Telomere replication, kinetochore organizers, and satellite DNA evolution (centromere/robertsonian rearrangement)

Size: px
Start display at page:

Download "Telomere replication, kinetochore organizers, and satellite DNA evolution (centromere/robertsonian rearrangement)"

Transcription

1 Proc. Nti. Acd. Sci. USA Vol. 76, No. 9, pp , Septemer 1979 Genetics Telomere repliction, kinetochore orgnizers, nd stellite DNA evolution (centromere/roertsonin rerrngement) GERALD P. HOLMQUIST* AND BARRY DANCISt *Kleerg Genetics Center, Deprtment of Medicine, Bylor College of Medicine, 1200 Moursund Avenue, Houston, Texs 77030; nd tdeprtment of Biology, Temple University, Phildelphi, Pennsylvni Communicted y Ernest R. Sers, June 11, 1979 ABSTRACT Roertsonin rerrngements demonstrte onerek chromosome rerrngement nd the reversile ppernce nd disppernce of telomeres nd centromeres. Such events re quite discordnt with clssicl cytogenetic theories, which ssume ll chromosome rerrngements to require t lest two reks nd consider centromeres nd telomeres s immutle structures rther thn structures determined y mutle DNA sequences. Cytogenetic dt from spontneous nd induced telomeretelomere fusions in mmmls sup ort moleculr model of terminl DNA synthesis in which ll ttelomeres re similr nd recomine efore repliction nd susequent seprtion. This, long with evidence for hypotheticl DNA sequence, the kinetochore orgnizer, redily explins ltent telomeres, ltent centromeres, nd reversile (onerek) Roertsonin rerrngements. A second model, involving simply recomintion etween like stellite DNA sequences on different chromosomes, explins not only how one stellite cn simultneously evolve on different chromosomes, ut lso why stellite DNA is usully locted ner centromeres or telomeres nd why it mintins preferred orienttion with respect to the centromere. Roertsonin rerrngement, telomeres, nd centromeres The most esily oserved fetures of chromosome re its ends (telomeres) nd its primry constriction (centromere). Broken chromosome ends, s cused y xrys or stretching on the spindle, show cpcity for fusion; they ehve s if sticky (1) in tht they fuse with themselves ut not with nturl ends (telomeres). McClintock (2) showed tht fter chromosomes with two roken ends fused, resulting dicentrics were unstle; the two centromeres would often seprte to opposite spindle poles nd rek the chromtid. Muller (1) then formulted two rules of chromosome structure nd mechnics. (i) All vile chromosome rerrngements require t lest two reks with susequent rejoining of the roken ends. (ii) Rerrnged chromosomes must hve exctly two telomeres (orgnelles locted t the ends) nd one centromere (n internl orgnelle) to e mechniclly stle. Roertsonin rerrngements etween rod chromosomes (Fig. 1 upper) to produce metcentric irmed chromosomes (Fig. 1 lower) re common mechnism of kryotype evolution nd occur spontneously t n pprecile frequency in mmmlin tissue culture (5) or even in the somtic tissue of certin fish (6). Reciprocl trnsloctions (Fig. l) re consistent with Muller's rules. The reverse exchnges, Roertsonin fission of metcentric into two rod chromosomes, hve een oserved, nd some (Fig. 1 nd c) pper s onerek rerrngements which do not require centric frgment to supply new centromere nd telomeres to the new chromosomes (5, The puliction costs of this rticle were defryed in prt y pge chrge pyment. This rticle must therefore e herey mrked "dvertisement" in ccordnce with 18 U. S. C. 173 solely to indicte this fct , 8). In ddition, Roertsonin metcentrics generlly possess twice the centric structure of rod chromosomes (710). In the grsshopper Neopodismopsis, Moens' (11) electron microgrphs showed this douled "kno"like structure to e penetrted y twice s mny microtuules s the single centric kno of rod chromosomes. Thus, metcentric's centric region often ppers douled nd cple of splitting y fission, ech hlf ecoming functionl centromere (8, 10). Roertsonin rerrngements, especilly the fissions, revel the indequcy of Muller's rules, especilly his concept of centromeres nd telomeres s immutle structures (1), nd imply some or ll of the following: (i) dicentrics cn e stle; (ii) fissions cn result from onerek rerrngements; (iii) centromeres nd telomeres cn reversily pper nd dispper; nd (iv) centromeres nd telomeres cn e terminl coincident structures. Dicentrics cn e stle, showing prllel chromtid seprtion when the two centromeres re close together. Hir (12) oserved n isodicentric through mny vegettive genertions in the plnt Agropyron. The originl dicentric ws unstle t mitosis; crisscross nd interlocking seprtion produced rekgefusion cycle tht resulted in shorter intercentric distnces. Dicentrics with short intercentric regions, however, were mitoticlly stle, oth centromeres on one chromtid seprting to the sme pole. Dicentrics cn lso e stle when one centromere is ltent (see review, ref. 13). In humns, most Roertsonin metcentrics re dicentric (1) in tht they show pericentric heterochromtin from oth prentl chromosomes; however, one of the centromeres is often inctive in tht it does not produce secondry constriction nd region of tight sisterchromtid piring (15). In one t(7:15)(p21;p1l), the C nding pericentric heterochromtin of chromosome 15 identified the second centric region, ut this centromere exhiited neither primry constriction nor tight sisterchromtid piring nd did not Cd nd (16). One interprettion of these dt is tht fourrek rerrngement occurred, producing trnsloction with simultneous deletion of centromere. In ccord with Hsu et l. (13), we lterntively interpret this s tworek rerrngement involving trnsloction nd inctivtion of centromere with concomitnt loss of the ltent centromere's Cd ndedness. Telomeres cn lso e ltent (reviewed in ref. 13), s clssiclly demonstrted during chromtin diminution in Prscris (17). Here, few polycentric germline chromosomes rek down into multitude of smll monocentric chromosomes with the de novo cretion of mny telomeres, presumly y ctivtion of preexisting ltent telomeres. Activtion of ltent telomere ppers s onerek rerrngement tht genertes two nonsticky ends, telomeres. If ltent telomere were locted within centric region (Fig. l), ctivtion would lso generte second centromere. Arevition: KO, kinetochore orgnizer.

2 Genetics: Acrocentrics 0 +.I 0 C~ qc Holmquist nd Dncis Telocentrics c01 olv),7* D c Acrocentrics o o Ln Qn CZ? FIG. 1. One trnsloction nd two fissionfusion models of Roertsonin rerrngement re shown with Cd nds (3) produced y ctive centromeres. () Reciprocl trnsloction etween crocentrics produces metcentric nd smll centric frgment which, if susequently lost, mkes this process irreversile. Centromere nd telomere numer is conserved. () Reversile fusion of two telocentrics (chromosomes with terminl centromeres) to produce metcentric. The fusionfission rerrngement requires only one chromosome rek. Two telomeres nd centromere reversily pper or dispper. (c) Reversile fusion of two crocentrics to produce metdicentric with pir of Cd nds (). Two telomeres reversily pper or dispper. The centromere nd kinetochore orgnizer The ctive loclized centromere of mitotic irmed chromosomes ppers, y light microscopy, s negtively heteropycnotic constriction (primry constriction) tht moves first to the spindle poles during nphse nd is necessry for disjunction of sister chromtids. This region stins y the Cdnding technique (3) nd morphologiclly is DNAcontining, iprtite, reverserepet structure of severl chromomeres flnked y regions of tight sisterchromtid piring (18). In formlinfixed electron microscopic sections of oth plnts nd nimls, the centromere ppers not so much s constriction, ut s region of lightly stining, thin chromtin fiers (19) in which ech sister chromtid possesses kinetochore plte (20) [pir of kinetochore filments (19)]. Spindle microtuules penetrte the plte (20) nd the plte itself is cple of ctlyzing tuulin polymeriztion (21, 22). The kinetochore plte is the site of spindle ttchment nd microtuule polymeriztion nd reflects centromeric ctivity. It proly lso induces the ncillry ttriutes of n ctive centromere, including primry constriction, pericentric regions of tight sisterchromtid piring, nd Cd nding. Brinkley nd Stulefield (19) proposed the kinetochore to e specilized gene, much like the nucleolus orgnizer defined y McClintock (23), ecuse it contins DNA (18), segregtes with the chromtids, nd is ctivted t specific (mitosis) stge of the cell cycle. We shll cll this gene kinetochore orgnizer (KO). Just s the nucleolus orgnizer cn e seprted from the structurl 18S nd 25S rrna genes whose product it orgnizes (2), the KO need not contin the genes coding for kinetochoreplte proteins, ut the KO must orgnize plte proteins into functionl structure when it is ctivted. We propose only one dditionl property of the KO to mke it consistent with cytologicl dt (ref. 13; Fig. 1): the KO cn e permnently inctivted y rerrngement. Thus, visile centromere reflects n ctive KO nd ltent centromere, n inctive KO. Vile chromosomes must hve t lest one ctive KO for proper disjunction of sister chromtids. Telomere repliction The chromtid contins one doulestrnded DNA helix (25), the termini of which re proly included in its two telomeres. DNA termini cnnot e replicted y conventionl mens ecuse digestion of the terminl RNA primer leves 5' gp (Fig. 2) tht no known polymerse cn fill (26). Solutions to this *. 1 I 7Th )D )0 Proc. Ntl. Acd. Sci. USA 76 (1979) 567 c Z lid Hollidy Structure DDiDt H >>II>II.' smll Plindrome lrge tndem repet replicted 2ZZZZ intermedite i FIG. 2. Types of fused metphse chromosomes rising s repliction intermedites from vrious models of telomere repliction. () Repliction with digestion of RNA primers nd ligtion of Okski frgments leves terminl 5' gps (26). If telomeres re complementry s in T7 phge (26), complementry gps could se pir, forming conctmeric telomere fusions, which, eing endless, re le to e replicted. Alterntively, ligtion nd stggered nicking (not shown) of the fused junction could convert it into pir of replicle 3' gps (27). () Btemn (28) ssumed the telomere to e covlently closed hirpin, mking it different from "sticky" roken end. Repliction genertes plindrome tht is nicked y restriction endonuclese, refolded, nd ligted. (c) A fusioneforerepliction model. All telomeres re identicl, covlently closed, nd contin lrge, repeted sequence, the sic unit of which is represented y the letters A nd T. Two telomeres recomine, forming Hollidy (29) structure, which, fter ligtion, hs no ends nd is therefore le to e replicted. Newly replicted DNA is represented y the drker lines. Fission of the replicted intermedite proceeds s in. Okski terminl dilemm for eukryotic telomeres hve een proposed (2628, 30), nd representtives re shown (Fig. 2 nd ). To explin cytogenetic dt, we proposed tht the telomeres must fuse pirwise efore repliction (31, 32). The most resonle moleculr model (Fig. 2c) required ll telomeres in cell to recomine vi common sequences efore repliction nd is consistent with Ruin's (33) cloning of 12kilose DNA sequence, four tndem repets of 3kilose sequence, which hyridized in situ to ll Drosophil melnogster telomeres nd to the ectopic strnds tht connect them, nd with Forte's nd Fngmn's (3) discovery tht yest (Scchromyces cerevisie) telomeres re covlently closed hirpins. Eukryotic chromosomes, in some specil instnces, pper fused end to end, nd in rre extreme cses the entire genome ppers s gint ring of fused chromosomes (3537). White (38) inferred tht telomere sesequence homology cused occsionl endtoend ssocitions of meiotic chromosomes. We extended this concept of homology y interpreting mitotic ssocitions s repliction intermedites (31, 32). Senescing Xi

3 568 Genetics: Holmquist nd Dncis humn primry cell lines(39) nd lymphocytes from ptients with ThiergeWeissench syndrome (0) ehve s if the restriction endonuclese of Fig. 2c does not cut efficiently in tht mny chromosomes re seen permnently fused end to end t the first mitoses fter fusion. The fused configurtions predicted y other repliction models (Fig. 2 nd ) were not seen. Insted, sister telomeres were fused to nother pir of sister telomeres (Fig. 2c), s is consistent with telomere fusions occurring efore repliction. Rndom telomere pirs were fused; ll telomeres were similr in their fusion potentil (39, 0) nd not composed of complementry pirs s in conctmeric fusion process (26) (Fig. 2). BrdUrd pulse leling indicted tht the chromtin t the fusion junction of ThiergeWeissench lymphocyte chromosomes replicted very erly in the S phse preceding mitotic fusion (0). This suggests tht in norml cells, telomeretelomere fusion is temporry event occurring in erly S phse nd would not e detected in synchronous cultures y either viscometric DNA moleculr weight nlyses (25) or y psorlin crosslinking (1) to revel the cloverlefshped Hollidy intermedite of Fig. 2c. Fig. 3type telomeretelomere fusion figures were induced in the first metphse fter tretment of mouse cells with mitomycin C, DNA crosslinking gent (2). Such figures would, however, e expected from the repliction model in Fig. 2c. If one crosslink prevented terminl rnch migrtion of the Hollidy structure, one pir of chromtids would seprte fter repliction while the other pir would remin fused (32). In conclusion, we view telomeres s structures tht contin DNA termini nd solve the specil prolem of terminl repliction. Cytogenetic dt support model requiring telomeretelomere fusion efore repliction, nd moleculr dt re most consistent with recomintion (Fig. 2c) mechnism of fusion. The model lso explins ltent telomeres nd some spects of Roertsonin fusion. Telomeres (stle nonsticky chromosome ends) re creted de novo during the differentition of som from germ line in Prscris. This is esily explined if differentition promotes the seprtion of ltent telomeres (fused telomere pirs) or, more specificlly, ctivtes restriction endonuclese tht cleves those plindromes (Fig. 2c) tht re ltent telomeres (27). Activtion of ltent telomere would pper cytogeneticlly s onerek rerrngement, generting two telomeres, nd would violte Muller's (1) rules. Roertsonin fusion would e specil cse of telomeretelomere fusion, involving the centric ends of two rod chromosomes. In the moleculr model (Fig. 2c), muttion in terminl hirpin sequence could prevent recognition y the restriction endonuclese of the repliction intermedite's plindrome (Fig. 2c), resulting in fusion. A susequent ck muttion would pper s Roertsonin fission of ltent telomere. The fusionfirst repliction mechnism necessittes symmetry. Specificlly, if one telomere contined n inverted Ruin sequence, it could fuse with other telomeres ut the intermedite could not seprte (32). Thus, telomeres with common Ruinsequence orienttion would e selected for, s portryed in Fig. Sc y the letters A pointing towrd the terminl hirpin. The letters A re lso pointing wy from n internlly locted centromere; thus we cn define for ll such telomeres common centric orienttion. Centric orienttion nd stellite DNA evolution Mouse stellite DNA sequences ll hve the sme centric orienttion (Fig. 8). Cytologists found this y using romodeoxyuridine's quenching of fluorescent dyes. They followed the Trich stellite strnds during few genertions of BrdUrd incorportion nd determined their reltive orienttions y Tetocentrics Al T V T V Al TV TV AI TV TV 11 I11I 11 3' 5' 3'5' opposite Sme Proc. Ntl. Acd. Sci. USA 76 (1979) Sme Metcentrics some orienttion rms Roertsonion 3' I >5 Rerrngement 5' 3 or 3 >>> I>> 5'S11FE TrnslocOtion Opposite orienttion rms: not oserved ir_ ieon o5' F<< ~ ~ 3 Prcentric inversion not oserved Opposite He 7 F (~ ~~~ +, FIG. 3. Ce tric orienttion of mouse stellite DNA round the KO (dot). () the reltive centric orienttion of stellite locks is determined y the segregtion of Trich stellite strnds in metcentrics. () A sepiringdependent trnsloction (XX) etween terminl locks of either opposite or similrly oriented stellite DNA would produce either n centric chromosome nd dicentric frgment or terminl exchnge. (c) The product(s) of intrchromosoml, sepiringdependent exchnges etween similrly oriented stellites. Centric orienttion (rrows) of the included sequences remins unchnged. Becuse of the sepiring requirement, the prcentric exchnge is deletion nd not n inversion s in. their segregtion in Roertsonin metcentrics (3) nd x ryinduced dicentrics (). Even in mouse Lcell mrker chromosomes, which were generted y multirek rerrngement nd contin mny interclry locks of stellite, ll stellites' centric orienttions were invrily mintined the sme (5). A prcentric inversion is one of severl rerrngements tht cn reverse (Fig. S) nd thus rndomize centric orienttion, ut evidence for this ws not foundt (5). Selection must ct to preserve common centric orienttion, nd ny tenle theory of stellite DNA evolution must explin this fct. Computer simultions y Smith (7) hve shown tht DNA whose sequence is not mintined y selection cn theoreticlly develop hierrchy of tndem periodicities (i.e., form stellite When, s in humns, two or more different locks of A.Trich stellite DNA re present on the sme chromosome rm, switches in Trich strnds (6) my represent the junction of two different stellite locks nd not switch in ny one stellite's centric orienttion.

4 Holmquist nd Dncis Genetics: Holmquist nd Dncis ~~Proc. Nti. Acd. Sci. USA 76 (1979) 569 sequences) s result of se piring etween sister chromtids followed y unequl sisterchromtid exchnge t the piring site. The ptterns of restrictionendonuclesesensitive sites oserved in mouse (8), D. melnogster (9), nd clf (50) stellite DNA definitely support Smith's prediction of hierrchil repet pttern of longrnge periodicities. Two consequences of this sepiringdependent mechnism re tht stellites evolve in locks, contiguous stretches of like sequences s shown for Drosophil (51, 52), nd tht the sequences within ny one lock hve the sme orienttion, s shown for mouse stellite (5). Bov'ini nd Cprini, of the superfmily Bovide, diverged over io0 yers go from common ncestor nd yet they still shre wekly crosshyridizing stellite DNA (55). For ny one species in the superfmily, the pttern of restrictionendonuclesesensitive sites of the stellite is simple hierrchicl one (50) even though the stellite DNA comes from mny different chromosomes. The simple pttern mens tht within species, the stellite on mny different chromosomes is very similr in its longrnge periodicities. A recent slttory event with susequent dispersion to the different chromosomes cnnot explin this ecuse the sme stellite ws presumly present on different chromosomes io0 yers go. The stellite must hve coevolved on different chromosomes, with stellite muttions eing communicted from chromosome to chromosome y some interchromosoml interction. Bsepiringdependent interchromosoml exchnge etween stellite locks of like sequence would explin oth coevolution nd centric orienttion of stellites. Such n exchnge etween terminl stellite locks on different chromosomes would produce n centric chromosome if the locks were of opposite centric orienttion (Fig. S) nd result in selection ginst opposite orienttions in one species. Terminl stellites, s in the mouse, could thus coevolve y exchnge nd mintin prticulr orienttion reltive to the KG ecuse the structure the KG orgnizes is essentil to the existence of ech chromtid. Similr exchnges occurring etween stellites of the sme orienttion on the sme chromosomes would determine preferred distriution of stellite locks. Prcentric exchnges would delete intervening genes (Fig. Sc) so tht homologous stellite locks on the sme chromosome rm would e selected ginst. Similrly, pericentric exchnges could lter linkge groups (Fig. Sc), nd interstitil homologous stellites on opposite rms would e disfvored. However, if the locks were pericentric or terminl s in most eukryotes, such exchnges would not lter linkge groups. This postulted exchnge mechnism presents dynmic view of stellite evolution with locks of similr sequence locted usully penicentric or terminl nd showing their dynmic stte through popultion polymorphisms of lock sizes or pericentric inversions, s consistent with present cytogenetic dt. The whole chromosome Muller (1) considered centromeres nd telomeres, s immutle structures; y ssociting structure with the loction of the structurl determinnt, he thought telomere nd centromere could not shre the sme loction, s in telocentric, thus oscuring the mechnism of reversile Roertsonin rerrngements (Fig. 1). We define ctive telomeres s structures (the kinetochore plte nd ncillry centric chromomeres) expressing KG DNA sequences. Thus, telocentric chromosome could hve terminl centromere (kinetochore plte overlpping the telomere) nd telomere tht functions for terminl repliction without hving the KG s terminl sequence (Fig. ). Similrly, if fusion of telocentrics rought two KOs close together so tht the pltes they orgnized overlpped (Fig. ), Monocentric Telocertric Mo.nocentric C Acrocentric fusion Dicentric FIG.. () A monocentric chromtid hs one kinetochore plte (thick line) which is orgnized y the physiclly smller KO sequence (dot) nd contins pericentric stellite (lrge letters) nd telomeric Ruin sequences (smll letters). Telomere fusion cn e trnsient, s in repliction (Fig. 2c), or permnent, s in Roertsonin fissionfusion ( nd c). Stellite nd Ruin sequences mintin constnt reltive orienttion; thus, telomeretelomere fusions produce the contrlterl symmetry of pericentric stellite oserved in mouse metcentrics (Fig. 3). In c, the kinetochore pltes do not cover the ends of the crocentrics nd show douled nture in the fused metdicentric. the fusion product would hve one centromere, one centromere nd two telomeres hving disppered during the fusion. This would lso explin why the centromere of Roertsonin metcentrics often shows douled nture (711). Fig. lso indictes tht ltent telomeres should e common in centric regions nd is consistent with the oservtion of Kto et l. (5) tht 2.9% of the cells in their CHG line showed evidence of t lest one fission event, spontneous reking of the centromere with concomitnt "heling" of the roken ends. The moleculr models we present, while proly inccurte in detil, do unite disprte dt nd, more importntly, remove the mysteriously immutle or discrete structurl properties scried to telomeres nd centromeres, presenting them insted s the expressions of DNA sequences tht cn mutte, rerrnge, nd e regulted. We thnk Dvid Comings, T. C. Hsu, Sm Ltt, Gerld Ruin, John Wilson, Sheldon Wolff, nd E. R. Sers for dvice nd Dottie Holmquist for the rt work. This work ws supported y Ntionl institutes of Helth Grnts GM to B.D., GM23905 to G.P.H., nd GM to Thoms Cskey. 1. Muller, H. J. (1938) Collection NetWoods Hole 13, McClintock, B. (1938) Genetics 23, Eierg, H. (197) Nture (London) 28,55.. Lu, Y.F. & Hsu, T. C. (1977) C~ytogenet. Cell Genet. 19, Kto, H., Sgi, T. & Yoshid, T. H. (1973) Chromosom 0, Ohno, 5. (1973) Cold Spring Hror Symp. Qunt. Biol. 38, John, B. & Freemn, M. (1975) Chromosom 52, Southern, D. I. (1969) Chromosom 26, Lewis, K. & John, B. (1975) Chromosome Hierrchy (Clrendon, Oxford). 10. Comings, D. E. & Okd, T. A. (1970) Cytogenetics 9, Moens, P. B. (1978) Chromosom 67, Hir, J. B. (1952) Heredity 6, Hsu, T. C., Pthk, S. & Chen, T. R. (1975) Cytogenet. Cell Genet. 15, Dniel, A. & LmPoTn, P. R. L. C. (1976) J. Med. Genet. 13, Neiuhr, E. (1972) Humn genetik 16, Nkgome, Y., Termur, F., Ktok, K. & Hosono, F. (1976) Clin. Genet. 9, White, M. J. D. (1973) Animl Cytology nd Evolution (The University Press, Cmridge), 3rd Ed. 18. LimdeFri, A. (1956) Heridits 2, Brinkley, B. R. & Stulefield, E. (1970) in Advnces in Cell Biology, eds. Prescott, D. M., Goldstein, L. & McConkey, E. (AppletonCenturyCrofts, New York), Vol. 1, pp

5 570 Genetics: Holmquist nd Dncis 20. Jokelinen, P. T. (1967) J. Ultrstruct. Res. 19, McGill, M. & Brinkley, B. R. (1975) J. Cell Aiol. 67, Telzer, B. R., Moses, M. J. & Rosenum, J. L. (1975) Proc. Ntl. Acd. Sci. USA 72, McClintock, B. (193) Z. Zellforsch. 21, Givens, J. & Phillips, R. (1976) Chromosom 57, Kvenoff, R., Klots, L. & Zimm, B. (1973) Cold Spring Hror Symp. Qunt. Biol. 38, Wtson, J. D. (1972) Nture (London) New Biol. 239, CvlierSmith, T. (197) Nture (London) 250, Btemn, A. J. (1975) Nture (London) 253, Hollidy, R. (196) Genet. Res. 5, Heumnn, J. (1976) Nucleic Acids Res. 3, Dncis, B. & Holmquist, G. (1977) Chromosomes Tody 6, Dncis, B. & Holmquist, G. (1979) J. Theor. Biol. 78, Ruin, G. M. (1977) Cold Spring Hror Symp. Qunt. Biol. 2, Forte, M. A. & Fngmn, W. L. (1978) J. Cell Biol. 79, DuPrw, E. J. (1970) DNA nd Chromosomes (Holt, Rinehrt & Winston, New York). 36. Bhr, G. F. (1977) in Moleculr Structure of Humn Chromosomes, ed. Yunis, J. (Acdemic, New York), pp Ashley, T. & Wgenr, E. B. (197) Cn. J. Genet. Cytol. 19, Proc. Ntl. Acd. Sci. USA 76 (1979) 38. White, M. J. D. (1961) Am. Nt. 95, Benn, P. A. (1976) Am. J. Hum. Genet. 28, Dutrillux, B., Auris, A., Couturier, J., Croquette, M. F. & ViegsPequignot, E. (1977) Chromosomes Tody 6, Cech, T. R. & Prdue, M. L. (1976) Proc. Ntl. Acd. Sci. USA 73, Hsu, T. C., Pthk, S., Bsen, B. M. & Strk, G. J. (1978) Cytogenet. Cell Genet. 21, Linn, M. S. & Dvidson, R. L. (1975) Science 185, Linn, M. S. & Dvidson, R. L. (1975) Nture (London) 25, Holmquist, G. & Comings, D. (1975) Chromosom 52, Angell, R. R. & Jcos, P. A. (1975) Chromosom 51, Smith, G. P. (1976) Science 191, Southern, E. M. (1975) J. Mol. Biol. 9, Crlson, M. & Brutlg, D. (1977) Cell 11, Mio, J. J., Brown, F. L. & Musich, P. (1977) J. Mol. Biol. 117, Holmquist, G. (1975) Nture (London) 257, Myfield, E. & Ellison, J. R. (197) J.,Cell Biol. 63, Kurnit, D. M., Brown, F. L. & Mio, J. J. (1978) Cytogenet. Cell Genet. 20,

EQUATIONS OF LINES AND PLANES

EQUATIONS OF LINES AND PLANES EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in point-direction nd twopoint

More information

FAULT TREES AND RELIABILITY BLOCK DIAGRAMS. Harry G. Kwatny. Department of Mechanical Engineering & Mechanics Drexel University

FAULT TREES AND RELIABILITY BLOCK DIAGRAMS. Harry G. Kwatny. Department of Mechanical Engineering & Mechanics Drexel University SYSTEM FAULT AND Hrry G. Kwtny Deprtment of Mechnicl Engineering & Mechnics Drexel University OUTLINE SYSTEM RBD Definition RBDs nd Fult Trees System Structure Structure Functions Pths nd Cutsets Reliility

More information

Helicopter Theme and Variations

Helicopter Theme and Variations Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the

More information

Answer, Key Homework 10 David McIntyre 1

Answer, Key Homework 10 David McIntyre 1 Answer, Key Homework 10 Dvid McIntyre 1 This print-out should hve 22 questions, check tht it is complete. Multiple-choice questions my continue on the next column or pge: find ll choices efore mking your

More information

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( ) Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +

More information

2 DIODE CLIPPING and CLAMPING CIRCUITS

2 DIODE CLIPPING and CLAMPING CIRCUITS 2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of

More information

Regular Sets and Expressions

Regular Sets and Expressions Regulr Sets nd Expressions Finite utomt re importnt in science, mthemtics, nd engineering. Engineers like them ecuse they re super models for circuits (And, since the dvent of VLSI systems sometimes finite

More information

Reasoning to Solve Equations and Inequalities

Reasoning to Solve Equations and Inequalities Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing

More information

Section 5-4 Trigonometric Functions

Section 5-4 Trigonometric Functions 5- Trigonometric Functions Section 5- Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form

More information

How To Set Up A Network For Your Business

How To Set Up A Network For Your Business Why Network is n Essentil Productivity Tool for Any Smll Business TechAdvisory.org SME Reports sponsored by Effective technology is essentil for smll businesses looking to increse their productivity. Computer

More information

Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered:

Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered: Appendi D: Completing the Squre nd the Qudrtic Formul Fctoring qudrtic epressions such s: + 6 + 8 ws one of the topics introduced in Appendi C. Fctoring qudrtic epressions is useful skill tht cn help you

More information

Gene Expression Programming: A New Adaptive Algorithm for Solving Problems

Gene Expression Programming: A New Adaptive Algorithm for Solving Problems Gene Expression Progrmming: A New Adptive Algorithm for Solving Prolems Cândid Ferreir Deprtmento de Ciêncis Agráris Universidde dos Açores 9701-851 Terr-Chã Angr do Heroísmo, Portugl Complex Systems,

More information

Small Businesses Decisions to Offer Health Insurance to Employees

Small Businesses Decisions to Offer Health Insurance to Employees Smll Businesses Decisions to Offer Helth Insurnce to Employees Ctherine McLughlin nd Adm Swinurn, June 2014 Employer-sponsored helth insurnce (ESI) is the dominnt source of coverge for nonelderly dults

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology

More information

Human Pedigrees. Independent Assortment. Mendel s Second Law. Independent Assortment Test Cross. 4 phenotypes. Pedigree analysis:

Human Pedigrees. Independent Assortment. Mendel s Second Law. Independent Assortment Test Cross. 4 phenotypes. Pedigree analysis: Biology 2250 rinciples of Genetics nnouncements B2250 edings nd roblems Lb 3 Informtion: B2250 (Innes) webpge downlod nd print before lb. Virtul fly: log in nd prctice http://biologylb.wlonline.com/ Ch.

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

A.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324

A.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324 A P P E N D I X A Vectors CONTENTS A.1 Scling vector................................................ 321 A.2 Unit or Direction vectors...................................... 321 A.3 Vector ddition.................................................

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology

More information

SPECIAL PRODUCTS AND FACTORIZATION

SPECIAL PRODUCTS AND FACTORIZATION MODULE - Specil Products nd Fctoriztion 4 SPECIAL PRODUCTS AND FACTORIZATION In n erlier lesson you hve lernt multipliction of lgebric epressions, prticulrly polynomils. In the study of lgebr, we come

More information

2. Transaction Cost Economics

2. Transaction Cost Economics 3 2. Trnsction Cost Economics Trnsctions Trnsctions Cn Cn Be Be Internl Internl or or Externl Externl n n Orgniztion Orgniztion Trnsctions Trnsctions occur occur whenever whenever good good or or service

More information

Or more simply put, when adding or subtracting quantities, their uncertainties add.

Or more simply put, when adding or subtracting quantities, their uncertainties add. Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re

More information

How To Network A Smll Business

How To Network A Smll Business Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

CS99S Laboratory 2 Preparation Copyright W. J. Dally 2001 October 1, 2001

CS99S Laboratory 2 Preparation Copyright W. J. Dally 2001 October 1, 2001 CS99S Lortory 2 Preprtion Copyright W. J. Dlly 2 Octoer, 2 Ojectives:. Understnd the principle of sttic CMOS gte circuits 2. Build simple logic gtes from MOS trnsistors 3. Evlute these gtes to oserve logic

More information

Bayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom

Bayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom Byesin Updting with Continuous Priors Clss 3, 8.05, Spring 04 Jeremy Orloff nd Jonthn Bloom Lerning Gols. Understnd prmeterized fmily of distriutions s representing continuous rnge of hypotheses for the

More information

Vectors and dyadics. Chapter 2. Summary. 2.1 Examples of scalars, vectors, and dyadics

Vectors and dyadics. Chapter 2. Summary. 2.1 Examples of scalars, vectors, and dyadics Chpter 2 Vectors nd dydics Summry Circ 1900 A.D., J. Willird Gis proposed the ide of vectors nd their higher-dimensionl counterprts dydics, tridics, ndpolydics. Vectors descrie three-dimensionl spce nd

More information

Econ 4721 Money and Banking Problem Set 2 Answer Key

Econ 4721 Money and Banking Problem Set 2 Answer Key Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in

More information

Vectors and dyadics. Chapter 2. Summary. 2.1 Examples of scalars, vectors, and dyadics

Vectors and dyadics. Chapter 2. Summary. 2.1 Examples of scalars, vectors, and dyadics Chpter 2 Vectors nd dydics Summry Circ 1900 A.D., J. Willird Gis proposed the ide of vectors nd their higher-dimensionl counterprts dydics, tridics, ndpolydics. Vectors descrie three-dimensionl spce nd

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100

Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100 hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by

More information

GFI MilArchiver 6 vs C2C Archive One Policy Mnger GFI Softwre www.gfi.com GFI MilArchiver 6 vs C2C Archive One Policy Mnger GFI MilArchiver 6 C2C Archive One Policy Mnger Who we re Generl fetures Supports

More information

Graphs on Logarithmic and Semilogarithmic Paper

Graphs on Logarithmic and Semilogarithmic Paper 0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl

More information

5 a LAN 6 a gateway 7 a modem

5 a LAN 6 a gateway 7 a modem STARTER With the help of this digrm, try to descrie the function of these components of typicl network system: 1 file server 2 ridge 3 router 4 ckone 5 LAN 6 gtewy 7 modem Another Novell LAN Router Internet

More information

Factoring Polynomials

Factoring Polynomials Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles

More information

baby on the way, quit today

baby on the way, quit today for mums-to-be bby on the wy, quit tody WHAT YOU NEED TO KNOW bout smoking nd pregnncy uitting smoking is the best thing you cn do for your bby We know tht it cn be difficult to quit smoking. But we lso

More information

AntiSpyware Enterprise Module 8.5

AntiSpyware Enterprise Module 8.5 AntiSpywre Enterprise Module 8.5 Product Guide Aout the AntiSpywre Enterprise Module The McAfee AntiSpywre Enterprise Module 8.5 is n dd-on to the VirusScn Enterprise 8.5i product tht extends its ility

More information

Homework 3 Solutions

Homework 3 Solutions CS 341: Foundtions of Computer Science II Prof. Mrvin Nkym Homework 3 Solutions 1. Give NFAs with the specified numer of sttes recognizing ech of the following lnguges. In ll cses, the lphet is Σ = {,1}.

More information

DlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report

DlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report DlNBVRGH + + THE CITY OF EDINBURGH COUNCIL Sickness Absence Monitoring Report Executive of the Council 8fh My 4 I.I...3 Purpose of report This report quntifies the mount of working time lost s result of

More information

Vector differentiation. Chapters 6, 7

Vector differentiation. Chapters 6, 7 Chpter 2 Vectors Courtesy NASA/JPL-Cltech Summry (see exmples in Hw 1, 2, 3) Circ 1900 A.D., J. Willird Gis invented useful comintion of mgnitude nd direction clled vectors nd their higher-dimensionl counterprts

More information

Math 135 Circles and Completing the Square Examples

Math 135 Circles and Completing the Square Examples Mth 135 Circles nd Completing the Squre Exmples A perfect squre is number such tht = b 2 for some rel number b. Some exmples of perfect squres re 4 = 2 2, 16 = 4 2, 169 = 13 2. We wish to hve method for

More information

Morgan Stanley Ad Hoc Reporting Guide

Morgan Stanley Ad Hoc Reporting Guide spphire user guide Ferury 2015 Morgn Stnley Ad Hoc Reporting Guide An Overview For Spphire Users 1 Introduction The Ad Hoc Reporting tool is ville for your reporting needs outside of the Spphire stndrd

More information

I calculate the unemployment rate as (In Labor Force Employed)/In Labor Force

I calculate the unemployment rate as (In Labor Force Employed)/In Labor Force Introduction to the Prctice of Sttistics Fifth Edition Moore, McCbe Section 4.5 Homework Answers to 98, 99, 100,102, 103,105, 107, 109,110, 111, 112, 113 Working. In the lnguge of government sttistics,

More information

An Undergraduate Curriculum Evaluation with the Analytic Hierarchy Process

An Undergraduate Curriculum Evaluation with the Analytic Hierarchy Process An Undergrdute Curriculum Evlution with the Anlytic Hierrchy Process Les Frir Jessic O. Mtson Jck E. Mtson Deprtment of Industril Engineering P.O. Box 870288 University of Albm Tuscloos, AL. 35487 Abstrct

More information

Quick Reference Guide: One-time Account Update

Quick Reference Guide: One-time Account Update Quick Reference Guide: One-time Account Updte How to complete The Quick Reference Guide shows wht existing SingPss users need to do when logging in to the enhnced SingPss service for the first time. 1)

More information

Treatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.

Treatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3. The nlysis of vrince (ANOVA) Although the t-test is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the t-test cn be used to compre the mens of only

More information

Lecture 3 Gaussian Probability Distribution

Lecture 3 Gaussian Probability Distribution Lecture 3 Gussin Probbility Distribution Introduction l Gussin probbility distribution is perhps the most used distribution in ll of science. u lso clled bell shped curve or norml distribution l Unlike

More information

Atypical regions in large genomic DNA sequences (DNA sequence analysis/markov chain/chromosome srcture)

Atypical regions in large genomic DNA sequences (DNA sequence analysis/markov chain/chromosome srcture) Proc. Nti. cd. Sci. US Vol. 91, pp. 7134-7138, July 1994 Genetics typicl regions in lrge genomic DN sequences (DN sequence nlysis/mrkov chin/chromosome srcture) STEWRT SCHERER*t*, MRY SR MCPEEK, ND TERENCE

More information

Network Configuration Independence Mechanism

Network Configuration Independence Mechanism 3GPP TSG SA WG3 Security S3#19 S3-010323 3-6 July, 2001 Newbury, UK Source: Title: Document for: AT&T Wireless Network Configurtion Independence Mechnism Approvl 1 Introduction During the lst S3 meeting

More information

Experiment 6: Friction

Experiment 6: Friction Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht

More information

All pay auctions with certain and uncertain prizes a comment

All pay auctions with certain and uncertain prizes a comment CENTER FOR RESEARC IN ECONOMICS AND MANAGEMENT CREAM Publiction No. 1-2015 All py uctions with certin nd uncertin prizes comment Christin Riis All py uctions with certin nd uncertin prizes comment Christin

More information

IaaS Configuration for Virtual Platforms

IaaS Configuration for Virtual Platforms IS Configurtion for Virtul Pltforms vcloud Automtion Center 6.0 This document supports the version of ech product listed nd supports ll susequent versions until the document is replced y new edition. To

More information

DAGmaps: Space Filling Visualization of Directed Acyclic Graphs

DAGmaps: Space Filling Visualization of Directed Acyclic Graphs Journl of Grph Algorithms nd Applictions http://jg.info/ vol. 13, no. 3, pp. 319 347 (2009) DAGmps: Spce Filling Visuliztion of Directed Acyclic Grphs Vssilis Tsirs 1,2 Sofi Trintfilou 1,2 Ionnis G. Tollis

More information

Section 5.2, Commands for Configuring ISDN Protocols. Section 5.3, Configuring ISDN Signaling. Section 5.4, Configuring ISDN LAPD and Call Control

Section 5.2, Commands for Configuring ISDN Protocols. Section 5.3, Configuring ISDN Signaling. Section 5.4, Configuring ISDN LAPD and Call Control Chpter 5 Configurtion of ISDN Protocols This chpter provides instructions for configuring the ISDN protocols in the SP201 for signling conversion. Use the sections tht reflect the softwre you re configuring.

More information

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 9 The Force Method of Anlysis: Bems (Continued) Version CE IIT, Khrgpur Instructionl Objectives

More information

VoIP for the Small Business

VoIP for the Small Business Reducing your telecommunictions costs VoIP (Voice over Internet Protocol) offers low cost lterntive to expensive trditionl phone services nd is rpidly becoming the communictions system of choice for smll

More information

VoIP for the Small Business

VoIP for the Small Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become vible solution for even the

More information

T H E S E C U R E T R A N S M I S S I O N P R O T O C O L O F S E N S O R A D H O C N E T W O R K

T H E S E C U R E T R A N S M I S S I O N P R O T O C O L O F S E N S O R A D H O C N E T W O R K Z E S Z Y T Y N A U K O W E A K A D E M I I M A R Y N A R K I W O J E N N E J S C I E N T I F I C J O U R N A L O F P O L I S H N A V A L A C A D E M Y 2015 (LVI) 4 (203) A n d r z e j M r c z k DOI: 10.5604/0860889X.1187607

More information

Health insurance marketplace What to expect in 2014

Health insurance marketplace What to expect in 2014 Helth insurnce mrketplce Wht to expect in 2014 33096VAEENBVA 06/13 The bsics of the mrketplce As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum

More information

Small Business Cloud Services

Small Business Cloud Services Smll Business Cloud Services Summry. We re thick in the midst of historic se-chnge in computing. Like the emergence of personl computers, grphicl user interfces, nd mobile devices, the cloud is lredy profoundly

More information

In addition, the following elements form an integral part of the Agency strike prevention plan:

In addition, the following elements form an integral part of the Agency strike prevention plan: UNITED STTES DEPRTMENT OF GRICULTURE Wshington, DC 20250 Federl Grin Inspection Service FGIS Directive 4711.2 6/16/80 STRIKE PREVENTION ND STRIKE CONTINGENCY PLNS I PURPOSE This Instruction: Estlishes

More information

Pentominoes. Pentominoes. Bruce Baguley Cascade Math Systems, LLC. The pentominoes are a simple-looking set of objects through which some powerful

Pentominoes. Pentominoes. Bruce Baguley Cascade Math Systems, LLC. The pentominoes are a simple-looking set of objects through which some powerful Pentominoes Bruce Bguley Cscde Mth Systems, LLC Astrct. Pentominoes nd their reltives the polyominoes, polycues, nd polyhypercues will e used to explore nd pply vrious importnt mthemticl concepts. In this

More information

METHODS & TECHNICAL Advances

METHODS & TECHNICAL Advances METHODS & TECHNICAL Advnces Ahmet Keles, DDS, DMSc 1 KELES KEYLESS EXPANDER: A NEW APPROACH FOR RAPID PALATAL EXPANSION Mxillry trnsverse constriction is mong the most common mlformtions in orthodontics.

More information

The Velocity Factor of an Insulated Two-Wire Transmission Line

The Velocity Factor of an Insulated Two-Wire Transmission Line The Velocity Fctor of n Insulted Two-Wire Trnsmission Line Problem Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Mrch 7, 008 Estimte the velocity fctor F = v/c nd the

More information

Health insurance exchanges What to expect in 2014

Health insurance exchanges What to expect in 2014 Helth insurnce exchnges Wht to expect in 2014 33096CAEENABC 02/13 The bsics of exchnges As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum mount

More information

MATH 150 HOMEWORK 4 SOLUTIONS

MATH 150 HOMEWORK 4 SOLUTIONS MATH 150 HOMEWORK 4 SOLUTIONS Section 1.8 Show tht the product of two of the numbers 65 1000 8 2001 + 3 177, 79 1212 9 2399 + 2 2001, nd 24 4493 5 8192 + 7 1777 is nonnegtive. Is your proof constructive

More information

VoIP for the Small Business

VoIP for the Small Business VoIP for the Smll Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become

More information

Drawing Diagrams From Labelled Graphs

Drawing Diagrams From Labelled Graphs Drwing Digrms From Lbelled Grphs Jérôme Thièvre 1 INA, 4, venue de l Europe, 94366 BRY SUR MARNE FRANCE Anne Verroust-Blondet 2 INRIA Rocquencourt, B.P. 105, 78153 LE CHESNAY Cedex FRANCE Mrie-Luce Viud

More information

Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.

Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions. Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd

More information

How To Reduce Telecommunictions Costs

How To Reduce Telecommunictions Costs Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become vible solution for even the

More information

Physics 43 Homework Set 9 Chapter 40 Key

Physics 43 Homework Set 9 Chapter 40 Key Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nm-wide region t x

More information

JaERM Software-as-a-Solution Package

JaERM Software-as-a-Solution Package JERM Softwre-s--Solution Pckge Enterprise Risk Mngement ( ERM ) Public listed compnies nd orgnistions providing finncil services re required by Monetry Authority of Singpore ( MAS ) nd/or Singpore Stock

More information

VoIP for the Small Business

VoIP for the Small Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become vible solution for even the

More information

Week 11 - Inductance

Week 11 - Inductance Week - Inductnce November 6, 202 Exercise.: Discussion Questions ) A trnsformer consists bsiclly of two coils in close proximity but not in electricl contct. A current in one coil mgneticlly induces n

More information

PHY 222 Lab 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS

PHY 222 Lab 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS PHY 222 Lb 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS Nme: Prtners: INTRODUCTION Before coming to lb, plese red this pcket nd do the prelb on pge 13 of this hndout. From previous experiments,

More information

1. In the Bohr model, compare the magnitudes of the electron s kinetic and potential energies in orbit. What does this imply?

1. In the Bohr model, compare the magnitudes of the electron s kinetic and potential energies in orbit. What does this imply? Assignment 3: Bohr s model nd lser fundmentls 1. In the Bohr model, compre the mgnitudes of the electron s kinetic nd potentil energies in orit. Wht does this imply? When n electron moves in n orit, the

More information

VoIP for the Small Business

VoIP for the Small Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become vible solution for even the

More information

P.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn

P.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn 33337_0P03.qp 2/27/06 24 9:3 AM Chpter P Pge 24 Prerequisites P.3 Polynomils nd Fctoring Wht you should lern Polynomils An lgeric epression is collection of vriles nd rel numers. The most common type of

More information

New Internet Radio Feature

New Internet Radio Feature XXXXX XXXXX XXXXX /XW-SMA3/XW-SMA4 New Internet Rdio Feture EN This wireless speker hs een designed to llow you to enjoy Pndor*/Internet Rdio. In order to ply Pndor/Internet Rdio, however, it my e necessry

More information

Unit 29: Inference for Two-Way Tables

Unit 29: Inference for Two-Way Tables Unit 29: Inference for Two-Wy Tbles Prerequisites Unit 13, Two-Wy Tbles is prerequisite for this unit. In ddition, students need some bckground in significnce tests, which ws introduced in Unit 25. Additionl

More information

9 CONTINUOUS DISTRIBUTIONS

9 CONTINUOUS DISTRIBUTIONS 9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete

More information

RTL Power Optimization with Gate-level Accuracy

RTL Power Optimization with Gate-level Accuracy RTL Power Optimiztion with Gte-level Accurcy Qi Wng Cdence Design Systems, Inc Sumit Roy Clypto Design Systems, Inc 555 River Oks Prkwy, Sn Jose 95125 2903 Bunker Hill Lne, Suite 208, SntClr 95054 qwng@cdence.com

More information

GFI MilArchiver 6 vs Quest Softwre Archive Mnger GFI Softwre www.gfi.com GFI MilArchiver 6 vs Quest Softwre Archive Mnger GFI MilArchiver 6 Quest Softwre Archive Mnger Who we re Generl fetures Supports

More information

Basic Ultrasound Views

Basic Ultrasound Views Bsic Ultrsound Views 2 Kenneth D. Horton K.D. Horton Echo/Vsculr Lortory, Intermountin Medicl Center, Murry, UT, USA e-mil: kd.horton@comcst.net T.P. Arhm (ed.), Cse Bsed Echocrdiogrphy, DOI: 10.1007/978-1-84996-151-6_2,

More information

An Integrate-and-fire Model of Prefrontal Cortex Neuronal Activity during Performance of Goal-directed Decision Making

An Integrate-and-fire Model of Prefrontal Cortex Neuronal Activity during Performance of Goal-directed Decision Making Cerebrl Cortex doi:10.1093/cercor/bhi072 An Integrte-nd-fire Model of Prefrontl Cortex Neuronl Activity during Performnce of Gol-directed Decision Mking NOT FOR PUBLIC RELEASE Rndl A. Koene nd Michel E.

More information

European Convention on Certain International Aspects of Bankruptcy

European Convention on Certain International Aspects of Bankruptcy Europen Trety Series - No. 136 Europen Convention on Certin Interntionl Aspects of Bnkruptcy Istnul, 5.VI.1990 Premle The memer Sttes of the Council of Europe, signtories hereto, Considering tht the im

More information

A Network Management System for Power-Line Communications and its Verification by Simulation

A Network Management System for Power-Line Communications and its Verification by Simulation A Network Mngement System for Power-Line Communictions nd its Verifiction y Simultion Mrkus Seeck, Gerd Bumiller GmH Unterschluerscher-Huptstr. 10, D-90613 Großhersdorf, Germny Phone: +49 9105 9960-51,

More information

THE PARAMETERS OF TRAPS IN K-FELDSPARS AND THE TL BLEACHING EFFICIENCY

THE PARAMETERS OF TRAPS IN K-FELDSPARS AND THE TL BLEACHING EFFICIENCY GEOCHRONOMETRIA Vol. 2, pp 15-2, 21 Journl on Methods nd Applictions of Asolute Chronology THE PARAMETERS OF TRAPS IN K-FELDSPARS AND THE TL BLEACHING EFFICIENCY ALICJA CHRUŒCIÑSKA 1, HUBERT L. OCZKOWSKI

More information

Dynamic TDMA Slot Assignment in Ad Hoc Networks

Dynamic TDMA Slot Assignment in Ad Hoc Networks Dynmic TDMA Slot Assignment in Ad Hoc Networks Akimitsu KANZAKI, Toshiki UEMUKAI, Tkhiro HARA, Shojiro NISHIO Dept. of Multimedi Eng., Grd. Sch. of Informtion Science nd Technology, Osk Univ. Dept. of

More information

How To Get A Free Phone Line From A Cell Phone To A Landline For A Business

How To Get A Free Phone Line From A Cell Phone To A Landline For A Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become vible solution for even the

More information

According to Webster s, the

According to Webster s, the dt modeling Universl Dt Models nd P tterns By Len Silversn According Webster s, term universl cn be defined s generlly pplicble s well s pplying whole. There re some very common ptterns tht cn be generlly

More information

VoIP for the Small Business

VoIP for the Small Business VoIP for the Smll Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become

More information

Transcription control reprogramming in genetic backup circuits

Transcription control reprogramming in genetic backup circuits Trnscription control reprogrmming in genetic ckup circuits Rn Kfri, Arren Br-Even & Yitzhk Pilpel A key question in moleculr genetics is why severe muttions often do not result in detectly norml phenotype.

More information

Vectors 2. 1. Recap of vectors

Vectors 2. 1. Recap of vectors Vectors 2. Recp of vectors Vectors re directed line segments - they cn be represented in component form or by direction nd mgnitude. We cn use trigonometry nd Pythgors theorem to switch between the forms

More information

VoIP for the Small Business

VoIP for the Small Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become vible solution for even the

More information

VoIP for the Small Business

VoIP for the Small Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become vible solution for even the

More information

Active & Retiree Plan: Trustees of the Milwaukee Roofers Health Fund Coverage Period: 06/01/2015-05/31/2016 Summary of Benefits and Coverage:

Active & Retiree Plan: Trustees of the Milwaukee Roofers Health Fund Coverage Period: 06/01/2015-05/31/2016 Summary of Benefits and Coverage: Summry of Benefits nd Coverge: Wht this Pln Covers & Wht it Costs Coverge for: Single & Fmily Pln Type: NPOS This is only summry. If you wnt more detil bout your coverge nd costs, you cn get the complete

More information

VoIP for the Small Business

VoIP for the Small Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become vible solution for even the

More information

VoIP for the Small Business

VoIP for the Small Business VoIP for the Smll Business Reducing your telecommunictions costs Reserch firm IDC 1 hs estimted tht VoIP system cn reduce telephony-relted expenses by 30%. Voice over Internet Protocol (VoIP) hs become

More information

How To Know What A Pressure Ulcer Is

How To Know What A Pressure Ulcer Is Pressure Ulcers ecourse: Module 2 Quiz I 1. Blck, brown or tn tissue tht dheres firmly to the wound bed or ulcer edges nd my be either firmer or softer thn surrounding tissue is:. Eschr b. Slough c. Grnultion

More information

Basic Analysis of Autarky and Free Trade Models

Basic Analysis of Autarky and Free Trade Models Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently

More information