Network Externalities, Competition, and Trade: East Asian Perspectives

Size: px
Start display at page:

Download "Network Externalities, Competition, and Trade: East Asian Perspectives"

Transcription

1 Ntwork Extrnalitis, Comptition, and Trad: East Asian Prspctivs Toru Kikuchi 1 and Chiharu Kobayashi Abstract Thr ar larg dviations in accss to tlcommunications infrastructur and trading pattrns within th East Asian rgion. W xamin how th ntwork xtrnalitis of communication activitis and trading opportunitis intract to dtrmin th structur of comparativ advantag. Ths intractions ar xamind by constructing a simpl two-country, two-good modl of trad involving a country-spcific communications ntwork sctor. Th rol of comptition of ntwork srvic providrs, which allows usrs of a ntwork asir accss to othr ntworks, is also xplord. (JEL Classification: D43, F12, L13) 1. Introduction As conomic intgration in East Asia progrsss, trad pattrns within th rgion ar displaying an vr-gratr complxity: Though intra-industry trad is growing in importanc, th shar of intr-industry trad still accounts for majority. In othr words, trad and production structurs vary widly within East Asian countris. 2 Rlatd to such phnomna, it is widly rcognizd that th growing connctivity of individuals and organizations achivd through nw typs of communications ntworks (.g., th Intrnt 1 W would lik to thank Michal Gilroy, Masami Imai, Fukunari Kimura, Tako Nakao, Elaina Ros, Kang Shi, Ryuhi Wakasugi and th participants of Kora and th World Economy IV confrnc for thir kind suggstions. This papr has also bnfitd from commnts by th ditor and two anonymous rfrs. Th first author is gratful for financial support providd to th 21st Cntury Cntr of Excllnc Projct by MEXT (Ministry of Education, Cultur, Sports, Scinc and Tchnology). Th scond author is gratful for financial support providd to Acadmic Frontir Projct, , by MEXT. 2 In this rspct, Fukao t al. (2003, pp ) conclud that, in East Asia, thr xist much highr barrirs against intra-rgional trad and FDI than in othr rgions (.g., EU), which ar likly to rduc intra-industry trad. Thy also suggst that thr is a high incom gap among East Asian countris, which is likly to rduc horizontal spcialization bcaus of th diffrncs in th industrial structur and prfrncs. 1

2 and satllit communications ntworks) and a consqunt incras in th information flow play an important rol as a dtrminant of trad structurs. 3 East Asian countris hav bcom incrasingly awar that both th quality and th scal of thir communications infrastructur hav bcom crucial factors dtrmining thir comparativ advantag. 4 Thr ar larg dviations in dvlopmnt lvls of tlcommunications infrastructur and computr tchnology within East Asian countris. Thr ar svral rasons for ths dviations, such as lack of infrastructur. Th cost of using tlcommunications and accssing th Intrnt is on of th most obvious barrirs. Rlatd to this, Hargittai s (1999) analysis of Intrnt connctivity concluds that th rgulatory nvironmnt and its influnc on comptition hav th largst impact on Intrnt pntration that is, th comptition btwn tlcom srvic providrs incrass Intrnt connctivity. Thus, w can say that comptition btwn srvic providrs is a ky fatur of communications ntworks. Th worldwid trnd toward drgulation and privatization in tlcommunications bgan in th 1980s and acclratd in th 1990s. Until lat in th 1990s, howvr, this trnd laggd in East Asian countris. In 2000, only half of th tlcommunications oprators in th Asia-Pacific rgion wr privatly ownd, compard with 63% in Europ and 74% in th Amricas. 5 Furthrmor, just undr 40% of local tlphon srvic providrs in th rgion xprincd any comptition. Howvr, in rcnt yars, East Asian countris hav undrgon dramatic rgulatory and policy changs, including introducing comptition into th sctor, stablishing a sparat rgulatory agncy and privatizing incumbnt carrirs (Tabl 1). Tabl 1: Lvl of Comptition in Slctd East Asian Economis For Slctd Tlcommunication Srvics, 2004 Economy Local Srvics Int l Sparat Rgulator Status of Main Fixd-Lin Oprator China Partial Partial No Stat-Ownd and Partially Privatizd Hong Kong Ys Ys Ys Privatizd Indonsia Partial Partial Ys Partially Privatizd Japan Ys Ys No Fully Privatizd Kora Ys Ys Ys Fully Privatizd 3 S Cairncross (1997), Sidornko and Findlay (2001). 4 According to this lin, Matoo t al. (2001) find that countris with th fully libralizd tlcommunications sctor can grow up to 1.5% pr yar fastr than thos with mor rstrictiv policis. S, also, Li and Xu (2002). 5 S, ITU (2000). According to this, Yusuf and Evntt (2002, ch. 5) conclud that East Asia still has much catching up to do. 2

3 Philippins Ys Ys Ys Fully Privatizd Singapor Ys Ys Ys Partially Privatizd Taiwan Ys Ys No Partially Privatizd Sourc: ITU (2004) Thr is anothr ky fatur of communications ntwork : th xistnc of strong ntwork xtrnalitis. Ntwork xtrnalitis occur if th valu of th good (or th srvic) to a usr dpnds on th numbr of usrs using th sam or similar good (srvic). 6 Although ntwork xtrnalitis ar oftn rgardd as consumption xtrnalitis, rcnt litratur on communications ntworks mphasizs th rol of ntwork xtrnalitis in th production sctors: du to an incrasd information flow, ach workr s productivity dpnds on th siz of th ntwork. 7 Givn that thr ar strong ntwork xtrnalitis in th production sctors, it is important to captur a crtain numbr of usrs to attain a favorabl siz of ntworks. In othr words, th siz of on country s ntwork plays an important rol as a dtrminant of trad structurs. Th world s broadband succss storis, such as on in Kora, shar such ky factors (.g., pro-comptitiv tlcommunications policis and rgulations, spcial incntivs for th provision of broadband to rural aras and thos population groups with lss attractiv conomic charactristics, and so on). Th sminal contribution to mphasizing th importanc of comptition btwn srvic providrs (and ntwork xtrnalitis) is Katz and Shapiro (1985). 8 Howvr, as thir modl is basd on a singl (or closd) markt for on consumption good, th rol of comptition btwn providrs as a dtrminant of comparativ advantag is downplayd in th analysis. Sinc th rol of comptition btwn domstic srvic providrs is mphasizd in th globalizd world, it sms important to xplor th rols of both (a) ntwork xtrnalitis in production and (b) comptition btwn srvic providrs in th trading-conomis stting. As its primary contribution, w xamin how th ntwork xtrnalitis of communication activitis, comptition btwn srvic providrs, and trading opportunitis intract to dtrmin th structur of comparativ advantag btwn countris, which also 6 Thr is an important concpt rlatd to ntwork xtrnalitis intrconnctivity which allows usrs of a ntwork to communicat with usrs of othr ntworks. Crmr t al. (2000) xplor th rol of intrconnctivity btwn Intrnt Srvic Providrs (ISPs) in th closd conomy stting. Kikuchi (2003, 2004) xplors th rol of intrconnctivity using a monopolistically comptitiv trad modl. 7 For xampl, David (2000) argus that th dvlopmnt of Intrnt tchnology has opnd th door to an ntirly nw class of organization-wid data-procssing applications and has standardizd th potntial for collctiv and cooprativ forms of work organization. Also, h has mphasizd th rol of ntwork xtrnalitis in th production sctors. 8 S Katz and Shapiro (1994), Economids (1996), Shy (2001) for survys of th rlvant litratur. Libowitz and Margolis (1994) distinguish btwn ntwork ffcts and ntwork xtrnalitis, qustioning th validity of th lattr concpt. 3

4 hlps to undrstand th rol of communications ntworks in East Asian trad pattrns. For ths purposs w construct a simpl two-country, two-good modl of trad with country-spcific communications ntworks. It will b shown that a comparativ advantag in th good that rquirs ntwork srvics is hld by th country with comptitiv srvic providrs (i.., a largr numbr of providrs). It is also mphasizd that, givn that thr ar strong ntwork xtrnalitis, diffrncs in comptitiv nvironmnt of srvic providrs work as a catalyst for intrnational spcialization. In othr words, thr is a circular procss btwn ntwork xpansion and trad cration. In th nxt sction w prsnt th basic modl. Th rol of comptition btwn ntwork srvic providrs as a dtrminant of trad pattrns is considrd in Sction 3, followd by concluding rmarks prsntd in Sction Th Modl Considr a world conomy consisting of two countris, Hom and Forign. 9 Thr ar two goods: a primary commodity which is producd only by labor and a high-tch product which is producd with both labor and communications srvics. Communications srvics ar assumd to b providd by country-spcific ntwork srvic providrs. Thr ar n (n*) idntical providrs in Hom (Forign): 10 thy ar playing a Cournot comptition. Providrs will b indxd by labl i (i = 1,..., n). Lt x i dnot th siz of th i-th providr (i.., th numbr of subscribrs), y i th siz of th ntwork with which th i-th providr is associatd, and lt z b th total numbr of ntwork usrs. For xampl, whn n providrs ar fully intrconnctd, z = y i = x x n holds. Lt th high-tch product b th numrair and p indicat th rlativ pric of th primary good. Th primary good is producd undr constant rturns tchnology; units ar chosn such that its unit input cofficint is unity. Each country is populatd by a continuum of workrs with population L. Each workr is ndowd with on unit of labor and som lvl of human capital for th production of th high-tch product, which is masurd by indx r. r is uniformly distributd ovr th intrval [0, L]. Each workr s productivity is also affctd by th lvl of ntwork xtrnalitis, vy i, whr v (v 1) is a valuation paramtr and i y is th workr s xpctation of th siz of th (i-th) ntwork. Th v trm capturs gains through incrasd information flow btwn individuals: if mor workrs join th communications 9 Th structur of this modl is basd on Kikuchi (2005) which mphasizs th rol of intrconnctivity as a dtrminant of trad pattrns. Howvr, in this papr, w mphasiz th rol of comptitiv nvironmnt of srvic providrs as a dtrminant of trad pattrns. 10 To kp mattrs simpl, w assum that th numbr of providrs is xognously dtrmind. Govrnmnt rgulation could b a major factor. Diffrncs in th lvl of ntry fixd cost could also b an important factor. Ths kinds of xtnsion nd furthr considration. 4

5 ntwork, ach workr can collct information mor fficintly. It is simply assumd that a typ-r workr can produc r + vy i units of th high-tch product. Workrs hav th choic of ithr supplying labor for th production of th primary good or bcoming a supplir of th high-tch product, and workrs will bcom th lattr only if thy connct to a communications ntwork. To connct to th i-th providr s ntwork, ach workr must pay a connction f, f i, in xchang for unlimitd accss up to th maximum throughput of thir particular connction. A typ-r workr chooss to connct to th ntwork for which r + vy ( f p) (1) i i + is largst. This can b intrprtd as follows. If r + vyi fi p holds for a particular workr, that workr pays th connction f and starts to produc th high-tch product. Howvr, if r + vyi fi < p holds, that workr chooss not to connct to th ntwork and producs th primary good instad. As p riss, mor workrs choos not to connct to th ntwork. Thus, on can intrprt (f i + p) as a connction f including th outsid option. In quilibrium, providrs i and j will both hav a positiv numbr of subscribrs only if ( f + p) vy = ( f + p) vy, (2) i i j j whr ( fi + p) vy i is th connction cost adjustd for ntwork siz. 11 Lt Φ dnot th common valu of this cost. For a givn valu of Φ, only thos workrs for whom r > Φ bcom producrs of th ntwork good. Givn th uniform distribution of r, thr ar L Φ workrs who choos to connct to th ntworks. Thus, if th total numbr of ntwork usrs is z, z = L Φ holds. Thn, by substituting Φ = ( fi + p) vy i into this, w obtain th condition for th connction f f i = L p + vy z. (3) i To simplify th analysis, w assum that th production cost for ach providr is qual to zro. Thus th i-th providr s profits ar π i = x i f i = x i (L p + vy z). (4) i Now considr th quilibrium supply lvl of th high-tch product. By Equations (1) and (3), a typ-r workr can produc r + z + f + p L units of product. Furthrmor, 11 (2) implis that all th xisting ntworks in quilibrium provid ncssarily th sam surplus, which is dfind as (1). 5

6 only thos workrs for whom r is gratr than L z join th ntwork, whil th othrs choos to produc th primary good. Intgrating all workrs who do connct to th ntworks, w can obtain th total output of th high-tch product: L 2 S( z) = ( ρ + z + f + p L) dρ = ( z / 2) + ( f + p) z. (5) L z W can intrprt this as th supply function of th high-tch product. This function is rprsntd by OS in Figur 1(b). As th total numbr of ntwork usrs bcoms largr, th avrag productivity of ach high-tch product supplir riss (this is shown as lins OA and OA in Figur 1(b)). Th conomy thus has a supply function that xhibits incrasing rturns to th siz of th ntworks. Mor notworthy is that, in trms of incom inquality btwn sctors, as th siz of th ntworks bcoms largr, incom inquality btwn sctors incrass. 6

7 7

8 Dpnding on th intrconnctivity btwn providrs, svral cass can mrg as th production quilibrium. For simplicity, lt us assum that n providrs ar fully intrconnctd (i.., y i = x x n =z). 12 A usr who conncts to on ntwork can communicat with usrs of othr ntworks. Intrconnctivity xpands th siz of ach ntwork to th total mmbrship of all providrs. This raiss th productivity gains njoyd by a workr who subscribs to only on providr s ntwork bcaus ntwork xtrnalitis dpnd on th total siz of th ntwork. Thus, maximizing (4) with rspct to x i, w obtain xi = L p + vz z. Imposing th rquirmnt that in quilibrium workrs xpctations ar fulfilld (Fulfilld Expctation Equilibrium), z = z = nx holds. Thn w obtain th quilibrium sals lvl for ach providr x = (L p)/(n + 1 nv). (6) By summing Equation (6) ovr all providrs, w obtain th total ntwork as a function of th rlativ pric of th high-tch product (1/p). z(1/p) = [n(l p)]/(n + 1 nv). (7) Th quilibrium is dpictd in Figur 1(a). Th horizontal axis shows th total siz of th ntwork, z, whil th vrtical axis shows th valus of L p+vz and [(n + 1)z]/n. Equilibrium is obtaind at an intrsction of two curvs: Lin ON rprsnts [(n+1)z]/n whil th othr lin rprsnts L p+vz. As p bcoms smallr, th lin will shift upward, which rsults in a largr total siz of th ntwork. Now turn to th impact of an incrasd comptition btwn providrs. An incras in th numbr of srvic providrs can b shown as a clockwis shift of lin ON (.g., ON ), which also rsults in a largr siz of th ntwork. As th total numbr of ntwork usrs bcoms largr, th avrag productivity of ach workr in th high-tch product sctor riss. Thr ar two sourcs of ths gains: (1) as th markt of ntwork srvics bcoms mor comptitiv, ach providr chooss to st a lowr connction f, which attracts mor workrs and (2) as mor workrs join th ntworks and th total numbr of subscribrs incrass, ach infra-marginal workr can attain highr productivity. 3. Comptition btwn Providrs and th Impact of Trad Intgration 12 As spac is limitd, w concntrat on th natur of th quilibrium and pay scant attntion to th factors that dtrmin intrconnctivity. 8

9 Suppos that th only diffrnc btwn two countris is th numbr of ntwork srvic providrs. Without loss of gnrality, Hom is assumd to hav mor providrs than Forign (i.., n > n*). Not that an incras in th numbr of providrs shifts th supply curv of th high-tch product to th right (Figur 2). Also, lt ach country hav th sam dmand function for th high-tch product, D(1/p), which is shown as a downward sloping curv in Figur In this cas, from Figur 2, Hom has th lowr autarky pric of th high-tch product (i.., (1/p) < (1/p*)). Now suppos that two countris (Hom and Forign) opn thir goods markts and 13 Not that w assum away any incom ffct. 9

10 hav a trad rlationship. Th opning of trad provids an opportunity for ntry into Hom s high-tch product sctor bcaus, with xpandd ntwork siz, th avrag productivity of Hom workrs is much highr than that of Forign workrs. On th othr hand, marginal workrs in Forign s high-tch product sctor stop producing th high-tch product du to th rducd rlativ pric. Thus th siz of Hom ntworks with comptitiv providrs will xpand, whil Forign ons with lss comptitiv providrs contract. Th diffrncs in th ntwork sizs will b rinforcd by this ntry-xit procss. That is, thr will b a cumulativ procss in which trading opportunitis bring an opportunity for largr ntworks, and th incrasd sizs of th ntworks promot (through intnsifid ntwork xtrnalitis) xports. This procss will continu until th pric diffrntial btwn countris disappars ((1/p T ) in Figur 2). Suprscript T indicats th trading quilibrium valu. Proposition 1: A comparativ advantag in th high-tch product is hld by a country with comptitiv srvic providrs. If th two countris commnc fr trad from autarky, th country with mor comptitiv providrs incompltly spcializs in th high-tch product and th country with lss comptitiv providrs incompltly spcializs in th primary good. [Proof] In th trading quilibrium, th following conditions must b hld: S(z(1/p T )) > S*(z*(1/p T )) and D (1/p T ) =D* (1/p T ). This implis that, du to intnsifid ntwork xtrnalitis, Hom bcoms an xportr of th high-tch product: S(z(1/p T )) - D (1/p T ) > 0. (Q. E. D.) Proposition 1 implis, givn that thr ar strong ntwork xtrnalitis, diffrncs in th numbr of srvic providrs (i.., th lvl of comptition) rsult in a larg variation in spcialization pattrns. This may hlp to xplain larg dviation in both th dvlopmnt of communications infrastructur and trading pattrns within th East Asian rgion. This proposition also mphasizs th importanc of comptition policy for th domstic communications sctor to surviv in th globalizd world conomy. Sinc th siz diffrntial btwn country-spcific ntworks is magnifid through intrnational trad, w also obtain th following proposition. Proposition 2: Opning intrnational trad incrass inquality in th country that xports th high-tch product and rducs inquality in th country that xports th primary good. [Proof] Sinc (1/p) < (1/p T ) < (1/p*) holds, th siz of th country-spcific ntwork changs as follows: z(1/p T ) > z(1/p) and z*(1/p T ) < z*(1/p*). This implis that Hom s incom inquality bcoms gratr whil Forign s bcoms smallr. (Q.E.D.) 10

11 4. Concluding Rmarks In this study, w xamin how th ntwork xtrnalitis of communication activitis, comptition btwn srvic providrs, and trading opportunitis intract to dtrmin th structur of comparativ advantag btwn countris, which also hlps to undrstand th rol of communications ntworks in East Asian trad pattrns. It should b mphasizd that diffrncs in comptitiv conditions among country-spcific ntwork srvic providrs dtrmin th comparativ advantags of countris: although ach country is ndowd with qual amount of labor, th country with comptitiv providrs can attain highr productivity through incrasd information flow. Mor notworthy is that thr is a circular procss btwn ntwork xpansion and trad cration which furthr affcts incom inqualitis within ach country. Although ths rsults ar drivd undr th assumption that communications ntworks ar purly country-spcific, it appars that somthing similar to this will occur in mor gnral sttings. Th prsnt analysis must b rgardd as vry tntativ. Hopfully it provids a usful paradigm for considring how communications infrastructur works as a driving forc for th dvlopmnt of th East Asian rgion. Rfrncs [1] Cairncross, F. Th Dath of Distanc, Boston, Mass.: Harvard Businss School Prss, [2] Crmr, J., P. Ry, and J. Tirol. Connctivity in th Commrcial Intrnt, Journal of Industrial Economics, 48, 2000, pp [3] David, P. A. Undrstanding Digital Tchnology s Evolution and th Path of Masurd Productivity Growth, in Undrstanding th Digital Economy, ditd by E. Brynjolfsson and B. Kahin. Cambridg, Mass.: MIT Prss, 2000, pp [4] Economids, N. Th Economics of Ntworks, Intrnational Journal of Industrial Organization, 14, 1996, pp [5] Fukao, K., H. Ishido, and K. Ito. Vrtical Intra-Industry Trad and Forign Dirct Invstmnt in East Asia, Journal of th Japans and Intrnational Economis, 17, 2003, pp [6] Hargittai, E. Waving th Wstrn Wb: Explaining Diffrncs in Intrnt Connctivity among OECD Countris, Tlcommunications Policy, 23, 1999, pp

12 [7] ITU (Intrnational Tlcommunications Union). Asia-Pacific Tlcommunications Indicators 2000, Gnva, [8] ITU (Intrnational Tlcommunications Union). Asia-Pacific Tlcommunications Indicators 2004, Gnva, [9] Katz, M. L., and C. Shapiro. Ntwork Extrnalitis, Comptition, and Compatibility, Amrican Economic Rviw, 75, 1985, pp [10] Katz, M. L., and C. Shapiro. Systms Comptition and Ntwork Effcts, Journal of Economic Prspctivs, 8(2), 1994, pp [11] Kikuchi, T. Intrconnctivity of Communications Ntworks and Intrnational Trad, Canadian Journal of Economics, 36, 2003, pp [12] Kikuchi, T. Communications Ntworks and Rgional Economic Dvlopmnt, Th Journal of th Koran Economy, 5 (1), 2004, pp [13] Kikuchi, T. Ntwork Extrnalitis as a Sourc of Comparativ Advantag, Economics Bulltin, 6 (7), 2005, pp [14] Li, W., and L. C. Xu. Th Political Economy of Privatization and Comptition: Cross-Country Evidnc from th Tlcommunications Sctor, Journal of Comparativ Economics, 30, 2002, pp [15] Libowitz, S. J., and S.-E. Margolis. Ntwork Extrnality: An Uncommon Tragdy, Journal of Economic Prspctivs, 8 (2), 1994, pp [16] Matoo, A., R. Rathindran, and A. Subramanian. Masuring Srvics Trad Libralization and Its Impact on Economic Growth: An Illustration, Working Papr 2655, World Bank, Washington D. C., [17] Sidornko, A., and C. Findlay. Th Digital Divid in East Asia, Asian- Pacific Economic Litratur, 15 (2), 2001, pp [18] Shy, O. Th Economics of Ntwork Industris, Cambridg Univrsity Prss, [19] Yusuf, S., and S. J. Evntt. Can East Asia Compt? Innovation for Global Markts, World Bank, Washington D. C.,

dr Bartłomiej Rokicki Chair of Macroeconomics and International Trade Theory Faculty of Economic Sciences, University of Warsaw

dr Bartłomiej Rokicki Chair of Macroeconomics and International Trade Theory Faculty of Economic Sciences, University of Warsaw dr Bartłomij Rokicki Chair of Macroconomics and Intrnational Trad Thory Faculty of Economic Scincs, Univrsity of Warsaw dr Bartłomij Rokicki Opn Economy Macroconomics Small opn conomy. Main assumptions

More information

The Open Economy in the Short Run

The Open Economy in the Short Run Economics 442 Mnzi D. Chinn Spring 208 Social Scincs 748 Univrsity of Wisconsin-Madison Th Opn Economy in th Short Run This st of nots outlins th IS-LM modl of th opn conomy. First, it covrs an accounting

More information

Chapter 13 Aggregate Supply

Chapter 13 Aggregate Supply Chaptr 13 Aggrgat Supply 0 1 Larning Objctivs thr modls of aggrgat supply in which output dpnds positivly on th pric lvl in th short run th short-run tradoff btwn inflation and unmploymnt known as th Phillips

More information

Diploma Macro Paper 2

Diploma Macro Paper 2 Diploma Macro Papr 2 Montary Macroconomics Lctur 6 Aggrgat supply and putting AD and AS togthr Mark Hays 1 Exognous: M, G, T, i*, π Goods markt KX and IS (Y, C, I) Mony markt (LM) (i, Y) Labour markt (P,

More information

4. Money cannot be neutral in the short-run the neutrality of money is exclusively a medium run phenomenon.

4. Money cannot be neutral in the short-run the neutrality of money is exclusively a medium run phenomenon. PART I TRUE/FALSE/UNCERTAIN (5 points ach) 1. Lik xpansionary montary policy, xpansionary fiscal policy rturns output in th mdium run to its natural lvl, and incrass prics. Thrfor, fiscal policy is also

More information

Two Products Manufacturer s Production Decisions with Carbon Constraint

Two Products Manufacturer s Production Decisions with Carbon Constraint Managmnt Scinc and Enginring Vol 7 No 3 pp 3-34 DOI:3968/jms9335X374 ISSN 93-34 [Print] ISSN 93-35X [Onlin] wwwcscanadant wwwcscanadaorg Two Products Manufacturr s Production Dcisions with Carbon Constraint

More information

A Prey-Predator Model with an Alternative Food for the Predator, Harvesting of Both the Species and with A Gestation Period for Interaction

A Prey-Predator Model with an Alternative Food for the Predator, Harvesting of Both the Species and with A Gestation Period for Interaction Int. J. Opn Problms Compt. Math., Vol., o., Jun 008 A Pry-Prdator Modl with an Altrnativ Food for th Prdator, Harvsting of Both th Spcis and with A Gstation Priod for Intraction K. L. arayan and. CH. P.

More information

Chapter 14 Aggregate Supply and the Short-run Tradeoff Between Inflation and Unemployment

Chapter 14 Aggregate Supply and the Short-run Tradeoff Between Inflation and Unemployment Chaptr 14 Aggrgat Supply and th Short-run Tradoff Btwn Inflation and Unmploymnt Modifid by Yun Wang Eco 3203 Intrmdiat Macroconomics Florida Intrnational Univrsity Summr 2017 2016 Worth Publishrs, all

More information

What are those βs anyway? Understanding Design Matrix & Odds ratios

What are those βs anyway? Understanding Design Matrix & Odds ratios Ral paramtr stimat WILD 750 - Wildlif Population Analysis of 6 What ar thos βs anyway? Undrsting Dsign Matrix & Odds ratios Rfrncs Hosmr D.W.. Lmshow. 000. Applid logistic rgrssion. John Wily & ons Inc.

More information

EXST Regression Techniques Page 1

EXST Regression Techniques Page 1 EXST704 - Rgrssion Tchniqus Pag 1 Masurmnt rrors in X W hav assumd that all variation is in Y. Masurmnt rror in this variabl will not ffct th rsults, as long as thy ar uncorrlatd and unbiasd, sinc thy

More information

ph People Grade Level: basic Duration: minutes Setting: classroom or field site

ph People Grade Level: basic Duration: minutes Setting: classroom or field site ph Popl Adaptd from: Whr Ar th Frogs? in Projct WET: Curriculum & Activity Guid. Bozman: Th Watrcours and th Council for Environmntal Education, 1995. ph Grad Lvl: basic Duration: 10 15 minuts Stting:

More information

Exchange rates in the long run (Purchasing Power Parity: PPP)

Exchange rates in the long run (Purchasing Power Parity: PPP) Exchang rats in th long run (Purchasing Powr Parity: PPP) Jan J. Michalk JJ Michalk Th law of on pric: i for a product i; P i = E N/ * P i Or quivalntly: E N/ = P i / P i Ida: Th sam product should hav

More information

Inflation and Unemployment

Inflation and Unemployment C H A P T E R 13 Aggrgat Supply and th Short-run Tradoff Btwn Inflation and Unmploymnt MACROECONOMICS SIXTH EDITION N. GREGORY MANKIW PowrPoint Slids by Ron Cronovich 2008 Worth Publishrs, all rights rsrvd

More information

Network Congestion Games

Network Congestion Games Ntwork Congstion Gams Assistant Profssor Tas A&M Univrsity Collg Station, TX TX Dallas Collg Station Austin Houston Bst rout dpnds on othrs Ntwork Congstion Gams Travl tim incrass with congstion Highway

More information

+ f. e f. Ch. 8 Inflation, Interest Rates & FX Rates. Purchasing Power Parity. Purchasing Power Parity

+ f. e f. Ch. 8 Inflation, Interest Rates & FX Rates. Purchasing Power Parity. Purchasing Power Parity Ch. 8 Inlation, Intrst Rats & FX Rats Topics Purchasing Powr Parity Intrnational Fishr Ect Purchasing Powr Parity Purchasing Powr Parity (PPP: Th purchasing powr o a consumr will b similar whn purchasing

More information

The van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012

The van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012 Th van dr Waals intraction D. E. Sopr 2 Univrsity of Orgon 20 pril 202 Th van dr Waals intraction is discussd in Chaptr 5 of J. J. Sakurai, Modrn Quantum Mchanics. Hr I tak a look at it in a littl mor

More information

Exam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator.

Exam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator. Exam N a m : _ S O L U T I O N P U I D : I n s t r u c t i o n s : It is important that you clarly show your work and mark th final answr clarly, closd book, closd nots, no calculator. T i m : h o u r

More information

The pn junction: 2 Current vs Voltage (IV) characteristics

The pn junction: 2 Current vs Voltage (IV) characteristics Th pn junction: Currnt vs Voltag (V) charactristics Considr a pn junction in quilibrium with no applid xtrnal voltag: o th V E F E F V p-typ Dpltion rgion n-typ Elctron movmnt across th junction: 1. n

More information

Homotopy perturbation technique

Homotopy perturbation technique Comput. Mthods Appl. Mch. Engrg. 178 (1999) 257±262 www.lsvir.com/locat/cma Homotopy prturbation tchniqu Ji-Huan H 1 Shanghai Univrsity, Shanghai Institut of Applid Mathmatics and Mchanics, Shanghai 272,

More information

Brief Introduction to Statistical Mechanics

Brief Introduction to Statistical Mechanics Brif Introduction to Statistical Mchanics. Purpos: Ths nots ar intndd to provid a vry quick introduction to Statistical Mchanics. Th fild is of cours far mor vast than could b containd in ths fw pags.

More information

(Upside-Down o Direct Rotation) β - Numbers

(Upside-Down o Direct Rotation) β - Numbers Amrican Journal of Mathmatics and Statistics 014, 4(): 58-64 DOI: 10593/jajms0140400 (Upsid-Down o Dirct Rotation) β - Numbrs Ammar Sddiq Mahmood 1, Shukriyah Sabir Ali,* 1 Dpartmnt of Mathmatics, Collg

More information

22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.

22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches. Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th Born-Oppnhimr approximation. Slction ruls for rotational-vibrational transitions. P, R branchs. CHE_P8_M

More information

Higher order derivatives

Higher order derivatives Robrto s Nots on Diffrntial Calculus Chaptr 4: Basic diffrntiation ruls Sction 7 Highr ordr drivativs What you nd to know alrady: Basic diffrntiation ruls. What you can larn hr: How to rpat th procss of

More information

On the Hamiltonian of a Multi-Electron Atom

On the Hamiltonian of a Multi-Electron Atom On th Hamiltonian of a Multi-Elctron Atom Austn Gronr Drxl Univrsity Philadlphia, PA Octobr 29, 2010 1 Introduction In this papr, w will xhibit th procss of achiving th Hamiltonian for an lctron gas. Making

More information

Bifurcation Theory. , a stationary point, depends on the value of α. At certain values

Bifurcation Theory. , a stationary point, depends on the value of α. At certain values Dnamic Macroconomic Thor Prof. Thomas Lux Bifurcation Thor Bifurcation: qualitativ chang in th natur of th solution occurs if a paramtr passs through a critical point bifurcation or branch valu. Local

More information

Principles of Humidity Dalton s law

Principles of Humidity Dalton s law Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid

More information

VALUING SURRENDER OPTIONS IN KOREAN INTEREST INDEXED ANNUITIES

VALUING SURRENDER OPTIONS IN KOREAN INTEREST INDEXED ANNUITIES VALUING SURRENDER OPTIONS IN KOREAN INTEREST INDEXED ANNUITIES Changi Kim* * Dr. Changi Kim is Lcturr at Actuarial Studis Faculty of Commrc & Economics Th Univrsity of Nw South Wals Sydny NSW 2052 Australia.

More information

Search sequence databases 3 10/25/2016

Search sequence databases 3 10/25/2016 Sarch squnc databass 3 10/25/2016 Etrm valu distribution Ø Suppos X is a random variabl with probability dnsity function p(, w sampl a larg numbr S of indpndnt valus of X from this distribution for an

More information

Equilibria in a Capacity-Constrained Di erentiated Duopoly

Equilibria in a Capacity-Constrained Di erentiated Duopoly Equilibria in a Capacity-Constraind Di rntiatd Duopoly Maxim Sinitsyn McGill Univrsity Prliminary and incomplt. Abstract In this papr I analyz th modl of pric-stting duopoly with capacity-constraind rms

More information

Extraction of Doping Density Distributions from C-V Curves

Extraction of Doping Density Distributions from C-V Curves Extraction of Doping Dnsity Distributions from C-V Curvs Hartmut F.-W. Sadrozinski SCIPP, Univ. California Santa Cruz, Santa Cruz, CA 9564 USA 1. Connction btwn C, N, V Start with Poisson quation d V =

More information

5.80 Small-Molecule Spectroscopy and Dynamics

5.80 Small-Molecule Spectroscopy and Dynamics MIT OpnCoursWar http://ocw.mit.du 5.80 Small-Molcul Spctroscopy and Dynamics Fall 008 For information about citing ths matrials or our Trms of Us, visit: http://ocw.mit.du/trms. Lctur # 3 Supplmnt Contnts

More information

r m r m 1 r m 2 y 1 y 2

r m r m 1 r m 2 y 1 y 2 An Explanation (Using th ISLM Modl) of How Volatilit in Expctations About th Profitabilit of Futur Invstmnt Projcts Can Mak Aggrgat Dmand Itslf Volatil. Th ISLM modl is a combination of two conomic modls;

More information

Economics 201b Spring 2010 Solutions to Problem Set 3 John Zhu

Economics 201b Spring 2010 Solutions to Problem Set 3 John Zhu Economics 20b Spring 200 Solutions to Problm St 3 John Zhu. Not in th 200 vrsion of Profssor Andrson s ctur 4 Nots, th charactrization of th firm in a Robinson Cruso conomy is that it maximizs profit ovr

More information

Einstein Equations for Tetrad Fields

Einstein Equations for Tetrad Fields Apiron, Vol 13, No, Octobr 006 6 Einstin Equations for Ttrad Filds Ali Rıza ŞAHİN, R T L Istanbul (Turky) Evry mtric tnsor can b xprssd by th innr product of ttrad filds W prov that Einstin quations for

More information

A Propagating Wave Packet Group Velocity Dispersion

A Propagating Wave Packet Group Velocity Dispersion Lctur 8 Phys 375 A Propagating Wav Packt Group Vlocity Disprsion Ovrviw and Motivation: In th last lctur w lookd at a localizd solution t) to th 1D fr-particl Schrödingr quation (SE) that corrsponds to

More information

That is, we start with a general matrix: And end with a simpler matrix:

That is, we start with a general matrix: And end with a simpler matrix: DIAGON ALIZATION OF THE STR ESS TEN SOR INTRO DUCTIO N By th us of Cauchy s thorm w ar abl to rduc th numbr of strss componnts in th strss tnsor to only nin valus. An additional simplification of th strss

More 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

The Ramsey Model. Reading: Firms. Households. Behavior of Households and Firms. Romer, Chapter 2-A;

The Ramsey Model. Reading: Firms. Households. Behavior of Households and Firms. Romer, Chapter 2-A; Th Ramsy Modl Rading: Romr, Chaptr 2-A; Dvlopd by Ramsy (1928), latr dvlopd furthr by Cass (1965) and Koopmans (1965). Similar to th Solow modl: labor and knowldg grow at xognous rats. Important diffrnc:

More information

INFLUENCE OF GROUND SUBSIDENCE IN THE DAMAGE TO MEXICO CITY S PRIMARY WATER SYSTEM DUE TO THE 1985 EARTHQUAKE

INFLUENCE OF GROUND SUBSIDENCE IN THE DAMAGE TO MEXICO CITY S PRIMARY WATER SYSTEM DUE TO THE 1985 EARTHQUAKE 13 th World Confrnc on Earthquak Enginring Vancouvr, B.C., Canada August 1-6, 2004 Papr No. 2165 INFLUENCE OF GROUND SUBSIDENCE IN THE DAMAGE TO MEXICO CITY S PRIMARY WATER SYSTEM DUE TO THE 1985 EARTHQUAKE

More information

LINEAR DELAY DIFFERENTIAL EQUATION WITH A POSITIVE AND A NEGATIVE TERM

LINEAR DELAY DIFFERENTIAL EQUATION WITH A POSITIVE AND A NEGATIVE TERM Elctronic Journal of Diffrntial Equations, Vol. 2003(2003), No. 92, pp. 1 6. ISSN: 1072-6691. URL: http://jd.math.swt.du or http://jd.math.unt.du ftp jd.math.swt.du (login: ftp) LINEAR DELAY DIFFERENTIAL

More information

Environmental Policy and Time Consistency: Emission Taxes and Emissions Trading

Environmental Policy and Time Consistency: Emission Taxes and Emissions Trading Environmntal Policy and Tim Consistncy: Emission Taxs and Emissions Trading Ptr W. Knndy 1 and Bnoît Laplant 2 1 Dpartmnt of Economics, Univrsity of Victoria, Victoria, British Columbia V8W 2Y2, Canada.

More information

Collisions between electrons and ions

Collisions between electrons and ions DRAFT 1 Collisions btwn lctrons and ions Flix I. Parra Rudolf Pirls Cntr for Thortical Physics, Unirsity of Oxford, Oxford OX1 NP, UK This rsion is of 8 May 217 1. Introduction Th Fokkr-Planck collision

More information

2008 AP Calculus BC Multiple Choice Exam

2008 AP Calculus BC Multiple Choice Exam 008 AP Multipl Choic Eam Nam 008 AP Calculus BC Multipl Choic Eam Sction No Calculator Activ AP Calculus 008 BC Multipl Choic. At tim t 0, a particl moving in th -plan is th acclration vctor of th particl

More information

arxiv: v3 [cs.gt] 1 Jan 2019

arxiv: v3 [cs.gt] 1 Jan 2019 Pric of Anarchy in Ntworks with Htrognous Latncy Functions Sanjiv Kapoor and Junghwan Shin arxiv:407.299v3 [cs.gt] Jan 209 Abstract W addrss th prformanc of slfish ntwork routing in multi-commodity flows

More information

Computing and Communications -- Network Coding

Computing and Communications -- Network Coding 89 90 98 00 Computing and Communications -- Ntwork Coding Dr. Zhiyong Chn Institut of Wirlss Communications Tchnology Shanghai Jiao Tong Univrsity China Lctur 5- Nov. 05 0 Classical Information Thory Sourc

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

2.3 Matrix Formulation

2.3 Matrix Formulation 23 Matrix Formulation 43 A mor complicatd xampl ariss for a nonlinar systm of diffrntial quations Considr th following xampl Exampl 23 x y + x( x 2 y 2 y x + y( x 2 y 2 (233 Transforming to polar coordinats,

More information

Cramér-Rao Inequality: Let f(x; θ) be a probability density function with continuous parameter

Cramér-Rao Inequality: Let f(x; θ) be a probability density function with continuous parameter WHEN THE CRAMÉR-RAO INEQUALITY PROVIDES NO INFORMATION STEVEN J. MILLER Abstract. W invstigat a on-paramtr family of probability dnsitis (rlatd to th Parto distribution, which dscribs many natural phnomna)

More information

The Economic Impact of Public Beta Testing: The Power of Word-of-Mouth

The Economic Impact of Public Beta Testing: The Power of Word-of-Mouth Supply Chain and Information Managmnt Confrnc Paprs, Postrs and Procdings Supply Chain and Information Systms 12-5-2011 Th Economic Impact of Public Bta Tsting: Th Powr of Word-of-Mouth Zhngrui Jiang Iowa

More information

Small Countries and Regionalism

Small Countries and Regionalism Small Countris and Rgionalism M. Ayhan Kos and Raymond Rizman Dpartmnt of Economics Univrsity of Iowa Iowa City, IA 52242 This vrsion: January 2, 1997 Abstract: Th numbr of rgional trad agrmnts has narly

More information

The influence of electron trap on photoelectron decay behavior in silver halide

The influence of electron trap on photoelectron decay behavior in silver halide Th influnc of lctron trap on photolctron dcay bhavior in silvr halid Rongjuan Liu, Xiaowi Li 1, Xiaodong Tian, Shaopng Yang and Guangshng Fu Collg of Physics Scinc and Tchnology, Hbi Univrsity, Baoding,

More information

Brief Notes on the Fermi-Dirac and Bose-Einstein Distributions, Bose-Einstein Condensates and Degenerate Fermi Gases Last Update: 28 th December 2008

Brief Notes on the Fermi-Dirac and Bose-Einstein Distributions, Bose-Einstein Condensates and Degenerate Fermi Gases Last Update: 28 th December 2008 Brif ots on th Frmi-Dirac and Bos-Einstin Distributions, Bos-Einstin Condnsats and Dgnrat Frmi Gass Last Updat: 8 th Dcmbr 8 (A)Basics of Statistical Thrmodynamics Th Gibbs Factor A systm is assumd to

More information

MEASURING ECONOMIC IMPACT OF A DISASTER WITHOUT DOUBLE COUNTING: A THEORETICAL ANALYSIS

MEASURING ECONOMIC IMPACT OF A DISASTER WITHOUT DOUBLE COUNTING: A THEORETICAL ANALYSIS MEASURING ECONOMIC IMPACT OF A DISASTER WITHOUT DOUBLE COUNTING: A THEORETICAL ANALYSIS ABSTRACT : H. Tatano and K. Nakano Profssor, Disastr Prvntion Rsarch Institut, Kyoto Univrsity, Uji. Japan Ph.D Candidat,

More information

Title: Vibrational structure of electronic transition

Title: Vibrational structure of electronic transition Titl: Vibrational structur of lctronic transition Pag- Th band spctrum sn in th Ultra-Violt (UV) and visibl (VIS) rgions of th lctromagntic spctrum can not intrprtd as vibrational and rotational spctrum

More information

Problem Set 6 Solutions

Problem Set 6 Solutions 6.04/18.06J Mathmatics for Computr Scinc March 15, 005 Srini Dvadas and Eric Lhman Problm St 6 Solutions Du: Monday, March 8 at 9 PM in Room 3-044 Problm 1. Sammy th Shark is a financial srvic providr

More information

SPECIALIZATION, WAGE BARGAINING AND TECHNOLOGY IN A MULTIGOODS GROWTH MODEL a/

SPECIALIZATION, WAGE BARGAINING AND TECHNOLOGY IN A MULTIGOODS GROWTH MODEL a/ SPECIALIZATION, WAGE BARGAINING AND TECHNOLOGY IN A MULTIGOODS GROWTH MODEL a/ Mario Cimoli ECLAC and Univrsity of Vnic Gabril Porcil Fdral Univrsity of Parana and CNPq, Brail Abstract Th papr dvlops th

More information

GEOMETRICAL PHENOMENA IN THE PHYSICS OF SUBATOMIC PARTICLES. Eduard N. Klenov* Rostov-on-Don, Russia

GEOMETRICAL PHENOMENA IN THE PHYSICS OF SUBATOMIC PARTICLES. Eduard N. Klenov* Rostov-on-Don, Russia GEOMETRICAL PHENOMENA IN THE PHYSICS OF SUBATOMIC PARTICLES Eduard N. Klnov* Rostov-on-Don, Russia Th articl considrs phnomnal gomtry figurs bing th carrirs of valu spctra for th pairs of th rmaining additiv

More information

Network Externalities and Interconnection Incentives

Network Externalities and Interconnection Incentives Ntwork Extrnalitis and Intrconnction Incntivs MARGIT A. VANBERG Cntr for Economic Rsarch (ZEW), Mannhim Prsntd on th 34th Tlcommunications Policy Rsarch Confrnc, Sptmbr 30, 2006 Sssion on Extrnalitis and

More information

Hospital Readmission Reduction Strategies Using a Penalty-Incentive Model

Hospital Readmission Reduction Strategies Using a Penalty-Incentive Model Procdings of th 2016 Industrial and Systms Enginring Rsarch Confrnc H. Yang, Z. Kong, and MD Sardr, ds. Hospital Radmission Rduction Stratgis Using a Pnalty-Incntiv Modl Michll M. Alvarado Txas A&M Univrsity

More information

Construction of asymmetric orthogonal arrays of strength three via a replacement method

Construction of asymmetric orthogonal arrays of strength three via a replacement method isid/ms/26/2 Fbruary, 26 http://www.isid.ac.in/ statmath/indx.php?modul=prprint Construction of asymmtric orthogonal arrays of strngth thr via a rplacmnt mthod Tian-fang Zhang, Qiaoling Dng and Alok Dy

More information

Market power, Growth and Unemployment

Market power, Growth and Unemployment Markt powr, Growth and Unmploymnt Pitro F Prtto Dpartmnt of Economics, Duk Univrsity Jun 13, 2011 Abstract I prsnt a modl whr firms and workrs st wags abov th markt-claring lvl Unmploymnt is thus gnratd

More information

CS 361 Meeting 12 10/3/18

CS 361 Meeting 12 10/3/18 CS 36 Mting 2 /3/8 Announcmnts. Homwork 4 is du Friday. If Friday is Mountain Day, homwork should b turnd in at my offic or th dpartmnt offic bfor 4. 2. Homwork 5 will b availabl ovr th wknd. 3. Our midtrm

More information

Elements of Statistical Thermodynamics

Elements of Statistical Thermodynamics 24 Elmnts of Statistical Thrmodynamics Statistical thrmodynamics is a branch of knowldg that has its own postulats and tchniqus. W do not attmpt to giv hr vn an introduction to th fild. In this chaptr,

More information

Hydrogen Atom and One Electron Ions

Hydrogen Atom and One Electron Ions Hydrogn Atom and On Elctron Ions Th Schrödingr quation for this two-body problm starts out th sam as th gnral two-body Schrödingr quation. First w sparat out th motion of th cntr of mass. Th intrnal potntial

More information

Part 7: Capacitance And Capacitors

Part 7: Capacitance And Capacitors Part 7: apacitanc And apacitors 7. Elctric harg And Elctric Filds onsidr a pair of flat, conducting plats, arrangd paralll to ach othr (as in figur 7.) and sparatd by an insulator, which may simply b air.

More information

Addition of angular momentum

Addition of angular momentum Addition of angular momntum April, 07 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat

More information

Random Access Techniques: ALOHA (cont.)

Random Access Techniques: ALOHA (cont.) Random Accss Tchniqus: ALOHA (cont.) 1 Exampl [ Aloha avoiding collision ] A pur ALOHA ntwork transmits a 200-bit fram on a shard channl Of 200 kbps at tim. What is th rquirmnt to mak this fram collision

More information

Answer Homework 5 PHA5127 Fall 1999 Jeff Stark

Answer Homework 5 PHA5127 Fall 1999 Jeff Stark Answr omwork 5 PA527 Fall 999 Jff Stark A patint is bing tratd with Drug X in a clinical stting. Upon admiion, an IV bolus dos of 000mg was givn which yildd an initial concntration of 5.56 µg/ml. A fw

More information

COMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Monday, April 04, 2005, 8:35 AM) PART I: CHAPTER TWO COMB MATH.

COMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Monday, April 04, 2005, 8:35 AM) PART I: CHAPTER TWO COMB MATH. C:\Dallas\0_Courss\03A_OpSci_67\0 Cgh_Book\0_athmaticalPrliminaris\0_0 Combath.doc of 8 COPUTER GENERATED HOLOGRAS Optical Scincs 67 W.J. Dallas (onday, April 04, 005, 8:35 A) PART I: CHAPTER TWO COB ATH

More information

Contemporary, atomic, nuclear, and particle physics

Contemporary, atomic, nuclear, and particle physics Contmporary, atomic, nuclar, and particl physics 1 Blackbody radiation as a thrmal quilibrium condition (in vacuum this is th only hat loss) Exampl-1 black plan surfac at a constant high tmpratur T h is

More information

REGISTER!!! The Farmer and the Seeds (a parable of scientific reasoning) Class Updates. The Farmer and the Seeds. The Farmer and the Seeds

REGISTER!!! The Farmer and the Seeds (a parable of scientific reasoning) Class Updates. The Farmer and the Seeds. The Farmer and the Seeds How dos light intract with mattr? And what dos (this say about) mattr? REGISTER!!! If Schrödingr s Cat walks into a forst, and no on is around to obsrv it, is h rally in th forst? sourc unknown Phys 1010

More information

Chapter 13 GMM for Linear Factor Models in Discount Factor form. GMM on the pricing errors gives a crosssectional

Chapter 13 GMM for Linear Factor Models in Discount Factor form. GMM on the pricing errors gives a crosssectional Chaptr 13 GMM for Linar Factor Modls in Discount Factor form GMM on th pricing rrors givs a crosssctional rgrssion h cas of xcss rturns Hors rac sting for charactristic sting for pricd factors: lambdas

More information

11/11/2018. Chapter 14 8 th and 9 th edition. Aggregate Supply and the Short-run Tradeoff Between Inflation and Unemployment.

11/11/2018. Chapter 14 8 th and 9 th edition. Aggregate Supply and the Short-run Tradeoff Between Inflation and Unemployment. Chaptr 14 8 th and 9 th dition Aggrgat Supply and th Short-run Tradoff Btwn Inflation and Unmploymnt W covr modls of aggrgat supply in which output dpnds positivly on th pric lvl in th short run. th short-run

More information

Radio Spectrum Valuation by Applying the Artificial Neural Network Model

Radio Spectrum Valuation by Applying the Artificial Neural Network Model Journal of Advancs in Computr Ntworks, Vol. 4, No. 1, March 2016 Radio Spctrum Valuation by Applying th Artificial Nural Ntwork Modl S. Malisuwan, N. Suriyakrai, and N. Madan qustioning, what should b

More information

Procdings of IC-IDC0 ( and (, ( ( and (, and (f ( and (, rspctivly. If two input signals ar compltly qual, phas spctra of two signals ar qual. That is

Procdings of IC-IDC0 ( and (, ( ( and (, and (f ( and (, rspctivly. If two input signals ar compltly qual, phas spctra of two signals ar qual. That is Procdings of IC-IDC0 EFFECTS OF STOCHASTIC PHASE SPECTRUM DIFFERECES O PHASE-OLY CORRELATIO FUCTIOS PART I: STATISTICALLY COSTAT PHASE SPECTRUM DIFFERECES FOR FREQUECY IDICES Shunsu Yamai, Jun Odagiri,

More information

Classical Magnetic Dipole

Classical Magnetic Dipole Lctur 18 1 Classical Magntic Dipol In gnral, a particl of mass m and charg q (not ncssarily a point charg), w hav q g L m whr g is calld th gyromagntic ratio, which accounts for th ffcts of non-point charg

More information

First derivative analysis

First derivative analysis Robrto s Nots on Dirntial Calculus Chaptr 8: Graphical analysis Sction First drivativ analysis What you nd to know alrady: How to us drivativs to idntiy th critical valus o a unction and its trm points

More information

Forces. Quantum ElectroDynamics. α = = We have now:

Forces. Quantum ElectroDynamics. α = = We have now: W hav now: Forcs Considrd th gnral proprtis of forcs mdiatd by xchang (Yukawa potntial); Examind consrvation laws which ar obyd by (som) forcs. W will nxt look at thr forcs in mor dtail: Elctromagntic

More information

The different consumption functions of products and product differentiation

The different consumption functions of products and product differentiation Th diffrnt consumption functions of products and product diffrntiation Waka Chung Dpartmnt of Economics, Monash Univrsity, Clayton, Vic 368, Australia Email: waka.chung@busco.monash.du.au Yw-Kwang Ng Dpartmnt

More information

Lecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields

Lecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields Lctur 37 (Schrödingr Equation) Physics 6-01 Spring 018 Douglas Filds Rducd Mass OK, so th Bohr modl of th atom givs nrgy lvls: E n 1 k m n 4 But, this has on problm it was dvlopd assuming th acclration

More information

Using Market Structure to Regulate a Vertically Integrated Monopolist

Using Market Structure to Regulate a Vertically Integrated Monopolist Using Markt Structur to Rgulat a Vrtically Intgratd Monopolist by Sang H. L and Jonathan H. Hamilton Dpartmnt ofeconomics Univrsity offlorida Gainsvill FL 32611 USA May 1998 W thank David Sappington, Sanford

More information

Observer Bias and Reliability By Xunchi Pu

Observer Bias and Reliability By Xunchi Pu Obsrvr Bias and Rliability By Xunchi Pu Introduction Clarly all masurmnts or obsrvations nd to b mad as accuratly as possibl and invstigators nd to pay carful attntion to chcking th rliability of thir

More information

SUNK COST EFFICIENCY WITH DISCRETE COMPETITORS

SUNK COST EFFICIENCY WITH DISCRETE COMPETITORS Sunk Cost Efficincy with Discrt Comptitors SUNK COST EFFICIENCY WITH DISCRETE COMPETITORS Linus Wilson, Univrsity of Louisiana at Lafaytt ABSTRACT Whn ntrants only diffr in thir xognous ntry costs, th

More information

15. Stress-Strain behavior of soils

15. Stress-Strain behavior of soils 15. Strss-Strain bhavior of soils Sand bhavior Usually shard undr draind conditions (rlativly high prmability mans xcss por prssurs ar not gnratd). Paramtrs govrning sand bhaviour is: Rlativ dnsity Effctiv

More information

The Analysis of Transitions in Economic Performance Using Covariate Dependent Statistical Models

The Analysis of Transitions in Economic Performance Using Covariate Dependent Statistical Models Th Analysis of Transitions in Economic Prformanc Using Covariat Dpndnt Statistical Modls Adam Baharum, M. Ataharul Islam Th Journal of Dvloping Aras, Volum 43, Numbr 2, Spring 2010, pp. 289-298 (Articl)

More information

Brief on APSCO Data Sharing Service Platform Project

Brief on APSCO Data Sharing Service Platform Project Brif on APSCO Data Sharing Srvic Platform Projct Bijing China, Novmbr, 2012 Origin - Originally, this projct proposal was put forward during th First Exprt Group Mting on Futur Plan (EGMFP-1) of Spac Activitis

More information

Einstein Rosen inflationary Universe in general relativity

Einstein Rosen inflationary Universe in general relativity PRAMANA c Indian Acadmy of Scincs Vol. 74, No. 4 journal of April 2010 physics pp. 669 673 Einstin Rosn inflationary Univrs in gnral rlativity S D KATORE 1, R S RANE 2, K S WANKHADE 2, and N K SARKATE

More information

Derangements and Applications

Derangements and Applications 2 3 47 6 23 Journal of Intgr Squncs, Vol. 6 (2003), Articl 03..2 Drangmnts and Applications Mhdi Hassani Dpartmnt of Mathmatics Institut for Advancd Studis in Basic Scincs Zanjan, Iran mhassani@iasbs.ac.ir

More information

Application of Vague Soft Sets in students evaluation

Application of Vague Soft Sets in students evaluation Availabl onlin at www.plagiarsarchlibrary.com Advancs in Applid Scinc Rsarch, 0, (6):48-43 ISSN: 0976-860 CODEN (USA): AASRFC Application of Vagu Soft Sts in studnts valuation B. Chtia*and P. K. Das Dpartmnt

More information

There is an arbitrary overall complex phase that could be added to A, but since this makes no difference we set it to zero and choose A real.

There is an arbitrary overall complex phase that could be added to A, but since this makes no difference we set it to zero and choose A real. Midtrm #, Physics 37A, Spring 07. Writ your rsponss blow or on xtra pags. Show your work, and tak car to xplain what you ar doing; partial crdit will b givn for incomplt answrs that dmonstrat som concptual

More information

ATMO 551a Homework 6 solutions Fall 08

ATMO 551a Homework 6 solutions Fall 08 . A rising air parcl in th cor of a thundrstorm achivs a vrtical vlocity of 8 m/s similar to th midtrm whn it rachs a nutral buoyancy altitud at approximatly 2 km and 2 mb. Assum th background atmosphr

More information

Evaluating Reliability Systems by Using Weibull & New Weibull Extension Distributions Mushtak A.K. Shiker

Evaluating Reliability Systems by Using Weibull & New Weibull Extension Distributions Mushtak A.K. Shiker Evaluating Rliability Systms by Using Wibull & Nw Wibull Extnsion Distributions Mushtak A.K. Shikr مشتاق عبذ الغني شخير Univrsity of Babylon, Collg of Education (Ibn Hayan), Dpt. of Mathmatics Abstract

More information

Where k is either given or determined from the data and c is an arbitrary constant.

Where k is either given or determined from the data and c is an arbitrary constant. Exponntial growth and dcay applications W wish to solv an quation that has a drivativ. dy ky k > dx This quation says that th rat of chang of th function is proportional to th function. Th solution is

More information

Addition of angular momentum

Addition of angular momentum Addition of angular momntum April, 0 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat th

More information

Estimation of apparent fraction defective: A mathematical approach

Estimation of apparent fraction defective: A mathematical approach Availabl onlin at www.plagiarsarchlibrary.com Plagia Rsarch Library Advancs in Applid Scinc Rsarch, 011, (): 84-89 ISSN: 0976-8610 CODEN (USA): AASRFC Estimation of apparnt fraction dfctiv: A mathmatical

More information

Chapter 8: Electron Configurations and Periodicity

Chapter 8: Electron Configurations and Periodicity Elctron Spin & th Pauli Exclusion Principl Chaptr 8: Elctron Configurations and Priodicity 3 quantum numbrs (n, l, ml) dfin th nrgy, siz, shap, and spatial orintation of ach atomic orbital. To xplain how

More information

1973 AP Calculus AB: Section I

1973 AP Calculus AB: Section I 97 AP Calculus AB: Sction I 9 Minuts No Calculator Not: In this amination, ln dnots th natural logarithm of (that is, logarithm to th bas ).. ( ) d= + C 6 + C + C + C + C. If f ( ) = + + + and ( ), g=

More information

Appendices * for. R&D Policies, Endogenous Growth and Scale Effects

Appendices * for. R&D Policies, Endogenous Growth and Scale Effects Appndics * for R&D Policis, Endognous Growth and Scal Effcts by Fuat Snr (Union Collg) Working Papr Fbruary 2007 * Not to b considrd for publication. To b mad availabl on th author s wb sit and also upon

More information

Physics 178/278 - David Kleinfeld - Fall checked Winter 2014

Physics 178/278 - David Kleinfeld - Fall checked Winter 2014 Physics 178/278 - David Klinfld - Fall 2005 - chckd Wintr 2014 1 Elctrodiffusion W prviously discussd how th motion of frly dissolvd ions and macromolculs is govrnd by diffusion, th random motion of molculs

More information

Abstract Interpretation: concrete and abstract semantics

Abstract Interpretation: concrete and abstract semantics Abstract Intrprtation: concrt and abstract smantics Concrt smantics W considr a vry tiny languag that manags arithmtic oprations on intgrs valus. Th (concrt) smantics of th languags cab b dfind by th funzcion

More information