Households' self-selection in a voluntary time-of-use electricity pricing experiment

Size: px
Start display at page:

Download "Households' self-selection in a voluntary time-of-use electricity pricing experiment"

Transcription

1 Housholds' slf-slcton n a voluntary tm-of-us lctrcty prcng xprmnt Torgr Ercson * Norwgan Unvrsty of Scnc and Tchnology, Dp. of Elctrcal Powr Engnrng, N-749 Trondhm, Norway. Optonal tm-dffrntatd lctrcty rats may only attract consumrs that us lttl lctrcty n pak hours and much lctrcty n off-pak hours. Elctrc utlts mght thn loos rvnus snc th consumrs can bnft from th rat structur wthout changng thr consumpton pattrns. On th othr hand, th rats may also attract consumrs wth gratr ablty and motvaton to rspond to th varyng prcs. In ths cas, utlts wll xprnc pak load rductons, whch s th ntnton of th rats. Ths papr uss a logstc rgrsson modl to nvstgat th charactrstcs of lctrcty consumrs that hav dcdd to thr partcpat n a dynamc TOU rat xprmnt or to rman on thr tradtonal tarff. Th rsults ndcat that consumrs do not consdr thr consumpton pattrns whn makng dcsons. Furthrmor, th rsults ndcat that th houshold most lkly to jon a smlar TOU program s a larg famly, lvng n a dtachd hous of nwr dat and of smallr sz, wth only lctrcty for hatng, and wth ncom n th lowr rang.. INTRODUCTION Tm-dffrntatd lctrcty rats ar ncrasngly offrd rsdntal lctrcty consumrs. Th ntnton s to motvat th consumrs to rduc consumpton n pak prods of th day whn rats ar hgh, and nstad shft usag to off-pak prods whn rats ar low. If th consumrs rspond to th prc sgnals, utlts wll xprnc rducd load n constrand prods, flattr load curvs, and mght thn dfr costly nvstmnts n nw gnraton and/or transmsson capacty. Th rats can b dsgnd n varous ways. Th most common s th tm-of-us (TOU) rat, whch nhabt a prc structur wth prcs that vary by blocks of hours of th day. A mor dynamc vrson s th crtcal-pak prcng rat. Ths s ssntally a TOU rat, but wth th possblty of mposng xtra hgh prcs f th systm s abnormally constrand, for nstanc n cold prods of th wntr. Wth tm-dffrntatd rats, consumpton nd to b mtrd as oftn as th prc changs, whch mght b svral tms a day, dpndnt on th prc structur. Tradtonal standard tarffs howvr, usually vary only a fw tms a yar, and lctrcty consumpton ar typcally rad manually onc a month or mor rarly. Hnc, bfor tm-dffrntatd rats can b ntroducd, utlts hav to chang old mtrs wth nw, and, stablsh routns to admnstrat th larg amount of consumpton masurmnt data. Ths s costly, and utlts want to know whthr bnfts from th nw mtrs and prcng schms wll xcd th costs. Cost-bnft analyss oftn hng on th consumrs' rsponss to th changng prcs (Faruqua and Gorg, 2002). Thus, for nw rat programs to prov proftabl t s mportant to attract consumrs that ar prc rsponsv. Howvr, whn th rats ar offrd on a voluntarly bass, t s possbl that only consumrs wth lttl lctrcty usag durng pak prc hours and much lctrcty usag durng off-pak prc hours wll slct th rats. Such * Tl: Fax: E-mal: torgr.rcson@rmbra.no. I am gratful to Bnt Halvorsn, Kjtl Tll, Gang Lu and Knut Rdar Wangn for hlp and valuabl dscussons. Many thanks to Statstcs Norway, Rsarch Dpartmnt for thr hosptalty and support. I acknowldg fnancal support from Nordc Enrgy Rsarch, Th Rsarch Councl of Norway, Norwgan Unvrsty of Scnc and Tchnology, Statntt and Rmbra AS

2 consumrs mght bnft by smply slctng th nw tarff, and contnu usng lctrcty as bfor wthout changng thr lctrcty consumng bhavor. As dscussd by Tran and Mhrz (995), utlts wll n ths cas not xprnc load rductons, whl at th sam tm rduc rvnu. In turn, thos losss wll typcally b shftd to th rst of th customrs by a gnral rat ncras. An mportant quston s; to what xtnt wll tm-dffrntatd tarffs only attract consumrs wth advantagous load curvs that alrady us lttl lctrcty n pak prods and much lctrcty n off-pak prods? Ths slf-slcton ssu can b nvstgatd by tstng whthr housholds' daly pak to off-pak consumpton rato s takn nto consdratons whn makng partcpaton dcsons. If t turns out that a low pak/offpak rato s corrlatd wth th dcson, stmatons of th customrs' prc rsponsvnss should tak ths nformaton nto account to avod possbl basd stmat. Th slf-slcton ssu has bn dalt wth n only a fw paprs analyzng TOU xprmnts. Agnr and Ghal (989) analyzd fv TOU xprmnts. Thy found that hgh pak prod consumpton n th pr-xprmnt prod rsultd n lowr partcpaton rat and that hgh off-pak consumpton rsultd n th oppost. Tran t al. (987) found smlar rsults n thr analyss of consumrs' rat choc. Thy usd a choc modl that ncludd th cost dffrntal btwn TOU and standard rats for a fxd lvl of lctrcty consumpton. Thy found th probablty of choosng TOU rats to dcras f th costs undr thos rats ncrasd. Howvr, Cavs t al. (989) found consumpton pattrns not to nflunc th rat choc. Thy analyzd data from a voluntary rsdntal TOU xprmnt, and compard thr fndngs wth rsults from arlr mandatory TOU programs. Thy found that voluntrs do not tak bttr advantag of partcpaton n such programs than th rst of th populaton wthout shftng usag. Thr stmatd substtuton lastcts wr much hghr than lastcts found n mandatory xprmnts, and xpland th partcpaton dcson by a gratr ablty of voluntrs to adjust thr consumpton to th varyng prcs. In ln wth ths fndng, Balad t al. (998) compard consumpton pattrns of voluntrs and non-voluntrs from a pr-tst prod n a TOU xprmnt. Thy found that on-pak usag shars wr ndstngushabl btwn th two groups, and thrfor th slf-slcton ssu appard to b nsgnfcant. Anothr analyss com from th ongong Enrgy-Smart Prcng Plan program, run by Th Communty Enrgy Coopratv. Thy offr rsdntal lctrcty customrs markt-basd, hourly prcs. Analyss of th program found dffrncs btwn partcpants and non-partcpants whch affctd th dcson to partcpat n th program. Howvr, th dffrncs wr not corrlatd wth th rspons to th hourly nrgy prcs (Summt Blu Consultng, 2004). Th mxd rsults from th dscusson abov suggst that smlar analyss should b carrd out n ach xprmnt. In addton to th ssu of possbl slf-slcton basd on advantagous load pattrn, t s usful to hav knowldg of th charactrstcs of housholds most wllng, and housholds most rluctant to jon a rat program f t s to b offrd consumrs on a voluntarly bass. If for xampl only small-consumpton housholds slct th nw rats, load rductons mght b lss n absolut trms than f larg-consumpton housholds slct th rats. Evrythng consdrd, ncrasd knowldg about housholds that voluntr for th rats wll gv utlts a bttr dcson bass whn dcdng whthr mplmntng nw mtrs and tarffs or not. Ths papr analyss data from a Norwgan tm-dffrntatd prcng xprmnt, whr a dynamc TOU ntwork tarff was offrd rsdntal lctrcty consumrs as an optonal tarff. Th am of th analyss s to assss th housholds' charactrstcs and try to rval whch mght xplan th choc of partcpaton n th rat program. Th customrs' avrag pak to off-pak lctrcty consumpton rato wll b an mportant varabl to xplan whthr lctrcty consumpton n ach TOU prod was a part of th consumrs' partcpaton dcson whn choosng th rats. Th customrs' soco-dmographc charactrstcs wll b mportant to charactrz consumrs that ar most wllng and most rluctant to voluntr for such rat programs. A qualtatv logstc rspons modl s usd to stmat th dcson procss.

3 2. EXPERIMENT AND DATA Dynamc tm-of-us prcng of rsdntal lctrcty consumpton was tstd n a larg-scal Norwgan xprmnt n Rsdntal lctrcty consumrs had nw tchnology nstalld that nabld hourly automatc mtrng of consumpton. Th housholds could choos a dynamc TOU ntwork rat or chos to rman on thr standard flat ntwork rat. Th rat was dynamc n th sns that t was actvatd whn tmpratur fll blow - 8 C. Whn actvatd, t had a two-lvl rat structur wth a pak prc of NOK n hour 8- (7 am - am) and hour 7-20 (4 pm - 8 pm) on workng days durng wntr, and an offpak prc of approxmatly NOK 0.3 n all othr hours n wknds and holdays, and n summr 3. Whn tmpraturs wr abov -8 C, th rat was constant on a lvl somwhat lowr than th standard ntwork tarff. 4 A day could thus b sparatd n two dffrnt prcng prods, an off-pak and a pak prod. Th off-pak prod was th hours -7, th hours 2-6 and th hours Th pak prod was th hours 8-, and th hours On of th goals by th analyss n ths papr s to nvstgat whthr th housholds' consumpton pattrn wr a part of th dcson procss wth rspct to thr partcpaton n th projct. To analyz ths ssu, on should prfrably hav consumpton data from th tst group and a control group that both wr on thr tradtonal standard tarffs, from th prod whn thy mad thr dcson. Unfortunatly such data dos not xst. Instad, data from two months, Novmbr and Dcmbr 2003, ar utlzd bcaus tmpraturs nvr fll blow th -8 C lmt n ths prod. Th dynamc TOU rat was consquntly not n ffct, and th customrs facd prcs smlar to th control group on th standard tarff. Thus, thy had no ncntv to adjust thr daly load pattrn to varatons n th prc. It s thrfor assumd that durng ths prod, th tst group bhavd n th sam mannr as thy dd pror to th tst prod wth rspct to thr hourly lctrcty consumpton. Ths maks t possbl to tst th hypothss about housholds makng partcpaton dcsons basd on thr daly load pattrn. As just dscrbd, th TOU rat had two dffrnt prc lvls durng a day. If housholds consdrd thr consumpton pattrn whn thy dcdd to partcpat, t s rasonabl to xpct thm to do so basd on thr usag n th sam two prods. To ndcat th rlaton btwn th consumpton n ach prod, a daly pak/off-pak consumpton rato s calculatd for ach houshold. Th avrag of ths rato for th whol Novmbr and Dcmbr months s usd to approxmat th rato that th consumrs basd thr partcpaton dcson on. In addton to th lctrcty consumpton rato, data from a survy ar usd to nvstgat othr charactrstcs that mght hav nfluncd th dcson. Ths s nformaton about typ of dwllng, typ of hatng qupmnt, ag of th dwllng, squar mtr of th dwllng, numbr of popl n th houshold and total ncom of th houshold. Som dscrptv statstcs for 48 housholds n th tst group that chos th dynamc TOU rat and 9 housholds n th control group that rmand on thr standard rat ar gvn n Tabl. Aftr th drgulaton of th Norwgan lctrcty markt n 99, ntwork and powr compans wr sparatd. Customrs now rcv on bll from thr local ntwork supplr, and on from a powr supplr that can b frly chosn among comptng compans. A consumr's total lctrcty prc wll thrfor b mad up of th ntwork prc plus th powr prc (plus taxs and VAT). 2 NOK ~ EUR VAT s not ncludd. Summr was dfnd as th months May to Octobr, and wntr as Novmbr to Aprl. 4 Th standard ntwork rat was approxmatly NOK 0.5.

4 Tabl : Summary statstcs of housholds' lctrcty consumpton and charactrstcs for th tst group and th control group Tst group: dynamc TOU rat Control group: standard rat Numbr of housholds 48 9 Bnary varabls Prcnt Prcnt Dwllng: Dtachd Dwllng: Sm-dtatchd Dwllng: Row Dwllng: Flat Hatng: Not l Hatng: El + substtuton Hatng: Only l Incom: Incom: Incom: Incom: Contnuous varabls Man Std. Dv. Man Std. Dv. No of houshold mmbrs Ag of Dwllng [yar] Sqm of Dwllng [m 2 ] El [kwh/h] Pak/Off-pak El rato From Tabl w can dscrb som of th charactrstcs of housholds n th tst group and n th control group. W s that th avrag daly pak/off-pak lctrcty consumpton rato s almost th sam for th two groups, but, th avrag lctrcty consumpton lvl ar largr for th tst group than t s for th control group 5. Whn t coms to dwllng typ, w s th prcntags shar of housholds lvng n dtachd houss ar largr n th tst group than t s n th control group, whl th shar lvng n sm-dtachd houss and flats ar smallr. Th shar of row houss s qut smlar for th two groups. Th housholds' hatng qupmnt s dvdd nto thr groups; dwllngs wth no lctrcty for hatng purposs, dwllngs wth lctrcty and substtuton possblts (ol and gas or wood-frng), and dwllngs wth only lctrcty for hatng. In both th tst and th control group, th man part of th housholds has som knd of hatng possblts bsds lctrcty. Th shar n th two groups do not dffr much (ca 80%). Howvr, th shar of housholds wthout lctrcty as a hatng sourc n th tst group ar only a thrd of what t s n th control group, and th prcntags shar of housholds wth only lctrcty as a hatng sourc ar somwhat largr n th tst group. For th total houshold ncom varabls, w s th prcntags shar n th lowst ncom group (ncom lss than NOK ) s blow half as many n th tst group as n th control group, whl narly twc as larg n th scond lowst ncom group. W also s that th two groups do not dffr much for th two hghst ncom lvls. Furthr, th numbr of houshold mmbrs n th tst group s on avrag largr than n th control group. At last, w s th dwllngs of th housholds n th tst group ar youngr than n th control group, but th squar mtr ar of about th sam sz. 3. METHOD AND MODEL Ths scton dscrbs th mthodology and th modl usd to stmat th housholds' partcpaton dcson. 5 Only masurmnts from workng days ar usd.

5 Lt V * dnot a latnt varabl that dtrmns th housholds' choc of rmanng on th tradtonal tarff, or slctng th dynamc TOU tarff. Ths s formulatd by a houshold dcson functon V * = x β+ε =, N whr x s a vctor of xplanatory varabls for houshold ; avrag pak/off-pak lctrcty consumpton rato and othr soco-dmographc varabls gathrd n th survy dscrbd prvously. ε s a logstc dstrbutd rror trm. Howvr, V * s not obsrvd, so an obsrvabl bnary ndcator, V, s usd to masur th housholds' choc as V * f V > 0 = 0 othrws I.. w obsrv th outcom V = f th houshold slctd th nw tarff, prsumably as a rsult of an valuaton of utlty bng gratr on th nw tarff, and V =0 as a rsult of th oppost consdraton. Th customrs' choc s modld by a qualtatv logstc rspons modl, whch stmats th probablts for th outcoms P[V = x ] = xβ x β + and P[V =0 x ] = x β + By usng maxmum lklhood, th jont probablty of obsrvng th sampl s maxmzd wth rspct to th paramtrs β, as: N = V V { P ( P ) } max = β N x max β = + β xβ V + xβ V 4. RESULTS AND DISCUSSION Th rsults from th logstc rgrsson usng Stata 8.0 ar shown n Tabl 2. Tabl 2: Rsults from th logstc rgrsson Varabl Cof. Std. Err. P> z Pak/Off-pak El rato Dwllng: Sm-dtatchd Dwllng: Row Dwllng: Flat Hatng: El + substtuton Hatng: Only l Incom: Incom: Incom: No of houshold mmbrs Ag of Dwllng Sqm of Dwllng Constant Log lklhood = LR ch2(2) = Psudo R2 = Prob > ch2 = Not: Dtachd dwllng, Hatng wthout lctrcty, and Incom ar takn out to avod multcollnarty.

6 Th stmat n Tabl 2 of th pak/off-pak rato of lctrcty consumpton has a ngatv sgn, whch ndcats th rluctanc of consumrs wth larg pak and low off-pak consumpton to partcpat n th xprmnt. Howvr, th stmat s far from bng sgnfcant. Ths fndng suggsts that th housholds voluntrng for th TOU rat dd not tak thr consumpton n th pak and off-pak prods nto consdraton whn thy slctd th TOU rat. From th othr stmats w fnd that housholds lvng n dtachd houss ar th on most lkly to partcpat n th xprmnt, compard wth thos lvng n othr typ of dwllngs. Th housholds lvng n flats wr comparably last lkly to chos th TOU rat. Th ngatv stmat of th dwllng sz coffcnt ndcats that th largr th dwllng s, th lss lkly s t for th houshold to partcpat. Sn togthr wth th last dscrbd rsults, th dwllng sz stmat may b ntrprtd as t s housholds n smallr dtachd houss that ar most lkly to partcpat. Th ngatv coffcnt of th ag of th dwllng ndcats that th oldr th dwllng s, th lss lkly t was for th houshold lvng thr to partcpat n th xprmnt. Th varabl that ndcats th numbr of popl n th housholds hav a postv sgn, whch suggst that th largr th famly s, th mor lkly t s for thr partcpaton n th projct. Howvr, th stmat s not sgnfcant. Whn t coms to ncom, th rsults ndcat that housholds wth th lowst total ncom wr th on last lkly to slct th nw rats. Nvrthlss, th rsults for th two hghst ncom groups ar not sgnfcantly dffrnt from th lowst ncom group. Comparably, th group most lkly to partcpat was th on wth an ncom btwn NOK 250,000 and 500,000,.. th scond lowst ncom group. As a summary of thos rsults t looks lk th houshold that most lkly wll jon a smlar xprmnt s a larg famly, lvng n a dtachd hous of nwr dat and of smallr sz and wth only lctrcty for hatng. Also, thr ncom s n th lowr rang, but not n th lowst ncom group. Thy do not consdr thr consumpton pattrns durng th day whn thy dcd whthr to partcpat or not. Othr xplanatory varabls wr also tstd n th modl. Th avrag lctrcty consumpton lvl gav far from sgnfcant rsults. Dffrnt famly typs, such as famly wth chldrn, coupls wthout chldrn or pnsonrs dd nthr xplan th partcpaton dcson. Aganst what on could blv dd ownrshp of strng systm for th lctrcty consumpton not xplan th partcpaton dcson. 5. CONCLUSION A logstc rgrsson modl has bn usd to nvstgat th charactrstcs of housholds that voluntrd for a Norwgan dynamc TOU rat program, and of housholds that dd not want to partcpat. Elctrcty consumpton masurmnts and nformaton from a survy has bn usd to xplan th housholds' partcpaton dcson. Th rsults ndcat that th daly pak to off-pak consumpton rato has not bn a part of th consdraton whn th housholds mad thr dcson of whthr to slct th TOU rat or not. Th stmats of th othr charactrstcs can b summd up as: th houshold most lkly to partcpat n a smlar xprmnt s a largr famly, lvng n a dtachd hous of nwr dat and of smallr sz and wth only lctrcty for hatng. Also, thr ncom s n th lowr rang, but not n th lowst ncom group. REFERENCES Agnr, J.A. and K. Ghal Slf-slcton n th rsdntal lctrcty tm-of-us prcng xprmnts. Journal of Appld Economtrcs. 4: S3-S44 Balad, S.M., J.A. Hrrgs and T.J. Swny Rsdntal rspons to voluntary tmof-us lctrcty rats. Rsourc and Enrgy Economcs. 20: Cavs, D.W., J.A. Hrrgs and K.A. Kustr Load Shftng Undr Voluntary Rsdntal Tm-of-Us Rats. Th Enrgy Journal. 0 (4): 83-99

7 Faruqua, A. and S.S. Gorg Th Valu of Dynamc Prcng n Mass Markts. Th Elctrcty Journal. July: Tran, K.E., D.L. McFaddn and A.A. Gott Consumr atttuds and Voluntary Rat Schduls for Publc Utlts. Th Rvw of Economcs and Statstcs. 69 (3): Tran, K. and G. Mhrz Th mpacts of optonal tm-of-us prcs: a cas study. Enrgy and buldngs. 22: Summt Blu Consultng, 2004, Evaluaton of th Enrgy-Smart Prcng Plan. Colorado

Analyzing Frequencies

Analyzing Frequencies Frquncy (# ndvduals) Frquncy (# ndvduals) /3/16 H o : No dffrnc n obsrvd sz frquncs and that prdctd by growth modl How would you analyz ths data? 15 Obsrvd Numbr 15 Expctd Numbr from growth modl 1 1 5

More information

Outlier-tolerant parameter estimation

Outlier-tolerant parameter estimation Outlr-tolrant paramtr stmaton Baysan thods n physcs statstcs machn larnng and sgnal procssng (SS 003 Frdrch Fraundorfr fraunfr@cg.tu-graz.ac.at Computr Graphcs and Vson Graz Unvrsty of Tchnology Outln

More information

ST 524 NCSU - Fall 2008 One way Analysis of variance Variances not homogeneous

ST 524 NCSU - Fall 2008 One way Analysis of variance Variances not homogeneous ST 54 NCSU - Fall 008 On way Analyss of varanc Varancs not homognous On way Analyss of varanc Exampl (Yandll, 997) A plant scntst masurd th concntraton of a partcular vrus n plant sap usng ELISA (nzym-lnkd

More information

Review - Probabilistic Classification

Review - Probabilistic Classification Mmoral Unvrsty of wfoundland Pattrn Rcognton Lctur 8 May 5, 6 http://www.ngr.mun.ca/~charlsr Offc Hours: Tusdays Thursdays 8:3-9:3 PM E- (untl furthr notc) Gvn lablld sampls { ɛc,,,..., } {. Estmat Rvw

More information

Lucas Test is based on Euler s theorem which states that if n is any integer and a is coprime to n, then a φ(n) 1modn.

Lucas Test is based on Euler s theorem which states that if n is any integer and a is coprime to n, then a φ(n) 1modn. Modul 10 Addtonal Topcs 10.1 Lctur 1 Prambl: Dtrmnng whthr a gvn ntgr s prm or compost s known as prmalty tstng. Thr ar prmalty tsts whch mrly tll us whthr a gvn ntgr s prm or not, wthout gvng us th factors

More information

Households Demand for Food Commodities: Evidence from Kurunegala Divisional Secretarial Division, Sri Lanka

Households Demand for Food Commodities: Evidence from Kurunegala Divisional Secretarial Division, Sri Lanka Housholds Dmand for Food Commodts: Evdnc from Kurungala Dvsonal Scrtaral Dvson, Sr Lanka U.W.B.M. Kumar and John Ngl Dpartmnt of Economcs and Statstcs, Unvrsty of Pradnya, Sr Lanka Kywords: Houshold dmand;

More information

Chapter 6 Student Lecture Notes 6-1

Chapter 6 Student Lecture Notes 6-1 Chaptr 6 Studnt Lctur Nots 6-1 Chaptr Goals QM353: Busnss Statstcs Chaptr 6 Goodnss-of-Ft Tsts and Contngncy Analyss Aftr compltng ths chaptr, you should b abl to: Us th ch-squar goodnss-of-ft tst to dtrmn

More information

COMPLEX NUMBER PAIRWISE COMPARISON AND COMPLEX NUMBER AHP

COMPLEX NUMBER PAIRWISE COMPARISON AND COMPLEX NUMBER AHP ISAHP 00, Bal, Indonsa, August -9, 00 COMPLEX NUMBER PAIRWISE COMPARISON AND COMPLEX NUMBER AHP Chkako MIYAKE, Kkch OHSAWA, Masahro KITO, and Masaak SHINOHARA Dpartmnt of Mathmatcal Informaton Engnrng

More information

Grand Canonical Ensemble

Grand Canonical Ensemble Th nsmbl of systms mmrsd n a partcl-hat rsrvor at constant tmpratur T, prssur P, and chmcal potntal. Consdr an nsmbl of M dntcal systms (M =,, 3,...M).. Thy ar mutually sharng th total numbr of partcls

More information

A Note on Estimability in Linear Models

A Note on Estimability in Linear Models Intrnatonal Journal of Statstcs and Applcatons 2014, 4(4): 212-216 DOI: 10.5923/j.statstcs.20140404.06 A Not on Estmablty n Lnar Modls S. O. Adymo 1,*, F. N. Nwob 2 1 Dpartmnt of Mathmatcs and Statstcs,

More information

Fakultät III Wirtschaftswissenschaften Univ.-Prof. Dr. Jan Franke-Viebach

Fakultät III Wirtschaftswissenschaften Univ.-Prof. Dr. Jan Franke-Viebach Unvrstät Sgn Fakultät III Wrtschaftswssnschaftn Unv.-rof. Dr. Jan Frank-Vbach Exam Intrnatonal Fnancal Markts Summr Smstr 206 (2 nd Exam rod) Avalabl tm: 45 mnuts Soluton For your attnton:. las do not

More information

Economics 600: August, 2007 Dynamic Part: Problem Set 5. Problems on Differential Equations and Continuous Time Optimization

Economics 600: August, 2007 Dynamic Part: Problem Set 5. Problems on Differential Equations and Continuous Time Optimization THE UNIVERSITY OF MARYLAND COLLEGE PARK, MARYLAND Economcs 600: August, 007 Dynamc Part: Problm St 5 Problms on Dffrntal Equatons and Contnuous Tm Optmzaton Quston Solv th followng two dffrntal quatons.

More information

Today s logistic regression topics. Lecture 15: Effect modification, and confounding in logistic regression. Variables. Example

Today s logistic regression topics. Lecture 15: Effect modification, and confounding in logistic regression. Variables. Example Today s stc rgrsson tocs Lctur 15: Effct modfcaton, and confoundng n stc rgrsson Sandy Eckl sckl@jhsh.du 16 May 28 Includng catgorcal rdctor crat dummy/ndcator varabls just lk for lnar rgrsson Comarng

More information

EEC 686/785 Modeling & Performance Evaluation of Computer Systems. Lecture 12

EEC 686/785 Modeling & Performance Evaluation of Computer Systems. Lecture 12 EEC 686/785 Modlng & Prformanc Evaluaton of Computr Systms Lctur Dpartmnt of Elctrcal and Computr Engnrng Clvland Stat Unvrsty wnbng@.org (basd on Dr. Ra Jan s lctur nots) Outln Rvw of lctur k r Factoral

More information

Optimal Ordering Policy in a Two-Level Supply Chain with Budget Constraint

Optimal Ordering Policy in a Two-Level Supply Chain with Budget Constraint Optmal Ordrng Polcy n a Two-Lvl Supply Chan wth Budgt Constrant Rasoul aj Alrza aj Babak aj ABSTRACT Ths papr consdrs a two- lvl supply chan whch consst of a vndor and svral rtalrs. Unsatsfd dmands n rtalrs

More information

External Equivalent. EE 521 Analysis of Power Systems. Chen-Ching Liu, Boeing Distinguished Professor Washington State University

External Equivalent. EE 521 Analysis of Power Systems. Chen-Ching Liu, Boeing Distinguished Professor Washington State University xtrnal quvalnt 5 Analyss of Powr Systms Chn-Chng Lu, ong Dstngushd Profssor Washngton Stat Unvrsty XTRNAL UALNT ach powr systm (ara) s part of an ntrconnctd systm. Montorng dvcs ar nstalld and data ar

More information

CHAPTER 33: PARTICLE PHYSICS

CHAPTER 33: PARTICLE PHYSICS Collg Physcs Studnt s Manual Chaptr 33 CHAPTER 33: PARTICLE PHYSICS 33. THE FOUR BASIC FORCES 4. (a) Fnd th rato of th strngths of th wak and lctromagntc forcs undr ordnary crcumstancs. (b) What dos that

More information

Naresuan University Journal: Science and Technology 2018; (26)1

Naresuan University Journal: Science and Technology 2018; (26)1 Narsuan Unvrsty Journal: Scnc and Tchnology 018; (6)1 Th Dvlopmnt o a Corrcton Mthod or Ensurng a Contnuty Valu o Th Ch-squar Tst wth a Small Expctd Cll Frquncy Kajta Matchma 1 *, Jumlong Vongprasrt and

More information

10/7/14. Mixture Models. Comp 135 Introduction to Machine Learning and Data Mining. Maximum likelihood estimation. Mixture of Normals in 1D

10/7/14. Mixture Models. Comp 135 Introduction to Machine Learning and Data Mining. Maximum likelihood estimation. Mixture of Normals in 1D Comp 35 Introducton to Machn Larnng and Data Mnng Fall 204 rofssor: Ron Khardon Mxtur Modls Motvatd by soft k-mans w dvlopd a gnratv modl for clustrng. Assum thr ar k clustrs Clustrs ar not rqurd to hav

More information

Physics of Very High Frequency (VHF) Capacitively Coupled Plasma Discharges

Physics of Very High Frequency (VHF) Capacitively Coupled Plasma Discharges Physcs of Vry Hgh Frquncy (VHF) Capactvly Coupld Plasma Dschargs Shahd Rauf, Kallol Bra, Stv Shannon, and Kn Collns Appld Matrals, Inc., Sunnyval, CA AVS 54 th Intrnatonal Symposum Sattl, WA Octobr 15-19,

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

Econ107 Applied Econometrics Topic 10: Dummy Dependent Variable (Studenmund, Chapter 13)

Econ107 Applied Econometrics Topic 10: Dummy Dependent Variable (Studenmund, Chapter 13) Pag- Econ7 Appld Economtrcs Topc : Dummy Dpndnt Varabl (Studnmund, Chaptr 3) I. Th Lnar Probablty Modl Suppos w hav a cross scton of 8-24 yar-olds. W spcfy a smpl 2-varabl rgrsson modl. Th probablty of

More information

The Hyperelastic material is examined in this section.

The Hyperelastic material is examined in this section. 4. Hyprlastcty h Hyprlastc matral s xad n ths scton. 4..1 Consttutv Equatons h rat of chang of ntrnal nrgy W pr unt rfrnc volum s gvn by th strss powr, whch can b xprssd n a numbr of dffrnt ways (s 3.7.6):

More information

te Finance (4th Edition), July 2017.

te Finance (4th Edition), July 2017. Appndx Chaptr. Tchncal Background Gnral Mathmatcal and Statstcal Background Fndng a bas: 3 2 = 9 3 = 9 1 /2 x a = b x = b 1/a A powr of 1 / 2 s also quvalnt to th squar root opraton. Fndng an xponnt: 3

More information

Logistic Regression I. HRP 261 2/10/ am

Logistic Regression I. HRP 261 2/10/ am Logstc Rgrsson I HRP 26 2/0/03 0- am Outln Introducton/rvw Th smplst logstc rgrsson from a 2x2 tabl llustrats how th math works Stp-by-stp xampls to b contnud nxt tm Dummy varabls Confoundng and ntracton

More information

You already learned about dummies as independent variables. But. what do you do if the dependent variable is a dummy?

You already learned about dummies as independent variables. But. what do you do if the dependent variable is a dummy? CHATER 5: DUMMY DEENDENT VARIABLES AND NON-LINEAR REGRESSION. Th roblm of Dummy Dpndnt Varabls You alrady larnd about dumms as ndpndnt varabls. But what do you do f th dpndnt varabl s a dummy? On answr

More information

Soft k-means Clustering. Comp 135 Machine Learning Computer Science Tufts University. Mixture Models. Mixture of Normals in 1D

Soft k-means Clustering. Comp 135 Machine Learning Computer Science Tufts University. Mixture Models. Mixture of Normals in 1D Comp 35 Machn Larnng Computr Scnc Tufts Unvrsty Fall 207 Ron Khardon Th EM Algorthm Mxtur Modls Sm-Suprvsd Larnng Soft k-mans Clustrng ck k clustr cntrs : Assocat xampls wth cntrs p,j ~~ smlarty b/w cntr

More information

A Probabilistic Characterization of Simulation Model Uncertainties

A Probabilistic Characterization of Simulation Model Uncertainties A Proalstc Charactrzaton of Sulaton Modl Uncrtants Vctor Ontvros Mohaad Modarrs Cntr for Rsk and Rlalty Unvrsty of Maryland 1 Introducton Thr s uncrtanty n odl prdctons as wll as uncrtanty n xprnts Th

More information

Reliability of time dependent stress-strength system for various distributions

Reliability of time dependent stress-strength system for various distributions IOS Joural of Mathmatcs (IOS-JM ISSN: 78-578. Volum 3, Issu 6 (Sp-Oct., PP -7 www.osrjourals.org lablty of tm dpdt strss-strgth systm for varous dstrbutos N.Swath, T.S.Uma Mahswar,, Dpartmt of Mathmatcs,

More information

NON-SYMMETRY POWER IN THREE-PHASE SYSTEMS

NON-SYMMETRY POWER IN THREE-PHASE SYSTEMS O-YMMETRY OWER THREE-HAE YTEM Llana Marlna MATCA nvrsty of Orada, nvrstat str., no., 487, Orada; lmatca@uorada.ro Abstract. For thr-phas lctrcal systms, n non-symmtrcal stuaton, an analyz mthod costs on

More information

??? Dynamic Causal Modelling for M/EEG. Electroencephalography (EEG) Dynamic Causal Modelling. M/EEG analysis at sensor level. time.

??? Dynamic Causal Modelling for M/EEG. Electroencephalography (EEG) Dynamic Causal Modelling. M/EEG analysis at sensor level. time. Elctroncphalography EEG Dynamc Causal Modllng for M/EEG ampltud μv tm ms tral typ 1 tm channls channls tral typ 2 C. Phllps, Cntr d Rchrchs du Cyclotron, ULg, Blgum Basd on slds from: S. Kbl M/EEG analyss

More information

2. Grundlegende Verfahren zur Übertragung digitaler Signale (Zusammenfassung) Informationstechnik Universität Ulm

2. Grundlegende Verfahren zur Übertragung digitaler Signale (Zusammenfassung) Informationstechnik Universität Ulm . Grundlgnd Vrfahrn zur Übrtragung dgtalr Sgnal (Zusammnfassung) wt Dc. 5 Transmsson of Dgtal Sourc Sgnals Sourc COD SC COD MOD MOD CC dg RF s rado transmsson mdum Snk DC SC DC CC DM dg DM RF g physcal

More information

HORIZONTAL IMPEDANCE FUNCTION OF SINGLE PILE IN SOIL LAYER WITH VARIABLE PROPERTIES

HORIZONTAL IMPEDANCE FUNCTION OF SINGLE PILE IN SOIL LAYER WITH VARIABLE PROPERTIES 13 th World Confrnc on Earthquak Engnrng Vancouvr, B.C., Canada August 1-6, 4 Papr No. 485 ORIZONTAL IMPEDANCE FUNCTION OF SINGLE PILE IN SOIL LAYER WIT VARIABLE PROPERTIES Mngln Lou 1 and Wnan Wang Abstract:

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

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

Introduction to logistic regression

Introduction to logistic regression Itroducto to logstc rgrsso Gv: datast D { 2 2... } whr s a k-dmsoal vctor of ral-valud faturs or attrbuts ad s a bar class labl or targt. hus w ca sa that R k ad {0 }. For ampl f k 4 a datast of 3 data

More information

Small Countries and Preferential Trade Agreements * How severe is the innocent bystander problem?

Small Countries and Preferential Trade Agreements * How severe is the innocent bystander problem? Small Countrs and Prfrntal Trad Agrmnts * How svr s th nnocnt bystandr problm? M. Ayhan Kos a and Raymond Rzman b Rvsd: 9/2/99 Prntd: 1/6/99 Abstract: Ths papr xamns th wlfar mplcatons of prfrntal trad

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

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

A primary objective of a phase II trial is to screen for antitumor activity; agents which are found to have substantial antitumor activity and an

A primary objective of a phase II trial is to screen for antitumor activity; agents which are found to have substantial antitumor activity and an SURVIVAL ANALYSIS A prmary objctv of a phas II tral s to scrn for anttumor actvty; agnts whch ar found to hav substantal anttumor actvty and an approprat spctrum of toxcty ar lkly ncorporatd nto combnatons

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

Discrete Shells Simulation

Discrete Shells Simulation Dscrt Shlls Smulaton Xaofng M hs proct s an mplmntaton of Grnspun s dscrt shlls, th modl of whch s govrnd by nonlnar mmbran and flxural nrgs. hs nrgs masur dffrncs btwns th undformd confguraton and th

More information

Fakultät III Univ.-Prof. Dr. Jan Franke-Viebach

Fakultät III Univ.-Prof. Dr. Jan Franke-Viebach Unv.Prof. r. J. FrankVbach WS 067: Intrnatonal Economcs ( st xam prod) Unvrstät Sgn Fakultät III Unv.Prof. r. Jan FrankVbach Exam Intrnatonal Economcs Wntr Smstr 067 ( st Exam Prod) Avalabl tm: 60 mnuts

More information

Math 34A. Final Review

Math 34A. Final Review Math A Final Rviw 1) Us th graph of y10 to find approimat valus: a) 50 0. b) y (0.65) solution for part a) first writ an quation: 50 0. now tak th logarithm of both sids: log() log(50 0. ) pand th right

More 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

Decentralized Adaptive Control and the Possibility of Utilization of Networked Control System

Decentralized Adaptive Control and the Possibility of Utilization of Networked Control System Dcntralzd Adaptv Control and th Possblty of Utlzaton of Ntworkd Control Systm MARIÁN ÁRNÍK, JÁN MURGAŠ Slovak Unvrsty of chnology n Bratslava Faculty of Elctrcal Engnrng and Informaton chnology Insttut

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

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding...

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding... Chmical Physics II Mor Stat. Thrmo Kintics Protin Folding... http://www.nmc.ctc.com/imags/projct/proj15thumb.jpg http://nuclarwaponarchiv.org/usa/tsts/ukgrabl2.jpg http://www.photolib.noaa.gov/corps/imags/big/corp1417.jpg

More 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

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

The Fourier Transform

The Fourier Transform /9/ Th ourr Transform Jan Baptst Josph ourr 768-83 Effcnt Data Rprsntaton Data can b rprsntd n many ways. Advantag usng an approprat rprsntaton. Eampls: osy ponts along a ln Color spac rd/grn/blu v.s.

More information

UNIT 8 TWO-WAY ANOVA WITH m OBSERVATIONS PER CELL

UNIT 8 TWO-WAY ANOVA WITH m OBSERVATIONS PER CELL UNIT 8 TWO-WAY ANOVA WITH OBSERVATIONS PER CELL Two-Way Anova wth Obsrvatons Pr Cll Structur 81 Introducton Obctvs 8 ANOVA Modl for Two-way Classfd Data wth Obsrvatons r Cll 83 Basc Assutons 84 Estaton

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

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

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

ACOUSTIC WAVE EQUATION. Contents INTRODUCTION BULK MODULUS AND LAMÉ S PARAMETERS

ACOUSTIC WAVE EQUATION. Contents INTRODUCTION BULK MODULUS AND LAMÉ S PARAMETERS ACOUSTIC WAE EQUATION Contnts INTRODUCTION BULK MODULUS AND LAMÉ S PARAMETERS INTRODUCTION As w try to vsualz th arth ssmcally w mak crtan physcal smplfcatons that mak t asr to mak and xplan our obsrvatons.

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

SØK/ECON 535 Imperfect Competition and Strategic Interaction. In the absence of entry barriers firms cannot make supernormal profits.

SØK/ECON 535 Imperfect Competition and Strategic Interaction. In the absence of entry barriers firms cannot make supernormal profits. SØK/ECON 535 Imprfct Comptton and Stratgc Intracton ENTRY AND EXIT Lctur nots 09.10.0 Introducton In th absnc of ntry barrrs frms cannot mak suprnormal profts. Barrrs to ntry govrnmnt rgulatons tchnologcal

More information

Lecture 14. Relic neutrinos Temperature at neutrino decoupling and today Effective degeneracy factor Neutrino mass limits Saha equation

Lecture 14. Relic neutrinos Temperature at neutrino decoupling and today Effective degeneracy factor Neutrino mass limits Saha equation Lctur Rlc nutrnos mpratur at nutrno dcoupln and today Effctv dnracy factor Nutrno mass lmts Saha quaton Physcal Cosmoloy Lnt 005 Rlc Nutrnos Nutrnos ar wakly ntractn partcls (lptons),,,,,,, typcal ractons

More information

Heisenberg Model. Sayed Mohammad Mahdi Sadrnezhaad. Supervisor: Prof. Abdollah Langari

Heisenberg Model. Sayed Mohammad Mahdi Sadrnezhaad. Supervisor: Prof. Abdollah Langari snbrg Modl Sad Mohammad Mahd Sadrnhaad Survsor: Prof. bdollah Langar bstract: n ths rsarch w tr to calculat analtcall gnvalus and gnvctors of fnt chan wth ½-sn artcls snbrg modl. W drov gnfuctons for closd

More information

Contributions of Social Capital Theory in Predicting Collective Action Behavior among Livestock Keeping Communities in Kenya

Contributions of Social Capital Theory in Predicting Collective Action Behavior among Livestock Keeping Communities in Kenya Contrbutons of Socal Captal Thory n Prdctng Collctv Acton Bhavor among Lvstock Kpng Communts n Knya Emly Ouma * and Awudu Abdula 2 Intrnatonal Insttut of Tropcal Agrcultur, c/o ISABU, Bujumbura B.P. 795

More information

Journal of Theoretical and Applied Information Technology 10 th January Vol. 47 No JATIT & LLS. All rights reserved.

Journal of Theoretical and Applied Information Technology 10 th January Vol. 47 No JATIT & LLS. All rights reserved. Journal o Thortcal and Appld Inormaton Tchnology th January 3. Vol. 47 No. 5-3 JATIT & LLS. All rghts rsrvd. ISSN: 99-8645 www.att.org E-ISSN: 87-395 RESEARCH ON PROPERTIES OF E-PARTIAL DERIVATIVE OF LOGIC

More information

Nan Hu. School of Business, Stevens Institute of Technology, 1 Castle Point Terrace, Hoboken, NJ U.S.A. Paul A.

Nan Hu. School of Business, Stevens Institute of Technology, 1 Castle Point Terrace, Hoboken, NJ U.S.A. Paul A. RESEARCH ARTICLE ON SELF-SELECTION BIASES IN ONLINE PRODUCT REVIEWS Nan Hu School of Busnss, Stvns Insttut of Tchnology, 1 Castl Pont Trrac, Hobokn, NJ 07030 U.S.A. {nhu4@stvns.du} Paul A. Pavlou Fox School

More information

Ερωτήσεις και ασκησεις Κεφ. 10 (για μόρια) ΠΑΡΑΔΟΣΗ 29/11/2016. (d)

Ερωτήσεις και ασκησεις Κεφ. 10 (για μόρια) ΠΑΡΑΔΟΣΗ 29/11/2016. (d) Ερωτήσεις και ασκησεις Κεφ 0 (για μόρια ΠΑΡΑΔΟΣΗ 9//06 Th coffcnt A of th van r Waals ntracton s: (a A r r / ( r r ( (c a a a a A r r / ( r r ( a a a a A r r / ( r r a a a a A r r / ( r r 4 a a a a 0 Th

More information

An Overview of Markov Random Field and Application to Texture Segmentation

An Overview of Markov Random Field and Application to Texture Segmentation An Ovrvw o Markov Random Fld and Applcaton to Txtur Sgmntaton Song-Wook Joo Octobr 003. What s MRF? MRF s an xtnson o Markov Procss MP (D squnc o r.v. s unlatral (causal: p(x t x,

More information

From Structural Analysis to FEM. Dhiman Basu

From Structural Analysis to FEM. Dhiman Basu From Structural Analyss to FEM Dhman Basu Acknowldgmnt Followng txt books wr consultd whl prparng ths lctur nots: Znkwcz, OC O.C. andtaylor Taylor, R.L. (000). Th FntElmnt Mthod, Vol. : Th Bass, Ffth dton,

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

Polytropic Process. A polytropic process is a quasiequilibrium process described by

Polytropic Process. A polytropic process is a quasiequilibrium process described by Polytropc Procss A polytropc procss s a quasqulbrum procss dscrbd by pv n = constant (Eq. 3.5 Th xponnt, n, may tak on any valu from to dpndng on th partcular procss. For any gas (or lqud, whn n = 0, th

More information

Advanced Macroeconomics

Advanced Macroeconomics Advancd Macroconomcs Chaptr 18 INFLATION, UNEMPLOYMENT AND AGGREGATE SUPPLY Thms of th chaptr Nomnal rgdts, xpctatonal rrors and mploymnt fluctuatons. Th short-run trad-off btwn nflaton and unmploymnt.

More information

1- Summary of Kinetic Theory of Gases

1- Summary of Kinetic Theory of Gases Dr. Kasra Etmad Octobr 5, 011 1- Summary of Kntc Thory of Gass - Radaton 3- E4 4- Plasma Proprts f(v f ( v m 4 ( kt 3/ v xp( mv kt V v v m v 1 rms V kt v m ( m 1/ v 8kT m 3kT v rms ( m 1/ E3: Prcntag of

More information

Epistemic Foundations of Game Theory. Lecture 1

Epistemic Foundations of Game Theory. Lecture 1 Royal Nthrlands cadmy of rts and Scncs (KNW) Mastr Class mstrdam, Fbruary 8th, 2007 Epstmc Foundatons of Gam Thory Lctur Gacomo onanno (http://www.con.ucdavs.du/faculty/bonanno/) QUESTION: What stratgs

More information

Unbalanced Panel Data Models

Unbalanced Panel Data Models Ubalacd Pal Data odls Chaptr 9 from Baltag: Ecoomtrc Aalyss of Pal Data 5 by Adrás alascs 4448 troducto balacd or complt pals: a pal data st whr data/obsrvatos ar avalabl for all crosssctoal uts th tr

More information

On Selection of Best Sensitive Logistic Estimator in the Presence of Collinearity

On Selection of Best Sensitive Logistic Estimator in the Presence of Collinearity Amrcan Journal of Appld Mathmatcs and Statstcs, 05, Vol. 3, No., 7- Avalabl onln at http://pubs.scpub.com/ajams/3// Scnc and Educaton Publshng DOI:0.69/ajams-3-- On Slcton of Bst Snstv Logstc Estmator

More information

A Panel Data Analysis of Code Sharing, Antitrust Immunity and Open Skies. Treaties in International Aviation Markets. W. Tom Whalen 1.

A Panel Data Analysis of Code Sharing, Antitrust Immunity and Open Skies. Treaties in International Aviation Markets. W. Tom Whalen 1. A Panl Data Analyss of Cod Sharng, Anttrust Immunty and Opn Sks Trats n Intrnatonal Avaton Markts by W. Tom Whaln May 6, 2005 Abstract Ths papr stmats th ffcts of cod sharng, anttrust mmunty and Opn Sks

More information

Lecture 3: Phasor notation, Transfer Functions. Context

Lecture 3: Phasor notation, Transfer Functions. Context EECS 5 Fall 4, ctur 3 ctur 3: Phasor notaton, Transfr Functons EECS 5 Fall 3, ctur 3 Contxt In th last lctur, w dscussd: how to convrt a lnar crcut nto a st of dffrntal quatons, How to convrt th st of

More information

u x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula

u x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula 7. Intgration by Parts Each drivativ formula givs ris to a corrsponding intgral formula, as w v sn many tims. Th drivativ product rul yilds a vry usful intgration tchniqu calld intgration by parts. Starting

More information

Davisson Germer experiment

Davisson Germer experiment Announcmnts: Davisson Grmr xprimnt Homwork st 5 is today. Homwork st 6 will b postd latr today. Mad a good guss about th Nobl Priz for 2013 Clinton Davisson and Lstr Grmr. Davisson won Nobl Priz in 1937.

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

Two Stage Procurement Processes With Competitive Suppliers and Uncertain Supplier Quality

Two Stage Procurement Processes With Competitive Suppliers and Uncertain Supplier Quality Unvrsty of Nbraska - Lncoln DgtalCommons@Unvrsty of Nbraska - Lncoln Supply Chan Managmnt and Analytcs Publcatons Busnss, Collg of 2014 Two Stag Procurmnt Procsss Wth Compttv Supplrs and Uncrtan Supplr

More information

ON THE COMPLEXITY OF K-STEP AND K-HOP DOMINATING SETS IN GRAPHS

ON THE COMPLEXITY OF K-STEP AND K-HOP DOMINATING SETS IN GRAPHS MATEMATICA MONTISNIRI Vol XL (2017) MATEMATICS ON TE COMPLEXITY OF K-STEP AN K-OP OMINATIN SETS IN RAPS M FARAI JALALVAN AN N JAFARI RA partmnt of Mathmatcs Shahrood Unrsty of Tchnology Shahrood Iran Emals:

More information

Function Spaces. a x 3. (Letting x = 1 =)) a(0) + b + c (1) = 0. Row reducing the matrix. b 1. e 4 3. e 9. >: (x = 1 =)) a(0) + b + c (1) = 0

Function Spaces. a x 3. (Letting x = 1 =)) a(0) + b + c (1) = 0. Row reducing the matrix. b 1. e 4 3. e 9. >: (x = 1 =)) a(0) + b + c (1) = 0 unction Spacs Prrquisit: Sction 4.7, Coordinatization n this sction, w apply th tchniqus of Chaptr 4 to vctor spacs whos lmnts ar functions. Th vctor spacs P n and P ar familiar xampls of such spacs. Othr

More information

CHAPTER 7d. DIFFERENTIATION AND INTEGRATION

CHAPTER 7d. DIFFERENTIATION AND INTEGRATION CHAPTER 7d. DIFFERENTIATION AND INTEGRATION A. J. Clark School o Engnrng Dpartmnt o Cvl and Envronmntal Engnrng by Dr. Ibrahm A. Assakka Sprng ENCE - Computaton Mthods n Cvl Engnrng II Dpartmnt o Cvl and

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

Nuclear reactions The chain reaction

Nuclear reactions The chain reaction Nuclar ractions Th chain raction Nuclar ractions Th chain raction For powr applications want a slf-sustaind chain raction. Natural U: 0.7% of 235 U and 99.3% of 238 U Natural U: 0.7% of 235 U and 99.3%

More information

Investing on the CAPM Pricing Error

Investing on the CAPM Pricing Error Tchnology and Invstmnt, 2017, 8, 67-82 http://www.scrp.org/journal/t ISSN Onln: 2150-4067 ISSN Prnt: 2150-4059 Invstng on th CAPM Prcng Error José Carlos d Souza Santos, Elas Cavalcant Flho Economcs Dpartmnt,

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

Application of Local Influence Diagnostics to the Linear Logistic Regression Models

Application of Local Influence Diagnostics to the Linear Logistic Regression Models Dhaka Unv. J. Sc., 5(): 6978 003(July) Applcaton of Local Influnc Dagnostcs to th Lnar Logstc Rgrsson Modls Monzur Hossan * and M. Ataharul Islam Dpartmnt of Statstcs, Unvrsty of Dhaka Rcvd on 5.0.00.

More information

0 +1e Radionuclides - can spontaneously emit particles and radiation which can be expressed by a nuclear equation.

0 +1e Radionuclides - can spontaneously emit particles and radiation which can be expressed by a nuclear equation. Radioactivity Radionuclids - can spontanously mit particls and radiation which can b xprssd by a nuclar quation. Spontanous Emission: Mass and charg ar consrvd. 4 2α -β Alpha mission Bta mission 238 92U

More 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

Physics 256: Lecture 2. Physics

Physics 256: Lecture 2. Physics Physcs 56: Lctur Intro to Quantum Physcs Agnda for Today Complx Numbrs Intrfrnc of lght Intrfrnc Two slt ntrfrnc Dffracton Sngl slt dffracton Physcs 01: Lctur 1, Pg 1 Constructv Intrfrnc Ths wll occur

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

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

Relate p and T at equilibrium between two phases. An open system where a new phase may form or a new component can be added

Relate p and T at equilibrium between two phases. An open system where a new phase may form or a new component can be added 4.3, 4.4 Phas Equlbrum Dtrmn th slops of th f lns Rlat p and at qulbrum btwn two phass ts consdr th Gbbs functon dg η + V Appls to a homognous systm An opn systm whr a nw phas may form or a nw componnt

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

Hostel Occupancy Survey (YHOS) Methodology

Hostel Occupancy Survey (YHOS) Methodology Hostl Occupancy Survy (HOS) Mthodology March 205 Indx rsntaton 3 2 Obctvs 4 3 Statstcal unt 5 4 Survy scop 6 5 fnton of varabls 7 6 Survy frawork and sapl dsgn 9 7 Estators 0 8 Inforaton collcton 3 9 Coffcnts

More information

Ch. 9 Common Emitter Amplifier

Ch. 9 Common Emitter Amplifier Ch. 9 Common mttr mplfr Common mttr mplfr nput and put oltags ar 180 o -of-phas, whl th nput and put currnts ar n-phas wth th nput oltag. Output oltag ( V ) V V V C CC C C C C and V C ar -of-phas 10 μ

More information

SCITECH Volume 5, Issue 1 RESEARCH ORGANISATION November 17, 2015

SCITECH Volume 5, Issue 1 RESEARCH ORGANISATION November 17, 2015 Journal of Informaton Scncs and Computng Tchnologs(JISCT) ISSN: 394-966 SCITECH Volum 5, Issu RESEARCH ORGANISATION Novmbr 7, 5 Journal of Informaton Scncs and Computng Tchnologs www.sctcrsarch.com/journals

More information

A NEW GENERALISATION OF SAM-SOLAI S MULTIVARIATE ADDITIVE GAMMA DISTRIBUTION*

A NEW GENERALISATION OF SAM-SOLAI S MULTIVARIATE ADDITIVE GAMMA DISTRIBUTION* A NEW GENERALISATION OF SAM-SOLAI S MULTIVARIATE ADDITIVE GAMMA DISTRIBUTION* Dr. G.S. Davd Sam Jayakumar, Assstant Profssor, Jamal Insttut of Managmnt, Jamal Mohamd Collg, Truchraall 620 020, South Inda,

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

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