SC450) n 550 (SC550) ys of g, n tsticulr growth btwn 365/450 (TG1), 450/550 (TG2) n 365/550 (TG3) ys of g. Th mol inclu contmporry group (currnt frm, yr n two-month prio of birth, sx, n mngmnt group) n g of m t clving, ivi into clsss s fix ffcts. Th mol lso inclu rnom ffcts for irct itiv, mtrnl itiv n mtrnl prmnnt nvironmntl, n rsiul ffcts. Th irct hritbility stimts rng from 0.23 to 0.39, 0.13 to 0.39 n 0.32 to 0.56 for wights t stnr gs, wight gins n tsticulr msurs, rspctivly. Th gntic corrltions btwn wights (0.69 to 0.94) n scrotl circumfrncs (0.91 to 0.97) msur t stnr gs wr highr thn thos btwn wight gin n tsticulr growth (0.18 to 0.97 n 0.36 to 0.77, rspctivly). Th wights t stnr gs rspon mor ffctivly to slction, n lso gv strong corrltions with th othr trits. Ky wors: Bf cttl; Gibbs smpls; Growth; Rprouctiv trits INTRODUCTION Th nw conomic orr, bs on comptition n constnt srch for prouctiv fficincy, hs forc livstock proucrs to opt nw tchnologis. Ths chngs in frm mngmnt r ccompni by gntic ltrtions of th hrs promot by th slction of nimls. This procss is support by th choic of critri comptibl with th objctiv of th ctivity n by th ccurt stimtion of (co)vrinc componnts of th trits slct. In bf cttl, wights n wight gins btwn crtin gs hv bn opt s slction critri bcus thy r sy to msur n intrprt, th possibility of promoting substntil gntic gin, n high gntic corrltions btwn ths msurs. In Brzil, gntic bring progrms inclu scrotl circumfrnc s rprouctiv critrion sinc, in ition to its sy msurmnt, this trit prsnts fvorbl gntic corrltions with prouctiv n rprouctiv trits in both fmls (Elr t l., 2004; Forni n Albuqurqu, 2005) n mls (Srriro t l., 2002; Kly t l., 2006). Th stimtion of (co)vrinc componnts for ny critri opt prmits th construction n ppliction of slction inics n of mix mol qutions, s wll s th clcultion of prmtrs such s hritbility n gntic corrltion, thus fcilitting th plnning of bring progrms n th intrprttion of gntic mchnisms involv in th xprssion of iffrnt trits (Hnrson, 1986). In viw of this importnc, vrious mthos of stimtion hv bn tst in quntittiv gntic nlyss to obtin ccurt stimts n to fcilitt th implmnttion of complx mols. In this rspct, Ginol n Frnno (1986) introuc th Bysin pproch in niml bring n Wng t l. (1993) subsquntly ppli it to linr mix mols using th Gibbs lgorithm. Th objctiv of th prsnt stuy ws to tst linr mix mols in combin nlyss by Bysin infrnc to stimt gntic prmtrs for iffrnt phss of boy n tsticulr growth until 550 ys of g in Nlor cttl, to contribut to slction progrms sign to improv ths trits. Gntics n Molculr Rsrch 10 (4): (2011) FUNPEC-RP

3 Gntic prmtrs for growth n rprouctiv trits 3129 MATERIAL AND METHODS Wight n scrotl rcors of Nlor nimls originting from 18 frms prticipting in th Brzilin Nlor Bring Progrm (PMGRN) wr us. Th following trits wr stui: wight t stnr gs of 120 (W120), 210 (W210), 365 (W365), 450 (W450), n 550 (W550) ys; wight gin btwn 120/210 (WG1), 210/365 (WG2), 365/450 (WG3), 450/550 (WG4), 120/365 (WG5), 120/450 (WG6), 120/550 (WG7), 210/450 (WG8), 210/550 (WG9), n 365/550 (WG10) ys of g; scrotl circumfrnc t 365 (SC365), 450 (SC450) n 550 (SC550) ys of g, n tsticulr growth btwn 365/450 (TG1), 450/550 (TG2) n 365/550 (TG3) ys of g. Explortory nlysis ws prform using th Sttisticl Anlysis Systm softwr (SAS Institut, 2003) to vlut th consistncy of th t. Th contmporry groups consist of currnt frm, yr n two-month prio of birth, sx, n mngmnt group. Rcors tht wr 3.5 stnr vitions bov or blow th mn of th group n contmporry groups contining progny from singl sir or fwr thn fiv nimls wr limint. Th fil contin t from 54,182 iniviuls (Tbl 1) n th numbr of nimls in th rltionship mtrix ws 82,692. Tbl 1. Summry of t structur n scriptiv sttistics for wight t stnr gs (W), wight gin (WG), scrotl circumfrnc (SC), n tsticulr growth (TG) in Nlor cttl. Trits N Mn SD Min. Mx. NS NM W120 (kg) 50, ,090 21,576 W210 (kg) 47, ,097 20,723 W365 (kg) 39, ,064 18,439 W450 (kg) 36, ,023 17,402 W550 (kg) 23, ,158 WG1 (kg) 45, ,061 19,936 WG2 (kg) 35, ,925 WG3 (kg) 31, ,805 WG4 (kg) 20, ,084 WG5 (kg) 37, ,008 17,795 WG6 (kg) 33, ,359 WG7 (kg) 21, ,152 WG8 (kg) 33, ,326 WG9 (kg) 21, ,112 WG10 (kg) 21, ,444 SC365 (cm) 12, ,665 SC450 (cm) 14, ,640 SC550 (cm) 7, ,013 TG1 (cm) 10, ,403 TG2 (cm) 6, ,216 TG3 (cm) 5, ,528 N = numbr of rcors; SD = stnr vition; NS = numbr of sirs; NM = numbr of mothrs. (Co)vrinc componnts wr stimt by multi-trit nlysis simultnously incluing th following trits: W120, SC365, WG1, WG2, WG3, WG4, TG1, n TG2. Th mol inclu contmporry group n g of m t clving ivi into clsss (for W120 n WG1) s fix ffcts. Th mol lso inclus rnom ffcts for irct itiv, mtrnl itiv (for W120 n WG1) n mtrnl prmnnt nvironmntl (for W120 n WG1), n rsiul. In viw of contrictory rsults in th litrtur, th covrinc btwn irct n mtrnl gntic ffcts ws fix t zro s on in othr stuis (Albuqurqu n Myr, 2001). Gntics n Molculr Rsrch 10 (4): (2011) FUNPEC-RP

4 F.R. Arujo Nto t l Th GIBBS2F90 progrm (Misztl, 2007) ws us for nlysis. A chin of 1,131,500 cycls ws gnrt, with burn-in prio of 30,000 itrtions n smpling intrvl of 100. Gntic prmtrs for th othr chrctristics (W205, W365, W450, W550, WG5, WG6, WG7, WG8, WG9, WG10, SC450, SC550, n TG3) wr stimt through th sum of vrincs in ch vctor Th mtrix prsnttion of th complt mol us for nlysis is: (Eqution 1) whr y, β,, m, c, n r vctors of obsrvtions, fix ffcts, irct itiv gntic ffcts, mtrnl itiv gntic ffcts, mtrnl prmnnt nvironmntl ffcts, n rsiul ffcts, rspctivly, n X, Z 1, Z 2, n W r incinc mtrics tht rlt β,, m, n c to th obsrvtions. Uniform n Gussin priors wr ssum for fix n rnom ffcts, rspctivly: (Eqution 2) whr A, G, G m, E p, R, n I r th rltionship mtrics, irct gntic, mtrnl gntic, n mtrnl prmnnt nvironmntl n rsiul covrincs, n intity, rspctivly, n is th oprtor of th Kronckr prouct. For vrinc componnts, priors riv from invrs Wishrt istributions, corrsponing to th invrs chi-squr istribution in univrit css, wr us (Vn Tssll n Vn Vlck, 1996). Thus: (Eqution 3) whr S n v, S m n v m, S p n v p, n S r n v r r priori vlus n grs of from for irct itiv, mtrnl itiv, mtrnl prmnnt nvironmntl, n rsiul covrincs, rspctivly. Th burn-in prio n th smpling intrvl wr stblish mpiriclly n post- Gibbs nlysis ws prform using th Gibnl progrm (Vn Km, 1997) to trmin convrgnc n th numbr of ffctiv smpls. Th popultion prmtrs wr clcult in ch vctor, n th mn, min n mo of postrior istributions wr stimt. In ition, th 95% high-nsity intrvl (HDI) ws clcult sinc this prmtr is mor informtiv thn confinc intrvls in th cs of symmtric or multimol istributions (Hynmn, 1996). Gntics n Molculr Rsrch 10 (4): (2011) FUNPEC-RP

5 Gntic prmtrs for growth n rprouctiv trits 3131 RESULTS AND DISCUSSION Anlysis of convrgnc, pnnc btwn smpls n rlibility of th stimts Th rsults obtin with th Gibnl progrm show tht th burn-in prio ws sufficint to trmin convrgnc of th chin. Th ffctiv smpl siz obtin for th prmtrs ws rltivly smll (22 to 1614) whn compr to th totl numbr of vctors gnrt. In gnrl, th corrltion stimts prsnt th grtst pnnc, with smllr ffctiv smpl siz bing ssocit with corrltions of mtrnl origin. Thrfor, th us of mol simultnously incluing lrg numbr of trits, lthough rprsnting mor xtnsiv sourc of informtion (Schffr, 1984), incrss th pnnc btwn smpls u to th numbr of prmtrs involv. In th cs of stimts rlt to mtrnl ffcts, th numbr of offspring pr m my hv incrs th pnnc btwn ths prmtrs, lthough othr fctors such s th numbr of ms with rcors lso intrfr with ths stimts (Hyrpour t l., 2008). Howvr, no minimum ffctiv smpl siz on which to infr hs bn rport in th litrtur. Th siz obtin in th prsnt stuy sm to b sufficint to obtin msurs of cntrl tnncy n vrition. With rspct to th rlibility of th stimts, hritbilitis n vrincs prsnt smll HDI n low stnr vition, finings inicting tht th prmtrs wr rlibl. Th corrltion stimts prsnt low stnr vitions, but xcptions wr obsrv. Gntic prmtr stimts n rspons to slction Th irct hritbility stimts for wights t stnr gs wr mort to high (0.23 to 0.39) n wr highr t olr gs (Tbl 2). Th mgnitu of vrition in ths stimts ws similr to tht rport by Albuqurqu n El Fro (2008), but th point stimts wr slightly highr. Th growing trn in th hritbility stimts, s lso monstrt by Albuqurqu n Myr (2001b) using rnom rgrssion, is u to th fct tht irct itiv vrinc incrss t highr rt thn rsiul vrinc with incrsing g s rsult of th combin ction of lrg numbr of gns on wights msur t th gs stui, whrs rnom nvironmntl ffcts tn to cncl ch othr ovr tim. With rspct to wight gins, th irct hritbility stimts rng from 0.13 to 0.39 n tn to b highr for wir intrvls (WG5 to WG9). Similr stimts hv bn rport in th litrtur. Pnto t l. (2002) obtin stimts rnging from 0.16 to 0.32 for totl gins btwn stnr gs. Krjcová t l. (2007), stuying ily wight gins ovr nin prios by multi-trit n rnom rgrssion nlysis, rport hritbilitis rnging from to Consiring th rsults prsnt, th slction bs on WG6 or WG7 ws foun to b s ffctiv s slction bs on wights t stnr gs, bcus substntil prt of th vrition ws u to th vrg ffct of gns. Howvr, it is importnt to consir th mgnitu of irct itiv vrinc, its rltionship with othr trits of intrst n oprtionl spcts, bcus it rquirs t lst two msurs in niml. With rspct to mtrnl ffcts, th hritbility stimts wr of low mgnitu n wr highr for wights t stnr gs (0.11 n 0.10 for W120 n W210, rspctivly) whn compr to wight gin (0.04 for WG1). Albuqurqu n Myr (2001b) rport highr mtrnl hritbilitis Gntics n Molculr Rsrch 10 (4): (2011) FUNPEC-RP

6 F.R. Arujo Nto t l Tbl 2. Dscriptiv sttistics of postrior istribution for vrinc componnts n gntic prmtrs for wight t stnr g (W) n wight gins (WG). Trits Prmtrs Mn Mo Min SD ES HDI (95%) W120 σ σ σ m σ pm h h m c W210 σ σ σ m σ pm h h m c W365 σ σ , h W450 σ , σ , h W550 σ , σ , h , WG1 σ σ σ m σ pm h h m c WG2 σ σ h WG3 σ σ h WG4 σ σ h WG5 σ σ h WG6 σ σ , h WG7 σ , σ , h , WG8 σ σ , h WG9 σ σ h , WG10 σ σ h 2 σ 2 = irct itiv vrinc; σ2 = rsiul vrinc; σ2 m = mtrnl itiv vrinc; σ2 pm = mtrnl prmnnt nvironmntl vrinc; h 2 = irct hritbility; h2 m = mtrnl hritbility; c2 = mtrnl prmnnt nvironmntl vrinc componnt s proportion of phnotypic vrincs; ES = numbr of ffctiv smpls; SD = stnr vition; HDI = high-nsity intrvl. Gntics n Molculr Rsrch 10 (4): (2011) FUNPEC-RP

7 Gntic prmtrs for growth n rprouctiv trits 3133 for wights t 120 (0.25) n 240 (0.20) ys of g. In contrst to ths uthors who obsrv crs in th mtrnl ffct with g, in th prsnt stuy this ffct ws stbl t 120 n 210 ys. Thrfor, in viw of th similrity of mtrnl ffcts t ths gs n th highr phnotypic vrinc obsrv t 210 ys, grtr rspons to slction is xpct for mtrnl bility t this g. Rgring msurs of tsticulr growth, th hritbility stimts wr high (0.32 to 0.56), xcpt for TG2 (Tbl 3). As obsrv for th wight trits, grtr rspons to slction cn b chiv through slction bs on th scrotl circumfrnc t stnr gs. For trits obtin t stnr gs, th stimts wr highr thn thos rport by Yokoo t l. (2007) (0.48, 0.53 n 0.42 for SC365, SC450 n SC550, rspctivly). Similr stimts for TG1 n TG2 wr obsrv by Pnto t l. (2002) (0.24 n 0.18 for scrotl growth btwn 365/455 n 455/550 ys of g). Tbl 3. Dscriptiv sttistics of postrior istribution for vrinc componnts n gntic prmtrs for scrotl circumfrnc (SC) n tsticulr growth (TG). Trits Prmtrs Mn Mo Min SD ES HDI (95%) SC365 σ 2 σ 2 h 2 SC450 σ 2 σ 2 h 2 SC550 σ 2 σ 2 h 2 TG1 σ 2 σ 2 h 2 TG2 σ 2 σ 2 h 2 TG3 σ 2 σ 2 h σ 2 = irct itiv vrinc; σ2 = rsiul vrinc; h2 = irct hritbility; SD = stnr vition; ES = numbr of ffctiv smpls; HDI = high-nsity intrvl. Th gntic corrltions btwn wights (0.69 to 0.94) n scrotl circumfrncs (0.91 to 0.97) msur t stnr gs wr highr thn thos btwn wight gin n tsticulr growth (0.18 to 0.97 n 0.36 to 0.77, rspctivly) (Tbl 4). High corrltions for wight gin n tsticulr growth wr only obsrv btwn ovrlpping msurs. Similr rsults hv bn rport by Albuqurqu n Myr (2001b) for wights t stnr gs using rnom rgrssion mols n by Yokoo t l. (2007) btwn msurs of scrotl circumfrnc t 365, 450 n 550 ys of g. Th gntic corrltions obtin for wight gins show mgnitu similr to tht rport by Krjcová t l. (2007), xcpt for som ngtiv corrltions ( to 0.958). For trits msur t stnr gs (wight n scrotl circumfrnc), n invrs rltionship ws obsrv btwn th gntic corrltion stimt n chronologicl istnc btwn th two msurs. Similr rsults hv bn rport by Albuqurqu n Myr (2001b) using rnom rgrssion mols for wights. Wight gins prsnt highr corrltions with wights just for g t th uppr limit of th intrvl tht trmin th wight gin. Gntics n Molculr Rsrch 10 (4): (2011) FUNPEC-RP

8 F.R. Arujo Nto t l Tbl 4. Estimts of postriori vrg n stnr vition (in prnthss) of th gntic (top right) n nvironmntl (bottom lft) corrltions btwn th chrctristics of wight n tsticulr vlopmnt [scrotl circumfrnc (SC) n tsticulr growth (TG)] in th Nlor cttl. W120 W210 W365 W450 W550 WG1 WG2 WG3 WG4 WG5 WG6 W (0.01) 0.78 (0.02) 0.73 (0.02) 0.69 (0.02) 0.55 (0.04) 0.12 (0.05) 0.24 (0.05) 0.29 (0.06) 0.35 (0.04) 0.36 (0.04) W (0.00) (0.01) 0.82 (0.01) 0.80 (0.02) 0.81 (0.02) 0.24 (0.05) 0.25 (0.05) 0.42 (0.05) 0.56 (0.03) 0.53 (0.03) W (0.01) 0.70 (0.01) (0.00) 0.94 (0.01) 0.80 (0.02) 0.66 (0.03) 0.43 (0.05) 0.47 (0.05) 0.86 (0.01) 0.83 (0.02) W (0.01) 0.61 (0.01) 0.85 (0.00) (0.00) 0.73 (0.03) 0.70 (0.02) 0.63 (0.04) 0.48 (0.06) 0.86 (0.01) 0.90 (0.01) W (0.01) 0.59 (0.01) 0.73 (0.01) 0.85 (0.00) (0.03) 0.67 (0.03) 0.60 (0.04) 0.68 (0.04) 0.85 (0.01) 0.88 (0.01) WG (0.01) 0.69 (0.01) 0.47 (0.01) 0.39 (0.01) 0.39 (0.01) (0.05) 0.18 (0.06) 0.52 (0.06) 0.74 (0.02) 0.65 (0.03) WG (0.01) (0.01) (0.01) (0.01) 0.33 (0.01) (0.01) (0.05) 0.31 (0.06) 0.89 (0.01) 0.88 (0.01) WG (0.00) (0.01) (0.01) 0.47 (0.01) 0.37 (0.01) (0.01) (0.01) (0.07) 0.44 (0.05) 0.71 (0.03) WG (0.01) 0.11 (0.01) (0.01) (0.01) 0.48 (0.01) 0.09 (0.01) (0.01) (0.01) (0.05) 0.47 (0.05) WG (0.01) 0.25 (0.01) 0.79 (0.01) 0.65 (0.01) 0.53 (0.01) 0.48 (0.01) 0.80 (0.00) (0.01) (0.01) (0.01) WG (0.01) 0.20 (0.01) 0.62 (0.01) 0.84 (0.00) 0.67 (0.01) 0.37 (0.01) 0.63 (0.01) 0.54 (0.01) (0.01) 0.79 (0.00) - WG (0.01) 0.24 (0.01) 0.53 (0.01) 0.69 (0.01) 0.88 (0.01) 0.38 (0.01) 0.45 (0.01) 0.41 (0.01) 0.52 (0.01) 0.63 (0.01) 0.79 (0.01) WG (0.01) (0.01) 0.41 (0.01) 0.68 (0.01) 0.50 (0.01) (0.01) 0.75 (0.00) 0.60 (0.01) (0.01) 0.58 (0.01) 0.86 (0.00) WG (0.01) (0.01) 0.34 (0.01) 0.55 (0.01) 0.76 (0.01) (0.01) 0.56 (0.01) 0.47 (0.01) 0.51 (0.01) 0.45 (0.01) 0.67 (0.01) WG (0.01) 0.07 (0.01) (0.01) 0.27 (0.01) 0.63 (0.01) 0.04 (0.01) (0.01) 0.62 (0.01) 0.73 (0.01) (0.01) 0.28 (0.01) SC (0.02) 0.39 (0.02) 0.52 (0.02) 0.49 (0.02) 0.44 (0.02) 0.27 (0.02) 0.26 (0.02) 0.06 (0.02) 0.02 (0.02) 0.40 (0.02) 0.37 (0.02) SC (0.02) 0.36 (0.02) 0.48 (0.02) 0.53 (0.02) 0.52 (0.02) 0.25 (0.02) 0.24 (0.02) 0.20 (0.02) 0.09 (0.03) 0.36 (0.02) 0.44 (0.02) SC (0.02) 0.38 (0.03) 0.46 (0.03) 0.50 (0.02) 0.57 (0.03) 0.26 (0.02) 0.20 (0.02) 0.18 (0.02) 0.25 (0.03) 0.33 (0.02) 0.39 (0.03) TG (0.02) 0.09 (0.02) 0.13 (0.02) 0.25 (0.02) 0.28 (0.02) 0.06 (0.02) 0.07 (0.02) 0.26 (0.02) 0.12 (0.02) 0.09 (0.02) 0.24 (0.02) TG (0.02) 0.10 (0.02) 0.07 (0.02) 0.06 (0.02) 0.20 (0.02) 0.06 (0.02) (0.02) (0.02) 0.27 (0.02) 0.02 (0.02) 0.02 (0.02) TG (0.02) 0.13 (0.02) 0.14 (0.02) 0.21 (0.02) 0.33 (0.02) 0.09 (0.02) 0.03 (0.02) 0.17 (0.02) 0.28 (0.02) 0.08 (0.02) 0.17 (0.02) Continu on nxt pg Gntics n Molculr Rsrch 10 (4): (2011) FUNPEC-RP

9 Gntic prmtrs for growth n rprouctiv trits 3135 Tbl 4. Continu. WG7 WG8 WG9 WG10 SC365 SC450 SC550 TG1 TG2 TG3 W (0.04) 0.19 (0.04) 0.27 (0.04) 0.34 (0.05) 0.49 (0.04) 0.41 (0.04) 0.40 (0.04) 0.16 (0.06) 0.13 (0.09) 0.18 (0.06) W (0.03) 0.27 (0.04) 0.39 (0.04) 0.43 (0.04) 0.56 (0.03) 0.49 (0.04) 0.48 (0.04) 0.24 (0.06) 0.17 (0.09) 0.25 (0.06) W (0.02) 0.66 (0.03) 0.71 (0.03) 0.57 (0.04) 0.53 (0.03) 0.49 (0.03) 0.49 (0.04) 0.28 (0.05) 0.24 (0.08) 0.32 (0.06) W (0.01) 0.77 (0.02) 0.80 (0.02) 0.68 (0.04) 0.44 (0.03) 0.41 (0.03) 0.42 (0.04) 0.25 (0.05) 0.22 (0.09) 0.28 (0.06) W (0.01) 0.74 (0.02) 0.86 (0.01) 0.81 (0.02) 0.42 (0.04) 0.38 (0.04) 0.41 (0.04) 0.22 (0.05) 0.26 (0.08) 0.29 (0.06) WG (0.03) 0.33 (0.05) 0.48 (0.05) 0.46 (0.05) 0.50 (0.04) 0.48 (0.04) 0.47 (0.05) 0.31 (0.06) 0.16 (0.10) 0.30 (0.07) WG (0.02) 0.92 (0.01) 0.84 (0.02) 0.49 (0.05) 0.22 (0.05) 0.23 (0.04) 0.26 (0.05) 0.19 (0.06) 0.24 (0.09) 0.26 (0.07) WG (0.04) 0.79 (0.03) 0.73 (0.03) 0.74 (0.03) (0.05) (0.05) (0.06) 0.04 (0.07) 0.02 (0.11) 0.02 (0.09) WG (0.03) 0.34 (0.06) 0.69 (0.03) 0.84 (0.02) 0.18 (0.06) 0.15 (0.06) 0.21 (0.06) 0.05 (0.07) 0.32 (0.10) 0.20 (0.07) WG (0.01) 0.82 (0.02) 0.84 (0.02) 0.58 (0.05) 0.40 (0.04) 0.39 (0.04) 0.41 (0.04) 0.29 (0.05) 0.25 (0.08) 0.33 (0.06) WG (0.01) 0.93 (0.01) 0.92 (0.01) 0.72 (0.03) 0.29 (0.04) 0.30 (0.04) 0.32 (0.04) 0.24 (0.05) 0.20 (0.09) 0.27 (0.06) WG (0.01) 0.97 (0.00) 0.86 (0.02) 0.29 (0.04) 0.29 (0.04) 0.32 (0.04) 0.20 (0.05) 0.27 (0.08) 0.28 (0.06) WG (0.01) (0.01) 0.68 (0.03) 0.12 (0.04) 0.14 (0.04) 0.17 (0.05) 0.16 (0.06) 0.17 (0.08) 0.20 (0.06) WG (0.00) 0.76 (0.01) (0.01) 0.17 (0.04) 0.18 (0.04) 0.22 (0.04) 0.14 (0.05) 0.27 (0.08) 0.24 (0.06) WG (0.01) 0.27 (0.01) 0.72 (0.01) (0.05) 0.09 (0.05) 0.13 (0.05) 0.06 (0.06) 0.22 (0.09) 0.16 (0.07) SC (0.02) 0.25 (0.02) 0.23 (0.02) 0.06 (0.02) (0.01) 0.91 (0.01) 0.63 (0.05) 0.26 (0.08) 0.57 (0.05) SC (0.03) 0.33 (0.02) 0.34 (0.03) 0.21 (0.02) 0.78 (0.01) (0.01) 0.83 (0.02) 0.32 (0.08) 0.74 (0.04) SC (0.03) 0.28 (0.02) 0.41 (0.03) 0.31 (0.02) 0.58 (0.02) 0.80 (0.01) (0.03) 0.54 (0.07) 0.85 (0.02) TG (0.02) 0.22 (0.02) 0.27 (0.02) 0.27 (0.02) 0.02 (0.03) 0.64 (0.02) 0.56 (0.03) (0.09) 0.87 (0.03) TG (0.02) (0.02) 0.17 (0.02) 0.21 (0.02) (0.04) (0.04) 0.49 (0.03) 0.01 (0.03) (0.05) TG (0.02) 0.14 (0.02) 0.30 (0.02) 0.33 (0.02) (0.04) 0.32 (0.03) 0.74 (0.02) 0.67 (0.02) 0.75 (0.01) - W = wight t stnr g; WG = wight gin. Gntics n Molculr Rsrch 10 (4): (2011) FUNPEC-RP

10 F.R. Arujo Nto t l Th highst rsiul corrltions (Tbl 4) wr obsrv btwn trits msur t stnr gs, whrs th mgnitu of rsiul corrltions btwn msurs of wight gin n tsticulr growth ws low n ngtiv corrltions wr frquntly obsrv btwn subsqunt msurmnts. Ngtiv n low rsiul corrltions wr lso obsrv btwn wight gin n wights n btwn tsticulr growth n msurs of scrotl circumfrnc. This fining inicts tht nvironmnts fvoring som trits cn b unfvorbl for othrs. Ths ngtiv n low rsiul corrltions spcilly btwn chronologiclly clos msurs suggst tht climtic chngs tht occur uring th yr r th min fctors rsponsibl, lthough th contmporry groups inclu this ffct. With rspct to wight n scrotl circumfrnc, th highst rsiul corrltion ws obsrv btwn jcnt msurs, i.., th mor istnt th two msurmnts, th mor istinct th nvironmntl conitions n th non-itiv gntic ffcts tht influnc thm. Anlyzing th corrltions btwn wight gins n wights t stnr gs, th highst corrltion ws foun btwn wight gin n wight msur t its uppr limit, s obsrv for gntic corrltions. Th highr hritbilitis for wight n scrotl circumfrnc msur t stnr gs whn compr to wight gin n scrotl growth lso sm to b th rsult of th lowr rsiul corrltions compr to gntic corrltions btwn gins. This fct lso xplins th incrs of hritbilitis for wight n scrotl circumfrnc with incrsing g of th nimls. Sinc wight n scrotl circumfrnc msur t stnr gs r normlly us in Brzil s th min slction critri for Nlor cttl, th rspons to slction of ths trits ws vlut using iffrnt critri tht coul b opt (Figurs 1 n 2). Th us of wights t stnr gs s slction critri show tht, xcpt for W210, irct slction is th most ffctiv pproch to incrs wight t crtin g. Slction for wight t crtin g shows similr fficincy to incrs wights t prvious gs s irct slction for ths trits. WG1, WG6 n WG7 wr foun to b th most ffctiv slction critri mong th wight gin trits. Among th tsticulr trits, SC365 ws th most ffctiv slction critrion to incrs wights in th nxt gnrtion. Whn th objctiv ws to incrs scrotl circumfrnc t iffrnt gs, th bst slction critri wr W365 n WG5 mong wight trits n TG1 mong tsticulr trits sinc ths trits show th highst incrss irrspctiv of g. With rspct to scrotl circumfrnc t stnr g, SC450 ws foun to b n ttrctiv critrion sinc th gins obtin by inirct slction t othr gs wr similr to thos obtin by irct slction. Consirtions rgring th choic of slction critri for Nlor cttl First, wights t stnr gs r th bst critri sinc thy rspon mor ffctivly to slction, proviing lso substntil inirct gins in othr trits. W550 ws foun to b th most ffctiv slction critrion mong th wight trits stui. Howvr, th choic of th slction critrion shoul tk into ccount th importnc of th trits for th brr n th cost of mintnnc of th nimls until th g of rcoring. Th stimt gntic corrltions btwn wight gin n wight t stnr g suggst th ltrntiv us of th formr s slction critrion sinc thy provok smllr incrs in birth wight n mtur wight. In ition, othr stuis hv monstrt fvorbl ssocitions btwn ths msurs n othr trits of conomic intrst (Arthur t l., 2001). Furthr stuis invstigting wight gin s slction critrion for Nlor cttl r ncssry. Gntics n Molculr Rsrch 10 (4): (2011) FUNPEC-RP

11 Gntic prmtrs for growth n rprouctiv trits 3137 Figur 1. Expct rspons to slction for wights t stnr gs, whn th slction is on through: A. wights t stnr gs (W, in kg), B. wight gin (WG, in kg), n C. scrotl circumfrnc (SC) n tsticulr growth (TG), both in cm. Gntics n Molculr Rsrch 10 (4): (2011) FUNPEC-RP

12 F.R. Arujo Nto t l Figur 2. Expct rspons to slction for scrotl circumfrnc, whn th slction is on through: A. wights t stnr gs (W, in kg), B. wight gin (WG, in kg), n C. scrotl circumfrnc (SC) n tsticulr growth (TG), both in cm. Gntics n Molculr Rsrch 10 (4): (2011) FUNPEC-RP

13 Gntic prmtrs for growth n rprouctiv trits 3139 With rspct to tsticulr trits, SC365 ws foun to b th bst slction critrion sinc its hritbility ws similr to tht of SC450 n SC550, in ition to prsnting highr gntic corrltion with wights t stnr gs. In this rspct, th fct tht this trit mnifsts t youngr g prmits ruction in th gnrtion intrvl. Accoring to Toll n Robison (1985), rly tsticulr trits r rflx of boy vlopmnt, whrs lt trits r influnc by th hormonl systm. This sttmnt is support by th highr gntic corrltions btwn wights n SC365 obsrv in this stuy, with highr tsticulr ctivity bing obsrv ftr this g in Zbu nimls. As consqunc, msurs obtin ftr 365 ys of g my prsnt highr corrltion with fml rprouctiv trits. ACKNOWLEDGMENTS W thnk th Ntionl Assocition of Cttl Brrs n Rsrchrs (ANCP) for proviing ccss to th tbs. Rsrch support by CAPES. REFERENCES Albuqurqu LG n Myr K (2001). Estimts of irct n mtrnl gntic ffcts for wights from birth to 600 ys of g in Nlor cttl. J. Anim. Br. Gnt. 118: Albuqurqu LG n Myr K (2001b). Estimts of covrinc functions for growth from birth to 630 ys of g in Nlor cttl. J. Anim. Sci. 79: Albuqurqu LG n El Fro L (2008). Comprçõs ntr os vlors gnéticos pr crctrístics crscimnto bovinos rç Nlor pritos com molos imnsão finit ou infinit. Rv. Brs. Zootc. 37: Arthur PF, Rnn G n Kruss D (2001). Gntic n phnotypic rltionships mong iffrnt msurs of growth n f fficincy in young Chrolis bulls. Livst. Pro. Sci. 68: Elr JP, Silv JA, Evns JL, Frrz JB, t l. (2004). Aitiv gntic rltionships btwn hifr prgnncy n scrotl circumfrnc in Nllor cttl. J. Anim. Sci. 82: Forni S n Albuqurqu LG (2005). Estimts of gntic corrltions btwn ys to clving n rprouctiv n wight trits in Nlor cttl. J. Anim. Sci. 83: Ginol D n Frnno RL (1986). Bysin mthos in niml bring thory. J. Anim. Sci. 63: Hnrson CR (1986). Rcnt vlopmnts in vrinc n covrinc stimtion. J. Anim. Sci. 63: Hyrpour M, Schffr LR n Yzi MH (2008). Influnc of popultion structur on stimts of irct n mtrnl prmtrs. J. Anim. Br. Gnt. 125: Hynmn RJ (1996). Computing n grphing highst nsity rgions. Am. Stt. 50: Kly CG, McNil MD, Tss MW, Gry TW, t l. (2006). Gntic prmtr stimts for scrotl circumfrnc n smn chrctristics of Lin 1 Hrfor bulls. J. Anim. Sci. 84: Krjcová H, Milnz N, Pribyl J n Schülr L (2007). Estimtion of gntic prmtrs for ily gins of bulls with multitrit n rnom rgrssion mols. Arch. Tirzucht. 50: Misztl I (2007). BLUPF90 fmily of progrms. Avilbl t [ Accss Mrch 12, Pnto JCC, Lmos DC, Bzrr LAF, Mrtins Filho R, t l. (2002). Estuo crctrístics quntittivs crscimnto os 120 os 550 is i m go Nlor. Rv. Brs. Zootc. 31: Srriro LC, Brgmnn JAG, Quirino CR, Pin NR, t l. (2002). Hrbili corrlção gnétic ntr prímtro scrotl, libio crctrístics sminis touros Nlor. Arq. Brs. M. Vt. Zootc. 54: SAS Institut (2003). SAS - Sttisticl Anlysis Systm. Usr s Gui, Cry. Schffr LR (1984). Sir n cow vlution unr multipl trit mols. J. Diry Sci. 67: Toll VD n Robison OW (1985). Estimts of gntic corrltions btwn tsticulr msurmnts n fml rprouctiv trits in cttl. J. Anim. Sci. 60: Vn Km JBCHM (1997). Gibnl: Anlyzing Progrm for Mrkov Chin Mont Crlo Squncs, Vrsion 2.4. Dpt. Anim. Sci., Wgningn Agric. Univ., Wgningn. Vn Tssll CP n Vn Vlck LD (1996). Multipl-trit Gibbs Smplr for niml mols: flxibl progrms for bysin n liklihoo-bs (co)vrinc componnt infrnc. J. Anim. Sci. 74: Gntics n Molculr Rsrch 10 (4): (2011) FUNPEC-RP

14 F.R. Arujo Nto t l Wng CS, Rutlg JJ n Ginol D (1993). Mrginl infrncs bout vrinc componnts in mix linr mol using Gibbs smpling. Gnt. Sl. Evol. 25: Yokoo MJI, Albuqurqu LG, Lôbo RB, Sinz RD, t l. (2007). Estimtivs prâmtros gnéticos pr ltur o postrior, pso circunfrênci scrotl m bovinos rç Nlor. Rv. Brs. Zootc. 36: Gntics n Molculr Rsrch 10 (4): (2011) FUNPEC-RP

Walk Like a Mathematician Learning Task:

Walk Like a Mathematician Learning Task: Gori Dprtmnt of Euction Wlk Lik Mthmticin Lrnin Tsk: Mtrics llow us to prform mny usful mthmticl tsks which orinrily rquir lr numbr of computtions. Som typs of problms which cn b on fficintly with mtrics

More information

ME 522 PRINCIPLES OF ROBOTICS. FIRST MIDTERM EXAMINATION April 19, M. Kemal Özgören

ME 522 PRINCIPLES OF ROBOTICS. FIRST MIDTERM EXAMINATION April 19, M. Kemal Özgören ME 522 PINCIPLES OF OBOTICS FIST MIDTEM EXAMINATION April 9, 202 Nm Lst Nm M. Kml Özgörn 2 4 60 40 40 0 80 250 USEFUL FOMULAS cos( ) cos cos sin sin sin( ) sin cos cos sin sin y/ r, cos x/ r, r 0 tn 2(

More information

Case Study VI Answers PHA 5127 Fall 2006

Case Study VI Answers PHA 5127 Fall 2006 Qustion. A ptint is givn 250 mg immit-rls thophyllin tblt (Tblt A). A wk ltr, th sm ptint is givn 250 mg sustin-rls thophyllin tblt (Tblt B). Th tblts follow on-comprtmntl mol n hv first-orr bsorption

More information

2-D ARMA MODEL PARAMETER ESTIMATION BASED ON THE EQUIVALENT 2-D AR MODEL APPROACH

2-D ARMA MODEL PARAMETER ESTIMATION BASED ON THE EQUIVALENT 2-D AR MODEL APPROACH -D AMA MODEL PAAMETE ESTIMATION BASED ON THE EQUIVALENT -D A MODEL APPOAH Ayın Kıılky Ahmt Hmi Kyrn -mil: yin@hituutr -mil: kyrn@hituutr Istnul Tchnicl Univrsity, Fculty of Elctricl n Elctronics Enginring,

More information

Section 3: Antiderivatives of Formulas

Section 3: Antiderivatives of Formulas Chptr Th Intgrl Appli Clculus 96 Sction : Antirivtivs of Formuls Now w cn put th is of rs n ntirivtivs togthr to gt wy of vluting finit intgrls tht is ct n oftn sy. To vlut finit intgrl f(t) t, w cn fin

More information

Integration Continued. Integration by Parts Solving Definite Integrals: Area Under a Curve Improper Integrals

Integration Continued. Integration by Parts Solving Definite Integrals: Area Under a Curve Improper Integrals Intgrtion Continud Intgrtion y Prts Solving Dinit Intgrls: Ar Undr Curv Impropr Intgrls Intgrtion y Prts Prticulrly usul whn you r trying to tk th intgrl o som unction tht is th product o n lgric prssion

More information

Floating Point Number System -(1.3)

Floating Point Number System -(1.3) Floting Point Numbr Sstm -(.3). Floting Point Numbr Sstm: Comutrs rrsnt rl numbrs in loting oint numbr sstm: F,k,m,M 0. 3... k ;0, 0 i, i,...,k, m M. Nottions: th bs 0, k th numbr o igits in th bs xnsion

More information

Floating Point Number System -(1.3)

Floating Point Number System -(1.3) Floting Point Numbr Sstm -(.3). Floting Point Numbr Sstm: Comutrs rrsnt rl numbrs in loting oint numbr sstm: F,k,m,M 0. 3... k ;0, 0 i, i,...,k, m M. Nottions: th bs 0, k th numbr o igts in th bs xnsion

More information

Errata for Second Edition, First Printing

Errata for Second Edition, First Printing Errt for Scond Edition, First Printing pg 68, lin 1: z=.67 should b z=.44 pg 1: Eqution (.63) should rd B( R) = x= R = θ ( x R) p( x) R 1 x= [1 G( x)] = θp( R) + ( θ R)[1 G( R)] pg 15, problm 6: dmnd of

More information

Chem 104A, Fall 2016, Midterm 1 Key

Chem 104A, Fall 2016, Midterm 1 Key hm 104A, ll 2016, Mitrm 1 Ky 1) onstruct microstt tl for p 4 configurtion. Pls numrt th ms n ml for ch lctron in ch microstt in th tl. (Us th formt ml m s. Tht is spin -½ lctron in n s oritl woul writtn

More information

Errata for Second Edition, First Printing

Errata for Second Edition, First Printing Errt for Scond Edition, First Printing pg 68, lin 1: z=.67 should b z=.44 pg 71: Eqution (.3) should rd B( R) = θ R 1 x= [1 G( x)] pg 1: Eqution (.63) should rd B( R) = x= R = θ ( x R) p( x) R 1 x= [1

More information

Chapter 16. 1) is a particular point on the graph of the function. 1. y, where x y 1

Chapter 16. 1) is a particular point on the graph of the function. 1. y, where x y 1 Prctic qustions W now tht th prmtr p is dirctl rltd to th mplitud; thrfor, w cn find tht p. cos d [ sin ] sin sin Not: Evn though ou might not now how to find th prmtr in prt, it is lws dvisl to procd

More information

Lecture 11 Waves in Periodic Potentials Today: Questions you should be able to address after today s lecture:

Lecture 11 Waves in Periodic Potentials Today: Questions you should be able to address after today s lecture: Lctur 11 Wvs in Priodic Potntils Tody: 1. Invrs lttic dfinition in 1D.. rphicl rprsnttion of priodic nd -priodic functions using th -xis nd invrs lttic vctors. 3. Sris solutions to th priodic potntil Hmiltonin

More information

On the Role of Fitness, Precision, Generalization and Simplicity in Process Discovery

On the Role of Fitness, Precision, Generalization and Simplicity in Process Discovery On th Rol of Fitnss, Prcision, Gnrliztion n Simplicity in Procss Discovry Joos Buijs Bouwijn vn Dongn Wil vn r Alst http://www.win.tu.nl/coslog/ Avncs in Procss ining ny procss iscovry n conformnc chcking

More information

1 Introduction to Modulo 7 Arithmetic

1 Introduction to Modulo 7 Arithmetic 1 Introution to Moulo 7 Arithmti Bor w try our hn t solvin som hr Moulr KnKns, lt s tk los look t on moulr rithmti, mo 7 rithmti. You ll s in this sminr tht rithmti moulo prim is quit irnt rom th ons w

More information

Instructions for Section 1

Instructions for Section 1 Instructions for Sction 1 Choos th rspons tht is corrct for th qustion. A corrct nswr scors 1, n incorrct nswr scors 0. Mrks will not b dductd for incorrct nswrs. You should ttmpt vry qustion. No mrks

More information

UNIT # 08 (PART - I)

UNIT # 08 (PART - I) . r. d[h d[h.5 7.5 mol L S d[o d[so UNIT # 8 (PRT - I CHEMICL INETICS EXERCISE # 6. d[ x [ x [ x. r [X[C ' [X [[B r '[ [B [C. r [NO [Cl. d[so d[h.5 5 mol L S d[nh d[nh. 5. 6. r [ [B r [x [y r' [x [y r'

More information

Page 1. Question 19.1b Electric Charge II Question 19.2a Conductors I. ConcepTest Clicker Questions Chapter 19. Physics, 4 th Edition James S.

Page 1. Question 19.1b Electric Charge II Question 19.2a Conductors I. ConcepTest Clicker Questions Chapter 19. Physics, 4 th Edition James S. ConTst Clikr ustions Chtr 19 Physis, 4 th Eition Jms S. Wlkr ustion 19.1 Two hrg blls r rlling h othr s thy hng from th iling. Wht n you sy bout thir hrgs? Eltri Chrg I on is ositiv, th othr is ngtiv both

More information

# 1 ' 10 ' 100. Decimal point = 4 hundred. = 6 tens (or sixty) = 5 ones (or five) = 2 tenths. = 7 hundredths.

# 1 ' 10 ' 100. Decimal point = 4 hundred. = 6 tens (or sixty) = 5 ones (or five) = 2 tenths. = 7 hundredths. How os it work? Pl vlu o imls rprsnt prts o whol numr or ojt # 0 000 Tns o thousns # 000 # 00 Thousns Hunrs Tns Ons # 0 Diml point st iml pl: ' 0 # 0 on tnth n iml pl: ' 0 # 00 on hunrth r iml pl: ' 0

More information

TOPIC 5: INTEGRATION

TOPIC 5: INTEGRATION TOPIC 5: INTEGRATION. Th indfinit intgrl In mny rspcts, th oprtion of intgrtion tht w r studying hr is th invrs oprtion of drivtion. Dfinition.. Th function F is n ntidrivtiv (or primitiv) of th function

More information

INTEGRALS. Chapter 7. d dx. 7.1 Overview Let d dx F (x) = f (x). Then, we write f ( x)

INTEGRALS. Chapter 7. d dx. 7.1 Overview Let d dx F (x) = f (x). Then, we write f ( x) Chptr 7 INTEGRALS 7. Ovrviw 7.. Lt d d F () f (). Thn, w writ f ( ) d F () + C. Ths intgrls r clld indfinit intgrls or gnrl intgrls, C is clld constnt of intgrtion. All ths intgrls diffr y constnt. 7..

More information

Ch 1.2: Solutions of Some Differential Equations

Ch 1.2: Solutions of Some Differential Equations Ch 1.2: Solutions of Som Diffrntil Equtions Rcll th fr fll nd owl/mic diffrntil qutions: v 9.8.2v, p.5 p 45 Ths qutions hv th gnrl form y' = y - b W cn us mthods of clculus to solv diffrntil qutions of

More information

, between the vertical lines x a and x b. Given a demand curve, having price as a function of quantity, p f (x) at height k is the curve f ( x,

, between the vertical lines x a and x b. Given a demand curve, having price as a function of quantity, p f (x) at height k is the curve f ( x, Clculus for Businss nd Socil Scincs - Prof D Yun Finl Em Rviw vrsion 5/9/7 Chck wbsit for ny postd typos nd updts Pls rport ny typos This rviw sht contins summris of nw topics only (This rviw sht dos hv

More information

Multi-Section Coupled Line Couplers

Multi-Section Coupled Line Couplers /0/009 MultiSction Coupld Lin Couplrs /8 Multi-Sction Coupld Lin Couplrs W cn dd multipl coupld lins in sris to incrs couplr ndwidth. Figur 7.5 (p. 6) An N-sction coupld lin l W typiclly dsign th couplr

More information

Theoretical Study on the While Drilling Electromagnetic Signal Transmission of Horizontal Well

Theoretical Study on the While Drilling Electromagnetic Signal Transmission of Horizontal Well 7 nd ntrntionl Confrnc on Softwr, Multimdi nd Communiction Enginring (SMCE 7) SBN: 978--6595-458-5 Thorticl Study on th Whil Drilling Elctromgntic Signl Trnsmission of Horizontl Wll Y-huo FAN,,*, Zi-ping

More information

CSE 373: AVL trees. Warmup: Warmup. Interlude: Exploring the balance invariant. AVL Trees: Invariants. AVL tree invariants review

CSE 373: AVL trees. Warmup: Warmup. Interlude: Exploring the balance invariant. AVL Trees: Invariants. AVL tree invariants review rmup CSE 7: AVL trs rmup: ht is n invrint? Mihl L Friy, Jn 9, 0 ht r th AVL tr invrints, xtly? Disuss with your nighor. AVL Trs: Invrints Intrlu: Exploring th ln invrint Cor i: xtr invrint to BSTs tht

More information

(2) If we multiplied a row of B by λ, then the value is also multiplied by λ(here lambda could be 0). namely

(2) If we multiplied a row of B by λ, then the value is also multiplied by λ(here lambda could be 0). namely . DETERMINANT.. Dtrminnt. Introution:I you think row vtor o mtrix s oorint o vtors in sp, thn th gomtri mning o th rnk o th mtrix is th imnsion o th prlllppi spnn y thm. But w r not only r out th imnsion,

More information

Lecture contents. Bloch theorem k-vector Brillouin zone Almost free-electron model Bands Effective mass Holes. NNSE 508 EM Lecture #9

Lecture contents. Bloch theorem k-vector Brillouin zone Almost free-electron model Bands Effective mass Holes. NNSE 508 EM Lecture #9 Lctur contnts Bloch thorm -vctor Brillouin zon Almost fr-lctron modl Bnds ffctiv mss Hols Trnsltionl symmtry: Bloch thorm On-lctron Schrödingr qution ch stt cn ccommo up to lctrons: If Vr is priodic function:

More information

VLSI Testing Assignment 2

VLSI Testing Assignment 2 1. 5-vlu D-clculus trut tbl or t XOR unction: XOR 0 1 X D ~D 0 0 1 X D ~D 1 1 0 X ~D D X X X X X X D D ~D X 0 1 ~D ~D D X 1 0 Tbl 1: 5-vlu D-clculus Trut Tbl or t XOR Function Sinc 2-input XOR t wors s

More information

Module graph.py. 1 Introduction. 2 Graph basics. 3 Module graph.py. 3.1 Objects. CS 231 Naomi Nishimura

Module graph.py. 1 Introduction. 2 Graph basics. 3 Module graph.py. 3.1 Objects. CS 231 Naomi Nishimura Moul grph.py CS 231 Nomi Nishimur 1 Introution Just lik th Python list n th Python itionry provi wys of storing, ssing, n moifying t, grph n viw s wy of storing, ssing, n moifying t. Bus Python os not

More information

Linear Algebra Existence of the determinant. Expansion according to a row.

Linear Algebra Existence of the determinant. Expansion according to a row. Lir Algbr 2270 1 Existc of th dtrmit. Expsio ccordig to row. W dfi th dtrmit for 1 1 mtrics s dt([]) = (1) It is sy chck tht it stisfis D1)-D3). For y othr w dfi th dtrmit s follows. Assumig th dtrmit

More information

CIVL 8/ D Boundary Value Problems - Rectangular Elements 1/7

CIVL 8/ D Boundary Value Problems - Rectangular Elements 1/7 CIVL / -D Boundr Vlu Prolms - Rctngulr Elmnts / RECANGULAR ELEMENS - In som pplictions, it m mor dsirl to us n lmntl rprsnttion of th domin tht hs four sids, ithr rctngulr or qudriltrl in shp. Considr

More information

Oppgavesett kap. 6 (1 av..)

Oppgavesett kap. 6 (1 av..) Oppgvstt kp. 6 (1 v..) hns.brnn@go.uio.no Problm 1 () Wht is homognous nucltion? Why dos Figur 6.2 in th book show tht w won't gt homognous nucltion in th tmosphr? ˆ Homognous nucltion crts cloud droplts

More information

REAL-TIME ESTIMATION OF O-D MATRICES WITH PARTIAL TRAJECTORIES FROM ETC TAG DATA

REAL-TIME ESTIMATION OF O-D MATRICES WITH PARTIAL TRAJECTORIES FROM ETC TAG DATA REAL-TIME ESTIMATION OF O-D MATRICES WITH PARTIAL TRAJECTORIES FROM ETC TAG DATA Jimyoung Kwon 1 Institut of Trnsporttion Stuis Univrsity of Cliforni, Brkly 6 Evns Hll, Brkly, CA 940-60 Tl: (510)64-1;

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY HAYSTACK OBSERVATORY WESTFORD, MASSACHUSETTS

MASSACHUSETTS INSTITUTE OF TECHNOLOGY HAYSTACK OBSERVATORY WESTFORD, MASSACHUSETTS VSRT MEMO #05 MASSACHUSETTS INSTITUTE OF TECHNOLOGY HAYSTACK OBSERVATORY WESTFORD, MASSACHUSETTS 01886 Fbrury 3, 009 Tlphon: 781-981-507 Fx: 781-981-0590 To: VSRT Group From: Aln E.E. Rogrs Subjct: Simplifid

More information

SOLVED EXAMPLES. be the foci of an ellipse with eccentricity e. For any point P on the ellipse, prove that. tan

SOLVED EXAMPLES. be the foci of an ellipse with eccentricity e. For any point P on the ellipse, prove that. tan LOCUS 58 SOLVED EXAMPLES Empl Lt F n F th foci of n llips with ccntricit. For n point P on th llips, prov tht tn PF F tn PF F Assum th llips to, n lt P th point (, sin ). P(, sin ) F F F = (-, 0) F = (,

More information

Case Study Vancomycin Answers Provided by Jeffrey Stark, Graduate Student

Case Study Vancomycin Answers Provided by Jeffrey Stark, Graduate Student Cas Stuy Vancomycin Answrs Provi by Jffry Stark, Grauat Stunt h antibiotic Vancomycin is liminat almost ntirly by glomrular filtration. For a patint with normal rnal function, th half-lif is about 6 hours.

More information

CONTINUITY AND DIFFERENTIABILITY

CONTINUITY AND DIFFERENTIABILITY MCD CONTINUITY AND DIFFERENTIABILITY NCERT Solvd mpls upto th sction 5 (Introduction) nd 5 (Continuity) : Empl : Chck th continuity of th function f givn by f() = + t = Empl : Emin whthr th function f

More information

A RELATIVISTIC LAGRANGIAN FOR MULTIPLE CHARGED POINT-MASSES

A RELATIVISTIC LAGRANGIAN FOR MULTIPLE CHARGED POINT-MASSES A RELATIVISTIC LAGRANGIAN FOR MULTIPLE CHARGED POINT-MASSES ADRIAAN DANIËL FOKKER (1887-197) A translation of: Ein invariantr Variationssatz für i Bwgung mhrrr lctrischr Massntilshn Z. Phys. 58, 386-393

More information

13. Binary tree, height 4, eight terminal vertices 14. Full binary tree, seven vertices v 7 v13. v 19

13. Binary tree, height 4, eight terminal vertices 14. Full binary tree, seven vertices v 7 v13. v 19 0. Spnning Trs n Shortst Pths 0. Consir th tr shown blow with root v 0.. Wht is th lvl of v 8? b. Wht is th lvl of v 0? c. Wht is th hight of this root tr?. Wht r th chilrn of v 0?. Wht is th prnt of v

More information

Present state Next state Q + M N

Present state Next state Q + M N Qustion 1. An M-N lip-lop works s ollows: I MN=00, th nxt stt o th lip lop is 0. I MN=01, th nxt stt o th lip-lop is th sm s th prsnt stt I MN=10, th nxt stt o th lip-lop is th omplmnt o th prsnt stt I

More information

Winter 2016 COMP-250: Introduction to Computer Science. Lecture 23, April 5, 2016

Winter 2016 COMP-250: Introduction to Computer Science. Lecture 23, April 5, 2016 Wintr 2016 COMP-250: Introduction to Computr Scinc Lctur 23, April 5, 2016 Commnt out input siz 2) Writ ny lgorithm tht runs in tim Θ(n 2 log 2 n) in wors cs. Explin why this is its running tim. I don

More information

Split-plot Experiments and Hierarchical Data

Split-plot Experiments and Hierarchical Data Split-plot Exprimnts nd Hirrchicl Dt Introduction Alx Stlzlni invstigtd th ffcts of fding rgim for bf nimls nd muscl typ on th tndrnss of mt. H ssignd ight nimls to ch of thr trtmnts. Th trtmnts wr th

More information

b. How many ternary words of length 23 with eight 0 s, nine 1 s and six 2 s?

b. How many ternary words of length 23 with eight 0 s, nine 1 s and six 2 s? MATH 3012 Finl Exm, My 4, 2006, WTT Stunt Nm n ID Numr 1. All our prts o this prolm r onrn with trnry strings o lngth n, i.., wors o lngth n with lttrs rom th lpht {0, 1, 2}.. How mny trnry wors o lngth

More information

Weighted Matching and Linear Programming

Weighted Matching and Linear Programming Wightd Mtching nd Linr Progrmming Jonthn Turnr Mrch 19, 01 W v sn tht mximum siz mtchings cn b found in gnrl grphs using ugmnting pths. In principl, this sm pproch cn b pplid to mximum wight mtchings.

More information

Minimum Spanning Trees

Minimum Spanning Trees Minimum Spnning Trs Minimum Spnning Trs Problm A town hs st of houss nd st of rods A rod conncts nd only houss A rod conncting houss u nd v hs rpir cost w(u, v) Gol: Rpir nough (nd no mor) rods such tht:

More information

MASTER CLASS PROGRAM UNIT 4 SPECIALIST MATHEMATICS SEMESTER TWO 2014 WEEK 11 WRITTEN EXAMINATION 1 SOLUTIONS

MASTER CLASS PROGRAM UNIT 4 SPECIALIST MATHEMATICS SEMESTER TWO 2014 WEEK 11 WRITTEN EXAMINATION 1 SOLUTIONS MASTER CLASS PROGRAM UNIT SPECIALIST MATHEMATICS SEMESTER TWO WEEK WRITTEN EXAMINATION SOLUTIONS FOR ERRORS AND UPDATES, PLEASE VISIT WWW.TSFX.COM.AU/MC-UPDATES QUESTION () Lt p ( z) z z z If z i z ( is

More information

Predictors of long term post-traumatic stress in mothers and fathers after a child s admission to PICU

Predictors of long term post-traumatic stress in mothers and fathers after a child s admission to PICU Prictors of log tr post-trutic strss i othrs fthrs ftr chil s issio to PICU Colvill G, Boyls C, Gry S, Ross O, Mht R PICU, Southpto Grl Hospitl Rlvt Litrtur Post Trutic Strss Disorr DSM IV critri Trutic

More information

( ) Geometric Operations and Morphing. Geometric Transformation. Forward v.s. Inverse Mapping. I (x,y ) Image Processing - Lesson 4 IDC-CG 1

( ) Geometric Operations and Morphing. Geometric Transformation. Forward v.s. Inverse Mapping. I (x,y ) Image Processing - Lesson 4 IDC-CG 1 Img Procssing - Lsson 4 Gomtric Oprtions nd Morphing Gomtric Trnsformtion Oprtions dpnd on Pil s Coordints. Contt fr. Indpndnt of pil vlus. f f (, ) (, ) ( f (, ), f ( ) ) I(, ) I', (,) (, ) I(,) I (,

More information

a b c cat CAT A B C Aa Bb Cc cat cat Lesson 1 (Part 1) Verbal lesson: Capital Letters Make The Same Sound Lesson 1 (Part 1) continued...

a b c cat CAT A B C Aa Bb Cc cat cat Lesson 1 (Part 1) Verbal lesson: Capital Letters Make The Same Sound Lesson 1 (Part 1) continued... Progrssiv Printing T.M. CPITLS g 4½+ Th sy, fun (n FR!) wy to tch cpitl lttrs. ook : C o - For Kinrgrtn or First Gr (not for pr-school). - Tchs tht cpitl lttrs mk th sm souns s th littl lttrs. - Tchs th

More information

CS61B Lecture #33. Administrivia: Autograder will run this evening. Today s Readings: Graph Structures: DSIJ, Chapter 12

CS61B Lecture #33. Administrivia: Autograder will run this evening. Today s Readings: Graph Structures: DSIJ, Chapter 12 Aministrivi: CS61B Ltur #33 Autogrr will run this vning. Toy s Rings: Grph Struturs: DSIJ, Chptr 12 Lst moifi: W Nov 8 00:39:28 2017 CS61B: Ltur #33 1 Why Grphs? For xprssing non-hirrhilly rlt itms Exmpls:

More information

PHYS ,Fall 05, Term Exam #1, Oct., 12, 2005

PHYS ,Fall 05, Term Exam #1, Oct., 12, 2005 PHYS1444-,Fall 5, Trm Exam #1, Oct., 1, 5 Nam: Kys 1. circular ring of charg of raius an a total charg Q lis in th x-y plan with its cntr at th origin. small positiv tst charg q is plac at th origin. What

More information

MATHEMATICS FOR MANAGEMENT BBMP1103

MATHEMATICS FOR MANAGEMENT BBMP1103 Objctivs: TOPIC : EXPONENTIAL AND LOGARITHM FUNCTIONS. Idntif pnntils nd lgrithmic functins. Idntif th grph f n pnntil nd lgrithmic functins. Clcult qutins using prprtis f pnntils. Clcult qutins using

More information

HIGHER ORDER DIFFERENTIAL EQUATIONS

HIGHER ORDER DIFFERENTIAL EQUATIONS Prof Enriqu Mtus Nivs PhD in Mthmtis Edution IGER ORDER DIFFERENTIAL EQUATIONS omognous linr qutions with onstnt offiints of ordr two highr Appl rdution mthod to dtrmin solution of th nonhomognous qution

More information

Examples and applications on SSSP and MST

Examples and applications on SSSP and MST Exampls an applications on SSSP an MST Dan (Doris) H & Junhao Gan ITEE Univrsity of Qunslan COMP3506/7505, Uni of Qunslan Exampls an applications on SSSP an MST Dijkstra s Algorithm Th algorithm solvs

More information

Mathematics. Mathematics 3. hsn.uk.net. Higher HSN23000

Mathematics. Mathematics 3. hsn.uk.net. Higher HSN23000 Highr Mthmtics UNIT Mthmtics HSN000 This documnt ws producd spcilly for th HSN.uk.nt wbsit, nd w rquir tht ny copis or drivtiv works ttribut th work to Highr Still Nots. For mor dtils bout th copyright

More information

GROWING ON CALCAREOUS SOILS

GROWING ON CALCAREOUS SOILS FLORIDA STATE HORTICULTURAL SOCIETY, 97 FIELD TESTS WITH NEW IRON CHELATES ON CITRUS GROWING ON CALCAREOUS SOILS C. D. Lonr Agriculturl Rsrch n Euction Cntr Lk Alfr n D. V. Clvrt Agriculturl Rsrch Cntr

More information

The Derivative of the Natural Logarithmic Function. Derivative of the Natural Exponential Function. Let u be a differentiable function of x.

The Derivative of the Natural Logarithmic Function. Derivative of the Natural Exponential Function. Let u be a differentiable function of x. Th Ntrl Logrithmic n Eponntil Fnctions: : Diffrntition n Intgrtion Objctiv: Fin rivtivs of fnctions involving th ntrl logrithmic fnction. Th Drivtiv of th Ntrl Logrithmic Fnction Lt b iffrntibl fnction

More information

SIGNIFICANCE OF SMITH CHART IN ANTENNA TECHNOLOGY

SIGNIFICANCE OF SMITH CHART IN ANTENNA TECHNOLOGY SIGNIFICANCE OF SMITH CHART IN ANTENNA TECHNOLOGY P. Poornima¹, Santosh Kumar Jha² 1 Associat Profssor, 2 Profssor, ECE Dpt., Sphoorthy Enginring Collg Tlangana, Hyraba (Inia) ABSTRACT This papr prsnts

More information

CSE303 - Introduction to the Theory of Computing Sample Solutions for Exercises on Finite Automata

CSE303 - Introduction to the Theory of Computing Sample Solutions for Exercises on Finite Automata CSE303 - Introduction to th Thory of Computing Smpl Solutions for Exrciss on Finit Automt Exrcis 2.1.1 A dtrministic finit utomton M ccpts th mpty string (i.., L(M)) if nd only if its initil stt is finl

More information

Paths. Connectivity. Euler and Hamilton Paths. Planar graphs.

Paths. Connectivity. Euler and Hamilton Paths. Planar graphs. Pths.. Eulr n Hmilton Pths.. Pth D. A pth rom s to t is squn o gs {x 0, x 1 }, {x 1, x 2 },... {x n 1, x n }, whr x 0 = s, n x n = t. D. Th lngth o pth is th numr o gs in it. {, } {, } {, } {, } {, } {,

More information

cycle that does not cross any edges (including its own), then it has at least

cycle 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 information

Similarity Search. The Binary Branch Distance. Nikolaus Augsten.

Similarity Search. The Binary Branch Distance. Nikolaus Augsten. Similrity Srh Th Binry Brnh Distn Nikolus Augstn nikolus.ugstn@sg..t Dpt. of Computr Sins Univrsity of Slzurg http://rsrh.uni-slzurg.t Vrsion Jnury 11, 2017 Wintrsmstr 2016/2017 Augstn (Univ. Slzurg) Similrity

More information

CSC Design and Analysis of Algorithms. Example: Change-Making Problem

CSC Design and Analysis of Algorithms. Example: Change-Making Problem CSC 801- Dsign n Anlysis of Algorithms Ltur 11 Gry Thniqu Exmpl: Chng-Mking Prolm Givn unlimit mounts of oins of nomintions 1 > > m, giv hng for mount n with th lst numr of oins Exmpl: 1 = 25, 2 =10, =

More information

However, many atoms can combine to form particular molecules, e.g. Chlorine (Cl) and Sodium (Na) atoms form NaCl molecules.

However, many atoms can combine to form particular molecules, e.g. Chlorine (Cl) and Sodium (Na) atoms form NaCl molecules. Lctur 6 Titl: Fundmntls of th Quntum Thory of molcul formtion Pg- In th lst modul, w hv discussd out th tomic structur nd tomic physics to undrstnd th spctrum of toms. Howvr, mny toms cn comin to form

More information

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory

Ch. 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 information

2. Finite Impulse Response Filters (FIR)

2. Finite Impulse Response Filters (FIR) .. Mthos for FIR filtrs implmntation. Finit Impuls Rspons Filtrs (FIR. Th winow mtho.. Frquncy charactristic uniform sampling. 3. Maximum rror minimizing. 4. Last-squars rror minimizing.. Mthos for FIR

More information

Exam 1 Solution. CS 542 Advanced Data Structures and Algorithms 2/14/2013

Exam 1 Solution. CS 542 Advanced Data Structures and Algorithms 2/14/2013 CS Avn Dt Struturs n Algorithms Exm Solution Jon Turnr //. ( points) Suppos you r givn grph G=(V,E) with g wights w() n minimum spnning tr T o G. Now, suppos nw g {u,v} is to G. Dsri (in wors) mtho or

More information

Multiple Short Term Infusion Homework # 5 PHA 5127

Multiple Short Term Infusion Homework # 5 PHA 5127 Multipl Short rm Infusion Homwork # 5 PHA 527 A rug is aministr as a short trm infusion. h avrag pharmacokintic paramtrs for this rug ar: k 0.40 hr - V 28 L his rug follows a on-compartmnt boy mol. A 300

More information

Genetic parameters for direct and maternal calving ability over parities in Piedmontese cattle 1

Genetic parameters for direct and maternal calving ability over parities in Piedmontese cattle 1 Gntic paramtrs for irct an matrnal calving ability ovr paritis in Pimonts cattl 1 P. Carnir*,, A. Albra, R. Dal Zotto*, A. F. Gron, M. Bona, an G. Bittant* *Dpartmnt of Animal Scinc, Univrsity of Paova,

More information

Why the Junction Tree Algorithm? The Junction Tree Algorithm. Clique Potential Representation. Overview. Chris Williams 1.

Why the Junction Tree Algorithm? The Junction Tree Algorithm. Clique Potential Representation. Overview. Chris Williams 1. Why th Juntion Tr lgorithm? Th Juntion Tr lgorithm hris Willims 1 Shool of Informtis, Univrsity of Einurgh Otor 2009 Th JT is gnrl-purpos lgorithm for omputing (onitionl) mrginls on grphs. It os this y

More information

12. Traffic engineering

12. Traffic engineering lt2.ppt S-38. Introution to Tltrffi Thory Spring 200 2 Topology Pths A tlommunition ntwork onsists of nos n links Lt N not th st of nos in with n Lt J not th st of nos in with j N = {,,,,} J = {,2,3,,2}

More information

Comparisons of economic values with and without risk for livestock trait improvement

Comparisons of economic values with and without risk for livestock trait improvement Livstock Production Scinc 79 (003) 183 191 www.lsvir.com/ loct/ livprodsci Comprisons of conomic vlus with nd without risk for livstock trit improvmnt, c K. Kulk, J. Wilton *, G. Fox, J. Dkkrs Dprtmnt

More information

Analysis of Algorithms - Elementary graphs algorithms -

Analysis of Algorithms - Elementary graphs algorithms - Analysis of Algorithms - Elmntary graphs algorithms - Anras Ermahl MRTC (Mälaralns Ral-Tim Rsarch Cntr) anras.rmahl@mh.s Autumn 004 Graphs Graphs ar important mathmatical ntitis in computr scinc an nginring

More information

Filter Design Techniques

Filter Design Techniques Fltr Dsgn chnqus Fltr Fltr s systm tht psss crtn frquncy componnts n totlly rcts ll othrs Stgs of th sgn fltr Spcfcton of th sr proprts of th systm ppromton of th spcfcton usng cusl scrt-tm systm Rlzton

More information

What do you know? Listen and find. Listen and circle. Listen and chant. Listen and say. Lesson 1. sheep. horse

What do you know? Listen and find. Listen and circle. Listen and chant. Listen and say. Lesson 1. sheep. horse Animls shp T h i nk Wht o you know? 2 2:29 Listn n fin. hors Wht s this? Wht s this? It s got ig nos. It s ig n gry. It s hors! YES! 2 Wht r ths? Wht r ths? Thy v got two lgs. Thy r smll n rown. Thy r

More information

CS September 2018

CS September 2018 Loil los Distriut Systms 06. Loil los Assin squn numrs to msss All ooprtin prosss n r on orr o vnts vs. physil los: rport tim o y Assum no ntrl tim sour Eh systm mintins its own lol lo No totl orrin o

More information

Garnir Polynomial and their Properties

Garnir Polynomial and their Properties Univrsity of Cliforni, Dvis Dprtmnt of Mthmtis Grnir Polynomil n thir Proprtis Author: Yu Wng Suprvisor: Prof. Gorsky Eugny My 8, 07 Grnir Polynomil n thir Proprtis Yu Wng mil: uywng@uvis.u. In this ppr,

More information

A Simple Code Generator. Code generation Algorithm. Register and Address Descriptors. Example 3/31/2008. Code Generation

A Simple Code Generator. Code generation Algorithm. Register and Address Descriptors. Example 3/31/2008. Code Generation A Simpl Co Gnrtor Co Gnrtion Chptr 8 II Gnrt o for singl si lok How to us rgistrs? In most mhin rhitturs, som or ll of th oprnsmust in rgistrs Rgistrs mk goo tmporris Hol vlus tht r omput in on si lok

More information

Algorithmic and NP-Completeness Aspects of a Total Lict Domination Number of a Graph

Algorithmic and NP-Completeness Aspects of a Total Lict Domination Number of a Graph Intrntionl J.Mth. Comin. Vol.1(2014), 80-86 Algorithmi n NP-Compltnss Aspts of Totl Lit Domintion Numr of Grph Girish.V.R. (PES Institut of Thnology(South Cmpus), Bnglor, Krntk Stt, Ini) P.Ush (Dprtmnt

More information

EE1000 Project 4 Digital Volt Meter

EE1000 Project 4 Digital Volt Meter Ovrviw EE1000 Projt 4 Diitl Volt Mtr In this projt, w mk vi tht n msur volts in th rn o 0 to 4 Volts with on iit o ury. Th input is n nlo volt n th output is sinl 7-smnt iit tht tlls us wht tht input s

More information

The Theory of Small Reflections

The Theory of Small Reflections Jim Stils Th Univ. of Knss Dt. of EECS 4//9 Th Thory of Smll Rflctions /9 Th Thory of Smll Rflctions Rcll tht w nlyzd qurtr-wv trnsformr usg th multil rflction viw ot. V ( z) = + β ( z + ) V ( z) = = R

More information

Using the Printable Sticker Function. Using the Edit Screen. Computer. Tablet. ScanNCutCanvas

Using the Printable Sticker Function. Using the Edit Screen. Computer. Tablet. ScanNCutCanvas SnNCutCnvs Using th Printl Stikr Funtion On-o--kin stikrs n sily rt y using your inkjt printr n th Dirt Cut untion o th SnNCut mhin. For inormtion on si oprtions o th SnNCutCnvs, rr to th Hlp. To viw th

More information

Lecture 12 Quantum chromodynamics (QCD) WS2010/11: Introduction to Nuclear and Particle Physics

Lecture 12 Quantum chromodynamics (QCD) WS2010/11: Introduction to Nuclear and Particle Physics Lctur Quntum chromodynmics (QCD) WS/: Introduction to Nuclr nd Prticl Physics QCD Quntum chromodynmics (QCD) is thory of th strong intrction - bsd on color forc, fundmntl forc dscribing th intrctions of

More information

Analysis of Algorithms - Elementary graphs algorithms -

Analysis of Algorithms - Elementary graphs algorithms - Analysis of Algorithms - Elmntary graphs algorithms - Anras Ermahl MRTC (Mälaralns Ral-Tim Rsach Cntr) anras.rmahl@mh.s Autumn 00 Graphs Graphs ar important mathmatical ntitis in computr scinc an nginring

More information

PH427/PH527: Periodic systems Spring Overview of the PH427 website (syllabus, assignments etc.) 2. Coupled oscillations.

PH427/PH527: Periodic systems Spring Overview of the PH427 website (syllabus, assignments etc.) 2. Coupled oscillations. Dy : Mondy 5 inuts. Ovrviw of th PH47 wsit (syllus, ssignnts tc.). Coupld oscilltions W gin with sss coupld y Hook's Lw springs nd find th possil longitudinl) otion of such syst. W ll xtnd this to finit

More information

10. EXTENDING TRACTABILITY

10. EXTENDING TRACTABILITY Coping with NP-compltnss 0. EXTENDING TRACTABILITY ining small vrtx covrs solving NP-har problms on trs circular arc covrings vrtx covr in bipartit graphs Q. Suppos I n to solv an NP-complt problm. What

More information

TURFGRASS DISEASE RESEARCH REPORT J. M. Vargas, Jr. and R. Detweiler Department of Botany and Plant Pathology Michigan State University

TURFGRASS DISEASE RESEARCH REPORT J. M. Vargas, Jr. and R. Detweiler Department of Botany and Plant Pathology Michigan State University I TURFGRASS DISEASE RESEARCH REPORT 9 J. M. Vrgs, Jr. n R. Dtwilr Dprtmnt f Btny n Plnt Pthlgy Mihign Stt Univrsity. Snw Ml Th 9 snw ml fungii vlutin trils wr nut t th Byn Highln Rsrt, Hrr Springs, Mihign

More information

The SuperFET: A High-Performance GaAs Voltage-Controlled Current Source for Cryogenic Applications

The SuperFET: A High-Performance GaAs Voltage-Controlled Current Source for Cryogenic Applications The SuperFT: High-Perormace Gas Voltage-Cotrolled Curret Source or Cryogeic pplicatios.v.cami, G.Pessia,.Previtali ad P. Ramaioli*. ipartimeto di Fisica dell'uiversita' ad Istituto Nazioale di Fisica Nucleare,

More information

Push trolley capacities from 1 2 through 10 Ton Geared trolley capacities from 1 2 through 100 Ton

Push trolley capacities from 1 2 through 10 Ton Geared trolley capacities from 1 2 through 100 Ton H o i s t n T r o l l y C o m i n t i o n s Push trolly cpcitis from 2 through 0 Ton Gr trolly cpcitis from 2 through 00 Ton CB n CF hn chin hoists cn suspn from ithr PT push trollys or GT gr trollys.

More information

DISTORTION OF PROBABILITY MODELS

DISTORTION OF PROBABILITY MODELS ISTORTION OF PROBABILITY MOELS VÁVRA Frntišk (ČR), NOVÝ Pvl (ČR), MAŠKOVÁ Hn (ČR), NETRVALOVÁ Arnoštk (ČR) Abstrct. Th proposd ppr dls with on o possibl mthods or modlling th rltion o two probbility modls

More information

CSE 373: More on graphs; DFS and BFS. Michael Lee Wednesday, Feb 14, 2018

CSE 373: More on graphs; DFS and BFS. Michael Lee Wednesday, Feb 14, 2018 CSE 373: Mor on grphs; DFS n BFS Mihl L Wnsy, F 14, 2018 1 Wrmup Wrmup: Disuss with your nighor: Rmin your nighor: wht is simpl grph? Suppos w hv simpl, irt grph with x nos. Wht is th mximum numr of gs

More information

Overview. Usages of Fault Simulators. Problem and Motivation. Alternatives and Their Limitations. VLSI Design Verification and Testing

Overview. Usages of Fault Simulators. Problem and Motivation. Alternatives and Their Limitations. VLSI Design Verification and Testing VLSI Dsin Vriiction n Tstin Fult Simultion Mohmm Thrnipoor Elctricl n Computr Eninrin Univrsity o Conncticut Ovrviw Prolm n motivtion Fult simultion lorithms Sril Prlll Ductiv Concurrnt Othr lorithms Rnom

More information

CSI35 Chapter 11 Review

CSI35 Chapter 11 Review 1. Which of th grphs r trs? c f c g f c x y f z p q r 1 1. Which of th grphs r trs? c f c g f c x y f z p q r . Answr th qustions out th following tr 1) Which vrtx is th root of c th tr? ) wht is th hight

More information

The Angular Momenta Dipole Moments and Gyromagnetic Ratios of the Electron and the Proton

The Angular Momenta Dipole Moments and Gyromagnetic Ratios of the Electron and the Proton Journl of Modrn hysics, 014, 5, 154-157 ublishd Onlin August 014 in SciRs. htt://www.scir.org/journl/jm htt://dx.doi.org/.436/jm.014.51415 Th Angulr Momnt Diol Momnts nd Gyromgntic Rtios of th Elctron

More information

First order differential equation Linear equation; Method of integrating factors

First order differential equation Linear equation; Method of integrating factors First orr iffrntial quation Linar quation; Mtho of intgrating factors Exampl 1: Rwrit th lft han si as th rivativ of th prouct of y an som function by prouct rul irctly. Solving th first orr iffrntial

More information

Kernels. ffl A kernel K is a function of two objects, for example, two sentence/tree pairs (x1; y1) and (x2; y2)

Kernels. ffl A kernel K is a function of two objects, for example, two sentence/tree pairs (x1; y1) and (x2; y2) Krnls krnl K is a function of two ojcts, for xampl, two sntnc/tr pairs (x1; y1) an (x2; y2) K((x1; y1); (x2; y2)) Intuition: K((x1; y1); (x2; y2)) is a masur of th similarity (x1; y1) twn (x2; y2) an ormally:

More information

Selection of Brahman crossbred-breeding bulls based on phenotypic performance

Selection of Brahman crossbred-breeding bulls based on phenotypic performance Sltion of Brhmn rossr-ring ulls s on phnotypi prformn MM Hqu 1, MA Hoqu* 1, NG Sh 1,2, AKFH Bhuiyn 1, MM Hossin 3, MA Hossin 4 1 Dprtmnt of Animl Bring n Gntis, Bnglsh Agriulturl Univrsity, Mymnsingh;

More information

Elliptical motion, gravity, etc

Elliptical motion, gravity, etc FW Physics 130 G:\130 lctur\ch 13 Elliticl motion.docx g 1 of 7 11/3/010; 6:40 PM; Lst rintd 11/3/010 6:40:00 PM Fig. 1 Elliticl motion, grvity, tc minor xis mjor xis F 1 =A F =B C - D, mjor nd minor xs

More information