The Economic Dynamics of Inflation and Unemployment
|
|
- Henry Martin Rich
- 7 years ago
- Views:
Transcription
1 Theoreical Ecoomics Leers, 0,, h://dx.doi.org/0.436/el.0.05 Published Olie May 0 (h:// The Ecoomic Dyamics of Iflaio ad Uemloyme Tamara Todorova Dearme of Ecoomics, America Uiversiy i Bulgaria, Blagoevgrad, Bulgaria odorova@aubg.bg Received November 8, 0; revised December, 0; acceed Jauary 3, 0 ABSTRACT We sudy he ime ah of iflaio ad uemloyme usig he Blachard reame of he relaioshi bewee he wo ad akig he moeary olicy codiio io accou. We solve he model boh i coiuous ad discree ime ad comare he resuls. The ecoomic dyamics of iflaio ad uemloyme shows ha hey flucuae aroud heir ieremoral equilibria, iflaio aroud he growh rae of omial moey suly, resecively, ad uemloyme aroud he aural rae of uemloyme. However, while he coiuous-ime case shows uiform ad smooh flucuaio for boh ecoomic variables, i discree ime heir ime ah is exlosive ad ooscillaory. The hyseresis case shows dyamic sabiliy ad covergece for iflaio ad uemloyme o heir ieremoral equilibria boh i discree ad coiuous ime. Whe iflaio affecs uemloyme adversely he ime ahs of he wo, boh i discree ad coiuous ime, are dyamically usable. Keywords: Ecoomic Dyamics; Secod-Order Differeial Equaios; Secod-Order Differece Equaios; Phillis Curve; Iflaio; Uemloyme. Iroducio The relaioshi bewee iflaio ad uemloyme illusraed by he so called Phillis curve was firs discussed by Phillis [] i a ah-breakig aer iled The Relaioshi bewee Uemloyme ad he Rae of Chage of Moey Wage Raes i he Uied Kigdom, The sadard reame of he relaioshi bewee iflaio ad uemloyme i dyamics ivolves he execaios-augmeed Philis curve, he adaive execaios hyohesis ad he moeary olicy codiio. Solvig he model allows sudyig he ecoomic dyamics of he variables reaed as fucios of ime. Thus, for examle, we are able o fid he ime ah ad codiios for dyamic sabiliy of acual iflaio as well as of real uemloyme. I sudyig he relaioshi bewee iflaio ad uemloyme ecoomiss such as Phels [,3] have foud o log-ru radeoff bewee hese wo, oosie o wha he Phillis curve imlies. I a iflueial 968 aer iled Moey- Wage Dyamics ad Labor Marke Equilibrium Phels [4] sudies he role of adaive execaios i seig wages ad rices. There he iroduces he coce of he aural rae of uemloyme ad argues ha labor marke equilibrium is ideede of he rae of iflaio. This fidig reders Keyesia heory of corollig he log-ru rae of uemloyme i he ecoomy ieffecive. I his book Macroecoomics Blachard [5] offers a aleraive reame of he relaioshi bewee iflaio ad uemloyme. He icororaes i he model he aural rae of uemloyme U a which he acual ad he execed iflaio raes are equal. The rae of chage of he iflaio rae is roorioal o he differece bewee he acual uemloyme rae U ad he aural rae of uemloyme U. The urose of our aer is o sudy he ecoomic dyamics ad ime ah of iflaio ad uemloyme from he ersecive of Blachard s equaio of he relaioshi bewee iflaio ad uemloyme. We solve he model boh i coiuous ad discree ime ad comare he resuls. We discuss hree cases, a simle model of Blachard s equaio wih he moeary olicy codiio ake io accou. The we exed he model o he hyseresis case, where iflaio is adversely affeced o oly by uemloyme bu by is rae of chage also. Fially, we solve he model whe here is he oosie effec, ha of iflaio o uemloyme. I sudyig he ime ah of iflaio ad uemloyme we fid ha hey flucuae aroud heir ieremoral equilibria, iflaio aroud he growh rae of omial moey suly, resecively, ad uemloyme aroud he aural rae of uemloyme. However, while he coiuous-ime case shows uiform ad smooh flucuaio for boh ecoomic variables, i discree ime heir ime ah is exlosive ad ooscillaory. Furhermore, i he secial case whe rese, o revious, iflaio is cosidered, he discree-ime soluio shows a o-flucua- Coyrigh 0 SciRes.
2 34 T. TODOROVA ig exlosive ime ah. I he hyseresis case he resuls are ideical ad show dyamic sabiliy ad covergece for iflaio ad uemloyme o heir ierermoral equilibria boh i discree ad coiuous ime. I he case whe iflaio affecs uemloyme adversely he ime ahs of he wo boh i discree ad coiuous ime are dyamically usable. The aer is orgaized as follows: Secio reveals he sadard reame of he ieremoral relaioshi bewee iflaio ad uemloyme. I Secio 3 we solve a iovaive model of his relaioshi usig Blachard s equaio. Secios 4 ad 5 exed his model o he hyseresis case ad reverse ifluece case, resecively. Secio 6 rasforms hese coiuous-ime soluios io discree-ime resuls. The aer eds wih cocludig remarks.. Iflaio ad Uemloyme: The Sadard Treame The sadard reame of he relaioshi bewee iflaio ad uemloyme has well bee sudied by mahemaical ecoomiss such as Chiag [6], Pembero ad Rau [7] ad Todorova [8]. The origial Phillis relaio shows ha he rae of iflaio is egaively relaed o he level of uemloyme ad osiively o he execed rae of iflaio such ha U hπ, 0,0h where is he rae of growh of he rice level, i.e., he iflaio rae, U is he rae of uemloyme ad π deoes he execed rae of iflaio. Thus he execaio of higher iflaio shaes he behavior of firms ad idividuals i a way ha simulaes iflaio, ideed (execig rices o rise, hey migh decide o buy more resely). As eole exec iflaio o go dow (as a resul of aroriae goverme olicies, for examle), his, ideed, brigs acual iflaio dow. This versio of he Phillis relaio ha accous for he execed rae of iflaio is called he execaios-augmeed Phillis relaio. The adaive execaios hyohesis furher shows how iflaioary execaios are formed. The equaio The exaded versio of he Phillis relaio icororaes he growh rae of moey wage w where he rae of iflaio is he differece bewee he icrease i wage ad he icrease i labor roduciviy T, ha is, w T. Thus iflaio would resul oly whe wage icreases faser ha roduciviy. Furhermore, wage growh is egaively relaed o uemloyme ad osiively o he execed rae of iflaio or w U hπ where U is he rae of uemloyme ad π is he execed rae of iflaio. If iflaioary reds ersis log eough, eole sar formig furher iflaioary execaios which shae heir moey-wage demads. j π 0 j illusraes ha whe he acual rae of iflaio exceeds he execed oe, his urures eole s execaios so 0. I he oosie case, if he acual iflaio is below he execed oe, his makes eole believe ha iflaio would go dow so π is reduced. If he rojeced ad he real iflaio ur ou o be equal, eole do o exec a chage i he level of iflaio. There is also he reverse effec, ha of iflaio o uemloyme. Whe iflaio is high for oo log, his may discourage eole from savig, cosequely reduce aggregae ivesme ad icrease he rae of uemloyme. We ca wrie km k 0 or uemloyme icreases roorioally wih real moey where m is he rae of growh of omial moey. The exressio m gives he rae of growh of real moey, or he differece bewee he growh rae of omial moey ad he rae of iflaio m m rm m where real moey is omial moey divided by he average rice level i he ecoomy. The model he becomes U hπ,, 0,0h (execaios-augmeed Philis relaio) j π 0 j (adaive execaios) km k 0 (moeary olicy) We solve his model by subsiuig he firs equaio io he secod which gives j U jh π Differeiaig furher wih resec o ime, U d π d j j h ad subsiuig for d U we obai d π jk m jh d d where he secod equaio of he model imlies Coyrigh 0 SciRes.
3 T. TODOROVA 35 π. Subsiuig his las exressio for j we obai j d π j k π m jh This is a secod-order differeial equaio i π rasforms io d π k j h jkπ jkm, or aleraively π k j h π jkπ jkm which Give he roeries of secod-order differeial equaios, we have he followig arameers a k j h a j k b jkm The coefficies a ad a are boh osiive i view of he sigs of he arameers. We fid he equilibrium rae of execed iflaio o be he aricular iegral b π a m Hece, he ieremoral equilibrium of he execed rae of iflaio is exacly he rae of growh of omial moey. I order o esablish he ime ah of π we eed o fid he characerisic roos of he differeial equaio which we ca do usig he formula r, a a 4a The ime ah of π would deed o he aricular values of he arameers. Oce we fid his ime ah we migh be able o deermie ha of uemloyme U or he rae of iflaio.. 3. Iflaio ad Uemloyme: A Exeded Model I his book Macroecoomics Blachard [5] offers a aleraive reame of he relaioshi bewee iflaio ad uemloyme. He iroduces i he model he aural rae of uemloyme U a which he acual ad he execed iflaio raes are equal. The rae of chage of he iflaio rae is roorioal o he differece bewee he acual uemloyme rae U ad he aural rae of uemloyme U such ha d U U 0 Therefore, whe U U, ha is, he acual rae of uemloyme exceeds he aural rae, he iflaio rae decreases ad whe U U, he iflaio rae icreases. The iuiive logic behid his is ha i bad ecoomic imes whe may eole are laid off, rices ed o fall. A his oi he acual uemloyme would exceed he ormal levels. I imes of a boom i he busiess cycle he rae of acual uemloyme would be raher low bu high aggregae demad would ush rices u. Blachard s equaio reveals a imora relaio as i gives aoher way of hikig abou he Phillis curve i erms of he acual ad he aural uemloyme raes ad he chage i he iflaio rae. Furhermore, i iroduces he aural rae of uemloyme as i relaes o he oacceleraig-iflaio rae of uemloyme (or NAIRU), he rae of uemloyme required o kee he iflaio rae cosa. We solve his aleraive model of he relaioshi bewee iflaio ad uemloyme by assumig ha U is cosa ad ha a ay give ime he acual uemloyme rae U is deermied by aggregae demad which, o is ow, deeds o he real value of moey suly give by omial moey suly M divided by he average rice level. Thus uem- loyme is egaively relaed o real moey suly M accordig o he relaioshi U l M, 0 We solve by differeiaig he firs equaio d ad he secod equaio o obai d U d U d dl l M M dl m We assume ha he growh rae of omial moey suly m is cosa which could be i accordace wih sysemaic goverme laig or moeary olicy. The equaio ha obais is ideical o he moeary-olicy equaio iroduced i he sadard reame of he Phillis curve. Combiig he wo resuls yields d m d m which is a secod-order differeial equaio i iflaio rae. Solvig he differeial equaio, we have Professor Blachard [5] formulaes his origial equaio i discree U U. ime as Coyrigh 0 SciRes.
4 36 T. TODOROVA a 0, a ad b m. Hece, he aricular iegral is m ad he characerisic equaio is e r r, 0 i where h 0 ad v Thus he geeral soluio ivolves comlex roos ad akes he form o () m e Bcos Bsi m Bcos Bsi Similar o he sadard model we ca sudy he dyamic sabiliy of acual iflaio. Sice h 0, he fucio of iflaio rae dislays uiform flucuaios aroud he rae of growh of moey suly which gives he equilibrium level of iflaio. 3 Sice he growh rae of omial moey suly deeds o goverme olicies ad chages wih hose, i is a movig equilibrium. Such flucuaig ime ah aroud he ieremoral equilibrium ca be grahed as i Figure. Alhough he ime ah is o coverge, moeary olicy ca somewha seer iflaio ad limi i wihi a uel as i flucuaes aroud m. Give he remises of he model ad he values of he arameers, a diverge ime ah ad, herefore, a ucorollable level of iflaio are imossible. To fid he ime ah of uemloyme U as he d ex se we exress as d Bsi Bcos ad subsiue i io d U U U Bsi Bcos U B si B cos where he cosas B ad B have o bee defiiized. I follows ha, similar o he iflaio rae, he uemloyme rae dislays regular flucuaios bu is ieremoral equilibrium is he aural rae of uemloyme. Sice his is he rae a which execed ad acual iflaio are equal, we ca view ieremoral equilibrium as he sae i which execaios coicide 3 The ime ah of a geeral comlemeary fucio of he ye h y e B cosvb si v c deeds o he sie ad cosie fucios h as well as o he erm e. Sice he eriod of he rigoomeric fucios is π ad heir amliude is, heir grahs reea heir shaes every ime he exressio v icreases by π. () 0 h 0 Figure. The ime ah of acual iflaio. wih realiy. Sice agai we have h 0, he ime ah of uemloyme is eiher coverge, or diverge. I follows, herefore, ha wih he assage of ime acual uemloyme cao subsaially deviae from he aural rae of uemloyme. 4. The Blachard Model: A Hyseresis Sysem The equaio formulaed by Professor Blachard ca be exeded furher o he so called hyseresis sysem. This versio of he model assumes ha he rae of chage of he iflaio rae is a decreasig fucio o oly of he level of uemloyme, bu also of is rae of chage. Thus eve he seed wih which uemloyme icreases will have a favourable effec o rice hikes. For examle, very low uemloyme ha icreases raidly would affec he iflaio rae egaively. The iflaio-uemloyme model he becomes d U U,, 0 U l M, 0 Subsiuig for U, d M d l U l ad differeiaig wih resec o order differeial equaio i d d m m M gives a secod- Agai, omial moey suly m is a saioary value for iflaio rae. Here we have a, a ad b m. Hece, he aricular iegral is m ad he characerisic roos are e r, a a 4a 4 Thus he geeral soluio for iflaio deeds o he values of he characerisic roos where if 4, we have real roos such ha Coyrigh 0 SciRes.
5 T. TODOROVA 37 r r m Ae Ae Sice he cosas ad are osiive, he roos (or heir real ar) ur ou o be egaive ad he equilibrium is dyamically sable. For he uemloyme rae from he firs equaio of he model we have d U U which is a firs-order differeial equaio i uemloyme wih a cosa coefficie ad a variable erm. For differeial equaios wih a variable erm ad a variable coefficie of he ye dy u y v where v 0, he geeral soluio is give by he formula u d u d d y e A ve. Subsiuig i his formula i order o solve he equaio, d U e A U e d where u ad v U ad rasformig furher, d U U Ae e where by differeiaio of he iflaio rae we have d r r A re Are ad, hece, r r U U Ae Are Are e r r U Ae Are Are r r Ar Ar U Ae e e r r The resuls are cosise wih our revious fidigs. The aural rae of uemloyme agai gives he ieremoral equilibrium rae for U. Furhermore, a dyamically sable ime ah for uemloyme is ossible, sice all exoeial erms could ed o zero. The firs exoeial erm disaears wih he assage of ime, while he secod ad he hird disaear whe r, r. 5. The Effec of Iflaio o Uemloyme Le us ow cosider a versio of he exeded iflaio-uemloyme model where here is o hyseresis, ha is, iflaio is uaffeced by he rae of chage of he uemloyme level bu, raher, here is he oosie effec, ha of iflaio o uemloyme. I fac, may socially orieed ecoomiss roose maiaiig some healhy levels of iflaio so ha o kee uemloyme low. Le us assume ha he rae of chage of he iflaio rae is a decreasig fucio of he level of uemloyme bu he uemloyme rae iself is a decreasig fucio of boh real moey suly M ad he ifla io rae. A icrease i, icreases aggregae demad ad, herefore, lowers uemloyme. Now he iflaio-uemloyme model akes he form d U U 0 U l M,, 0 We ca agai aalyze he ime ahs of Subsiuig for U, d M l U ad differeiaig wih resec o d m d ad U. Agai, omial moey suly m is a saioary value for iflaio rae. Here he arameers are a, a ad b m. Hece, he aricular iegral is m ad he characerisic roos are r, a a 4a 4 Thus he geeral soluio for iflaio would deed o he values of he characerisic roos. If i haes ha 4, we have real roos. If 4, he we obai com lex roos for he ime ah of iflaio. I all cases, hough, we kow ha his ime ah is usable sice he arameers ad are osiive ad he real ar of he characerisic roos is also osiive. r r () m Ae Ae From he exressio for he uemloyme rae we obai U U d which agai gives he aural rae of uemloyme as he equilibrium rae for U. The geeral soluio for uemloyme by differeiaio of he iflaio rae is r r U U Are A re ad shows a dyamically usable ime ah for uemloyme. Coyrigh 0 SciRes.
6 38 T. TODOROVA 6. Iflaio ad Uemloyme i Discree Time U U formu- by Professor Blachard i discree ime. I is laed equivale o he firs equaio i our coiuous-ime iflaio-uemloyme model Cosider he equaio d U U 0 m 0 We ow cover he model i a discree-ime form ad solve for he ime ah of iflaio. From he firs eq uaio of he model by furher differeiaio we ob- d aied. I discree ime his ivolves a secod differece of rice o he lef side, ha is, The equaio i is discree form becomes U U where from he secod equaio of he model we have i discree ime U U m Thus he ew model becomes U U m U U m Subsiuig he differece er for uemloyme gives a secod-order differece equaio i : m The equilibrium value for is m m. This resul is cosise wih our revious fidigs. The comlemeary fucio of he secod-order differece equaio obaied is of he ye y y y Ab Ab c where for he characerisic roos we have b, a a 4a 44( ) i i which ur ou o be comlex umbers so he ime ah of he iflaio rae mus ivolve seed flucuaio. Sice R a where boh ad are osiive cosas, i mus be ha R. He ce, he flucuaig ah of iflaio, give he assumios of he model, mus be exlosive, as show i Figure. If we assume ha he differece for uemloyme is give b y U U m, ha is, he icrease i uemloyme deeds o iflaio i he rese, o i he revious eriod, he model becomes U U U U m Subsiuig agai he differece erm for uemloyme resuls i m The equilibrium value for is m m. Agai, he ieremoral equilibrium of iflaio is he growh rae of omial moey suly. The characerisic roos are a a 4a b, 4 4 By aalyzig he roos furher we fid b b a a ad b b ( ) 0 Sice boh ad are osiive cosas, oe ossibiliy is for boh roos o be egaive where oe is a fracio. From he secod equaio we also see ha oe () 0 Figure. The discree ime ah of acual iflaio. m Coyrigh 0 SciRes.
7 T. TODOROVA 39 roo is recirocal of he oher. Therefore, we coclude ha b, b 0 b ad b Sice he absolue value of oe of he roos urs ou o be greaer ha, he ime ah of iflaio is diverge ad ooscillaory. Such ime ah is illusraed by Figure 3. I he secial case of hyseresis he coiuous-ime form of he model was d U U, 0 m 0 We cover he model i a discree-ime form ad solve for he ime ah of iflaio. From he firs equaio of he model by furher differeiaio we have d d U I discree ime his ivolves a secod differece of rice o he lef side ad a secod differece of he rae of uemloyme o he righ side such ha U U U U U U U U U U U The equaio i is discree form becomes U U U U U where from he secod equaio of he model we have i discree ime U U m ad also () 0 Figure 3. The discree ime ah of acual iflaio: rese eriod. m U U U Therefore, he equaio for iflaio becomes m The equilibrium value for is m m which we have obaied reviously. Aalyzig he characerisic roos, b b a ad a b b 0 The las resul imlies ha he characerisic roos ca boh be bigger ha or smaller ha. This meas ha a coverge ime ah for iflaio is o imossible. The codiio 0 esures he dyamic sabiliy of iflaio. If we assume he differece for uemloyme o be U U m, he chage i uemloy me deeds o curre, o o revious, iflaio. The equaio of iflaio is sill U U U U U where U U m ad U U U ( ) Subsiuig i he firs equaio, m The equilibrium value for is m m. For he characerisic roos we have b b a a b b b b 0 The las resul agai shows ha a coverge ime ah for iflaio is o imossible. However, his deeds o he exac values of he arameers. Furhermore, we see ha could be less ha, give he osiive val- Coyrigh 0 SciRes.
8 40 T. TODOROVA ues of he arameers, which also allows for covergece. If he exeded iflaio-uemloyme model i is coiuous-ime form is d U U 0 d m, 0 we modify he model i a discree-ime form U U U U m Subsiuig he differece erm for uemloyme gives a secod-order differece equaio i, m The equilibrium value for m m. For he characerisic roos we have a a is b b b b 0 Here sice cao be bewee 0 ad, he roos cao boh be fracios. Therefore he ime ah of iflaio would o be dyamically sable. If a differe assumio is made abou uemloyme such as U U m he equaio becomes m The ieremoral equilibrium for is m m. For he characerisic roos we have a a b b 0 Here sice cao be bew ee 0 ad, he roos cao boh be fracios. Therefo re he ime ah of iflaio would o be dyamically sable agai. 7. Coclusio Sudyig he ecoomic dyamics of iflaio ad uemloyme we fid ha heir ime ahs show flucuaio boh i coiuous ad discree ime. Boh iflaio ad uemloyme flucuae aroud heir ieremoral equilibria, iflaio aroud he growh rae of omial moey suly, reflecig he moeary olicy of he goverme, ad uemloyme aroud he aural rae of uemloyme. However, while he coiuous-ime case shows uiform ad smooh flucuaio for boh ecoomic variables, i discree ime heir ime ah is exlosive ad ooscillaory. Furhermore, i he secial case whe rese, o revious, iflaio is cosidered, he discree-ime soluio shows a o-flucuaig exlosive ime ah. I sudyig he hyseresis case where iflaio is adversely affeced o oly by uemloyme bu by is rae of chage also, he resuls are ideical i boh discree ad coiuous ime. The hyseresis case shows dyamic sabiliy ad covergece for iflaio ad uemloyme o heir ieremoral equilibria. Fially, i he case whe iflaio affecs uemloyme he ime ahs of he wo boh i discree ad coiuous ime are dyamically usable. I all cases he dyamic sabiliy of iflaio ad acual uemloyme deeds o he secific values of he arameers. REFERENCES [] A. W. Phillis, The Relaioshi bewee Uemloyme ad he Rae of Chage of Moey Wage Raes i he Uied Kigdom, , Ecoomica, New Series, Vol. 5, No. 00, 958, [] E. S. Phels, e al., Microecoomic Foudaios of Emloyme ad Iflaio Theory, W. W. Noro, New York, 970. [3] E. S. Phels, Iflaio Policy ad Uemloyme Theory, W. W. Noro, New York, 97. [4] E. S. Phels, Moey-Wage Dyamics ad Labor Marke Equilibrium, Joural of Poliical Ecoomy, Vol. 76, No. 4, 968, doi:0.086/ [5] O. J. Blachard, Macroecoomics, d Ediio, Chaers 8-9, Preice Hall Ieraioal, Uer Saddle River, 000. [6] A. Chiag, Fudameal Mehods of Mahemaical Ecoomics, 3rd Ediio, McGraw-Hill, Ic., New York, 984. [7] M. Pembero ad N. Rau, Mahemaics for Ecoomiss: a Iroducory Texbook, Macheser Uiversiy Press, Macheser, 00. [8] T. P. Todorova, Problems Book o Accomay Mahemaics for Ecoomiss, Wiley, Hoboke, 00. Coyrigh 0 SciRes.
Bullwhip Effect Measure When Supply Chain Demand is Forecasting
J. Basic. Appl. Sci. Res., (4)47-43, 01 01, TexRoad Publicaio ISSN 090-4304 Joural of Basic ad Applied Scieific Research www.exroad.com Bullwhip Effec Measure Whe Supply Chai emad is Forecasig Ayub Rahimzadeh
More informationFORECASTING MODEL FOR AUTOMOBILE SALES IN THAILAND
FORECASTING MODEL FOR AUTOMOBILE SALES IN THAILAND by Wachareepor Chaimogkol Naioal Isiue of Developme Admiisraio, Bagkok, Thailad Email: wachare@as.ida.ac.h ad Chuaip Tasahi Kig Mogku's Isiue of Techology
More informationWhy we use compounding and discounting approaches
Comoudig, Discouig, ad ubiased Growh Raes Near Deb s school i Souher Colorado. A examle of slow growh. Coyrigh 000-04, Gary R. Evas. May be used for o-rofi isrucioal uroses oly wihou ermissio of he auhor.
More informationCHAPTER 22 ASSET BASED FINANCING: LEASE, HIRE PURCHASE AND PROJECT FINANCING
CHAPTER 22 ASSET BASED FINANCING: LEASE, HIRE PURCHASE AND PROJECT FINANCING Q.1 Defie a lease. How does i differ from a hire purchase ad isalme sale? Wha are he cash flow cosequeces of a lease? Illusrae.
More informationReaction Rates. Example. Chemical Kinetics. Chemical Kinetics Chapter 12. Example Concentration Data. Page 1
Page Chemical Kieics Chaper O decomposiio i a isec O decomposiio caalyzed by MO Chemical Kieics I is o eough o udersad he soichiomery ad hermodyamics of a reacio; we also mus udersad he facors ha gover
More informationMechanical Vibrations Chapter 4
Mechaical Vibraios Chaper 4 Peer Aviabile Mechaical Egieerig Deparme Uiversiy of Massachuses Lowell 22.457 Mechaical Vibraios - Chaper 4 1 Dr. Peer Aviabile Modal Aalysis & Corols Laboraory Impulse Exciaio
More informationThe Term Structure of Interest Rates
The Term Srucure of Ieres Raes Wha is i? The relaioship amog ieres raes over differe imehorizos, as viewed from oday, = 0. A cocep closely relaed o his: The Yield Curve Plos he effecive aual yield agais
More informationAPPLICATIONS OF GEOMETRIC
APPLICATIONS OF GEOMETRIC SEQUENCES AND SERIES TO FINANCIAL MATHS The mos powerful force i he world is compoud ieres (Alber Eisei) Page of 52 Fiacial Mahs Coes Loas ad ivesmes - erms ad examples... 3 Derivaio
More informationIntroduction to Hypothesis Testing
Iroducio o Hyohei Teig Iroducio o Hyohei Teig Scieific Mehod. Sae a reearch hyohei or oe a queio.. Gaher daa or evidece (obervaioal or eerimeal) o awer he queio. 3. Summarize daa ad e he hyohei. 4. Draw
More information1/22/2007 EECS 723 intro 2/3
1/22/2007 EES 723 iro 2/3 eraily, all elecrical egieers kow of liear sysems heory. Bu, i is helpful o firs review hese coceps o make sure ha we all udersad wha his heory is, why i works, ad how i is useful.
More informationUNDERWRITING AND EXTRA RISKS IN LIFE INSURANCE Katarína Sakálová
The process of uderwriig UNDERWRITING AND EXTRA RISKS IN LIFE INSURANCE Kaaría Sakálová Uderwriig is he process by which a life isurace compay decides which people o accep for isurace ad o wha erms Life
More informationTHE PRESSURE DERIVATIVE
Tom Aage Jelmer NTNU Dearmen of Peroleum Engineering and Alied Geohysics THE PRESSURE DERIVATIVE The ressure derivaive has imoran diagnosic roeries. I is also imoran for making ye curve analysis more reliable.
More informationA GLOSSARY OF MAIN TERMS
he aedix o his glossary gives he mai aggregae umber formulae used for cosumer rice (CI) uroses ad also exlais he ierrelaioshis bewee hem. Acquisiios aroach Addiiviy Aggregae Aggregaio Axiomaic, or es aroach
More informationDeterminants of Public and Private Investment An Empirical Study of Pakistan
eraioal Joural of Busiess ad Social Sciece Vol. 3 No. 4 [Special ssue - February 2012] Deermias of Public ad Privae vesme A Empirical Sudy of Pakisa Rabia Saghir 1 Azra Kha 2 Absrac This paper aalyses
More informationACCOUNTING TURNOVER RATIOS AND CASH CONVERSION CYCLE
Problems ad Persecives of Maageme, 24 Absrac ACCOUNTING TURNOVER RATIOS AND CASH CONVERSION CYCLE Pedro Orí-Ágel, Diego Prior Fiacial saemes, ad esecially accouig raios, are usually used o evaluae acual
More informationRanking of mutually exclusive investment projects how cash flow differences can solve the ranking problem
Chrisia Kalhoefer (Egyp) Ivesme Maageme ad Fiacial Iovaios, Volume 7, Issue 2, 2 Rakig of muually exclusive ivesme projecs how cash flow differeces ca solve he rakig problem bsrac The discussio abou he
More informationModeling the Nigerian Inflation Rates Using Periodogram and Fourier Series Analysis
CBN Joural of Applied Saisics Vol. 4 No.2 (December, 2013) 51 Modelig he Nigeria Iflaio Raes Usig Periodogram ad Fourier Series Aalysis 1 Chukwuemeka O. Omekara, Emmauel J. Ekpeyog ad Michael P. Ekeree
More informationHilbert Transform Relations
BULGARIAN ACADEMY OF SCIENCES CYBERNEICS AND INFORMAION ECHNOLOGIES Volume 5, No Sofia 5 Hilber rasform Relaios Each coiuous problem (differeial equaio) has may discree approximaios (differece equaios)
More informationResearch Article Dynamic Pricing of a Web Service in an Advance Selling Environment
Hidawi Publishig Corporaio Mahemaical Problems i Egieerig Volume 215, Aricle ID 783149, 21 pages hp://dx.doi.org/1.1155/215/783149 Research Aricle Dyamic Pricig of a Web Service i a Advace Sellig Evirome
More informationSECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES
SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,
More informationREVISTA INVESTIGACION OPERACIONAL VOL. 31, No.2, 159-170, 2010
REVISTA INVESTIGACION OPERACIONAL VOL. 3, No., 59-70, 00 AN ALGORITHM TO OBTAIN AN OPTIMAL STRATEGY FOR THE MARKOV DECISION PROCESSES, WITH PROBABILITY DISTRIBUTION FOR THE PLANNING HORIZON. Gouliois E.
More informationOptimal Combination of International and Inter-temporal Diversification of Disaster Risk: Role of Government. Tao YE, Muneta YOKOMATSU and Norio OKADA
京 都 大 学 防 災 研 究 所 年 報 第 5 号 B 平 成 9 年 4 月 Auals of Disas. Prev. Res. Is., Kyoo Uiv., No. 5 B, 27 Opimal Combiaio of Ieraioal a Ier-emporal Diversificaio of Disaser Risk: Role of Goverme Tao YE, Muea YOKOMATSUaNorio
More informationThe Norwegian Shareholder Tax Reconsidered
The Norwegia Shareholder Tax Recosidered Absrac I a aricle i Ieraioal Tax ad Public Fiace, Peer Birch Sørese (5) gives a i-deph accou of he ew Norwegia Shareholder Tax, which allows he shareholders a deducio
More informationTeaching Bond Valuation: A Differential Approach Demonstrating Duration and Convexity
JOURNAL OF EONOMIS AND FINANE EDUATION olume Number 2 Wier 2008 3 Teachig Bod aluaio: A Differeial Approach Demosraig Duraio ad ovexi TeWah Hah, David Lage ABSTRAT A radiioal bod pricig scheme used i iroducor
More information11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements
Inroducion Chaper 14: Dynamic D-S dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuing-edge
More informationExchange Rates, Risk Premia, and Inflation Indexed Bond Yields. Richard Clarida Columbia University, NBER, and PIMCO. and
Exchage Raes, Risk Premia, ad Iflaio Idexed Bod Yields by Richard Clarida Columbia Uiversiy, NBER, ad PIMCO ad Shaowe Luo Columbia Uiversiy Jue 14, 2014 I. Iroducio Drawig o ad exedig Clarida (2012; 2013)
More informationEstimating Non-Maturity Deposits
Proceedigs of he 9h WSEAS Ieraioal Coferece o SIMULATION, MODELLING AND OPTIMIZATION Esimaig No-Mauriy Deposis ELENA CORINA CIPU Uiversiy Poliehica Buchares Faculy of Applied Scieces Deparme of Mahemaics,
More informationTHE IMPACT OF FINANCING POLICY ON THE COMPANY S VALUE
THE IMPACT OF FINANCING POLICY ON THE COMPANY S ALUE Pirea Marile Wes Uiversiy of Timişoara, Faculy of Ecoomics ad Busiess Admiisraio Boțoc Claudiu Wes Uiversiy of Timişoara, Faculy of Ecoomics ad Busiess
More informationOutline. Numerical Analysis Boundary Value Problems & PDE. Exam. Boundary Value Problems. Boundary Value Problems. Solution to BVProblems
Oulie Numericl Alysis oudry Vlue Prolems & PDE Lecure 5 Jeff Prker oudry Vlue Prolems Sooig Meod Fiie Differece Meod ollocio Fiie Eleme Fll, Pril Differeil Equios Recp of ove Exm You will o e le o rig
More informationSoving Recurrence Relations
Sovig Recurrece Relatios Part 1. Homogeeous liear 2d degree relatios with costat coefficiets. Cosider the recurrece relatio ( ) T () + at ( 1) + bt ( 2) = 0 This is called a homogeeous liear 2d degree
More informationUnsteady State Molecular Diffusion
Chaper. Differeial Mass Balae Useady Sae Moleular Diffusio Whe he ieral oeraio gradie is o egligible or Bi
More information1. C. The formula for the confidence interval for a population mean is: x t, which was
s 1. C. The formula for the cofidece iterval for a populatio mea is: x t, which was based o the sample Mea. So, x is guarateed to be i the iterval you form.. D. Use the rule : p-value
More informationhttp://www.ejournalofscience.org Monitoring of Network Traffic based on Queuing Theory
VOL., NO., November ISSN XXXX-XXXX ARN Joural of Sciece a Techology - ARN Jourals. All righs reserve. hp://www.ejouralofsciece.org Moiorig of Newor Traffic base o Queuig Theory S. Saha Ray,. Sahoo Naioal
More informationCapital Budgeting: a Tax Shields Mirage?
Theoreical ad Applied Ecoomics Volume XVIII (211), No. 3(556), pp. 31-4 Capial Budgeig: a Tax Shields Mirage? Vicor DRAGOTĂ Buchares Academy of Ecoomic Sudies vicor.dragoa@fi.ase.ro Lucia ŢÂŢU Buchares
More informationPRESSURE BUILDUP. Figure 1: Schematic of an ideal buildup test
Tom Aage Jelmer NTNU Dearmen of Peroleum Engineering and Alied Geohysics PRESSURE BUILDUP I is difficul o kee he rae consan in a roducing well. This is no an issue in a buildu es since he well is closed.
More informationWHAT ARE OPTION CONTRACTS?
WHAT ARE OTION CONTRACTS? By rof. Ashok anekar An oion conrac is a derivaive which gives he righ o he holder of he conrac o do 'Somehing' bu wihou he obligaion o do ha 'Somehing'. The 'Somehing' can be
More informationCOLLECTIVE RISK MODEL IN NON-LIFE INSURANCE
Ecoomic Horizos, May - Augus 203, Volume 5, Number 2, 67-75 Faculy of Ecoomics, Uiversiy of Kragujevac UDC: 33 eissn 227-9232 www. ekfak.kg.ac.rs Review paper UDC: 005.334:368.025.6 ; 347.426.6 doi: 0.5937/ekohor30263D
More informationSection 11.3: The Integral Test
Sectio.3: The Itegral Test Most of the series we have looked at have either diverged or have coverged ad we have bee able to fid what they coverge to. I geeral however, the problem is much more difficult
More informationCircularity and the Undervaluation of Privatised Companies
CMPO Workig Paper Series No. 1/39 Circulariy ad he Udervaluaio of Privaised Compaies Paul Grou 1 ad a Zalewska 2 1 Leverhulme Cere for Marke ad Public Orgaisaio, Uiversiy of Brisol 2 Limburg Isiue of Fiacial
More informationSequences and Series
CHAPTER 9 Sequeces ad Series 9.. Covergece: Defiitio ad Examples Sequeces The purpose of this chapter is to itroduce a particular way of geeratig algorithms for fidig the values of fuctios defied by their
More informationA formulation for measuring the bullwhip effect with spreadsheets Una formulación para medir el efecto bullwhip con hojas de cálculo
irecció y rgaizació 48 (01) 9-33 9 www.revisadyo.com A formulaio for measurig he bullwhip effec wih spreadshees Ua formulació para medir el efeco bullwhip co hojas de cálculo Javier Parra-Pea 1, Josefa
More informationEXISTENCE OF A SOLUTION FOR THE FRACTIONAL FORCED PENDULUM
Jourl of Alied Mhemics d Comuiol Mechics 4, 3(), 5-4 EXISENCE OF A SOUION FOR HE FRACIONA FORCED PENDUUM Césr orres Dermeo de Igeierí Memáic, Cero de Modelmieo Memáico Uiversidd de Chile, Sigo, Chile corres@dim.uchile.cl
More information12. Spur Gear Design and selection. Standard proportions. Forces on spur gear teeth. Forces on spur gear teeth. Specifications for standard gear teeth
. Spur Gear Desig ad selecio Objecives Apply priciples leared i Chaper 11 o acual desig ad selecio of spur gear sysems. Calculae forces o eeh of spur gears, icludig impac forces associaed wih velociy ad
More informationChapter 4 Return and Risk
Chaper 4 Reur ad Risk The objecives of his chaper are o eable you o:! Udersad ad calculae reurs as a measure of ecoomic efficiecy! Udersad he relaioships bewee prese value ad IRR ad YTM! Udersad how obai
More informationHanna Putkuri. Housing loan rate margins in Finland
Haa Pukuri Housig loa rae margis i Filad Bak of Filad Research Discussio Papers 0 200 Suome Pakki Bak of Filad PO Box 60 FI-000 HESINKI Filad +358 0 83 hp://www.bof.fi E-mail: Research@bof.fi Bak of Filad
More information.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth
Questio 1: What is a ordiary auity? Let s look at a ordiary auity that is certai ad simple. By this, we mea a auity over a fixed term whose paymet period matches the iterest coversio period. Additioally,
More informationTHE FOREIGN EXCHANGE EXPOSURE OF CHINESE BANKS
Workig Paper 07/2008 Jue 2008 THE FOREIGN ECHANGE EPOSURE OF CHINESE BANKS Prepared by Eric Wog, Jim Wog ad Phyllis Leug 1 Research Deparme Absrac Usig he Capial Marke Approach ad equiy-price daa of 14
More informationIncremental calculation of weighted mean and variance
Icremetal calculatio of weighted mea ad variace Toy Fich faf@cam.ac.uk dot@dotat.at Uiversity of Cambridge Computig Service February 009 Abstract I these otes I eplai how to derive formulae for umerically
More informationAcceleration Lab Teacher s Guide
Acceleraion Lab Teacher s Guide Objecives:. Use graphs of disance vs. ime and velociy vs. ime o find acceleraion of a oy car.. Observe he relaionship beween he angle of an inclined plane and he acceleraion
More informationLecture 2: Telegrapher Equations For Transmission Lines. Power Flow.
Whies, EE 481 Lecure 2 Page 1 of 13 Lecure 2: Telegraher Equaions For Transmission Lines. Power Flow. Microsri is one mehod for making elecrical connecions in a microwae circui. I is consruced wih a ground
More informationConfidence Intervals. CI for a population mean (σ is known and n > 30 or the variable is normally distributed in the.
Cofidece Itervals A cofidece iterval is a iterval whose purpose is to estimate a parameter (a umber that could, i theory, be calculated from the populatio, if measuremets were available for the whole populatio).
More informationProperties of MLE: consistency, asymptotic normality. Fisher information.
Lecture 3 Properties of MLE: cosistecy, asymptotic ormality. Fisher iformatio. I this sectio we will try to uderstad why MLEs are good. Let us recall two facts from probability that we be used ofte throughout
More informationI. Chi-squared Distributions
1 M 358K Supplemet to Chapter 23: CHI-SQUARED DISTRIBUTIONS, T-DISTRIBUTIONS, AND DEGREES OF FREEDOM To uderstad t-distributios, we first eed to look at aother family of distributios, the chi-squared distributios.
More informationcooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)
Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer
More informationIn nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008
I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces
More informationUNIT ROOTS Herman J. Bierens 1 Pennsylvania State University (October 30, 2007)
UNIT ROOTS Herma J. Bieres Pesylvaia Sae Uiversiy (Ocober 30, 2007). Iroducio I his chaper I will explai he wo mos frequely applied ypes of ui roo ess, amely he Augmeed Dickey-Fuller ess [see Fuller (996),
More informationON THE RISK-NEUTRAL VALUATION OF LIFE INSURANCE CONTRACTS WITH NUMERICAL METHODS IN VIEW ABSTRACT KEYWORDS 1. INTRODUCTION
ON THE RISK-NEUTRAL VALUATION OF LIFE INSURANCE CONTRACTS WITH NUMERICAL METHODS IN VIEW BY DANIEL BAUER, DANIELA BERGMANN AND RÜDIGER KIESEL ABSTRACT I rece years, marke-cosise valuaio approaches have
More informationManaging Learning and Turnover in Employee Staffing*
Maagig Learig ad Turover i Employee Saffig* Yog-Pi Zhou Uiversiy of Washigo Busiess School Coauhor: Noah Gas, Wharo School, UPe * Suppored by Wharo Fiacial Isiuios Ceer ad he Sloa Foudaio Call Ceer Operaios
More information3 Energy. 3.3. Non-Flow Energy Equation (NFEE) Internal Energy. MECH 225 Engineering Science 2
MECH 5 Egieerig Sciece 3 Eergy 3.3. No-Flow Eergy Equatio (NFEE) You may have oticed that the term system kees croig u. It is ecessary, therefore, that before we start ay aalysis we defie the system that
More information4 Convolution. Recommended Problems. x2[n] 1 2[n]
4 Convoluion Recommended Problems P4.1 This problem is a simple example of he use of superposiion. Suppose ha a discree-ime linear sysem has oupus y[n] for he given inpus x[n] as shown in Figure P4.1-1.
More informationEconomics Honors Exam 2008 Solutions Question 5
Economics Honors Exam 2008 Soluions Quesion 5 (a) (2 poins) Oupu can be decomposed as Y = C + I + G. And we can solve for i by subsiuing in equaions given in he quesion, Y = C + I + G = c 0 + c Y D + I
More information4. International Parity Conditions
4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency
More informationOur aim is to show that under reasonable assumptions a given 2π-periodic function f can be represented as convergent series
8 Fourier Series Our aim is to show that uder reasoable assumptios a give -periodic fuctio f ca be represeted as coverget series f(x) = a + (a cos x + b si x). (8.) By defiitio, the covergece of the series
More informationRanking Optimization with Constraints
Rakig Opimizaio wih Cosrais Fagzhao Wu, Ju Xu, Hag Li, Xi Jiag Tsighua Naioal Laboraory for Iformaio Sciece ad Techology, Deparme of Elecroic Egieerig, Tsighua Uiversiy, Beijig, Chia Noah s Ark Lab, Huawei
More informationLesson 15 ANOVA (analysis of variance)
Outlie Variability -betwee group variability -withi group variability -total variability -F-ratio Computatio -sums of squares (betwee/withi/total -degrees of freedom (betwee/withi/total -mea square (betwee/withi
More informationA Heavy Traffic Approach to Modeling Large Life Insurance Portfolios
A Heavy Traffic Approach o Modelig Large Life Isurace Porfolios Jose Blache ad Hery Lam Absrac We explore a ew framework o approximae life isurace risk processes i he sceario of pleiful policyholders,
More informationHow To Find Out If A Moey Demad Is A Zero Or Zero (Or Ear Zero) In A Zero ( Or Ear Zero (Var)
The effec of he icrease i he moeary base o Japa s ecoomy a zero ieres raes: a empirical aalysis 1 Takeshi Kimura, Hiroshi Kobayashi, Ju Muraaga ad Hiroshi Ugai, 2 Bak of Japa Absrac I his paper, we quaify
More informationHYPERBOLIC DISCOUNTING IS RATIONAL: VALUING THE FAR FUTURE WITH UNCERTAIN DISCOUNT RATES. J. Doyne Farmer and John Geanakoplos.
HYPERBOLIC DISCOUNTING IS RATIONAL: VALUING THE FAR FUTURE WITH UNCERTAIN DISCOUNT RATES By J. Doye Farmer ad Joh Geaakoplos Augus 2009 COWLES FOUNDATION DISCUSSION PAPER NO. 1719 COWLES FOUNDATION FOR
More information0.7 0.6 0.2 0 0 96 96.5 97 97.5 98 98.5 99 99.5 100 100.5 96.5 97 97.5 98 98.5 99 99.5 100 100.5
Sectio 13 Kolmogorov-Smirov test. Suppose that we have a i.i.d. sample X 1,..., X with some ukow distributio P ad we would like to test the hypothesis that P is equal to a particular distributio P 0, i.e.
More informationPresent Value Factor To bring one dollar in the future back to present, one uses the Present Value Factor (PVF): Concept 9: Present Value
Cocept 9: Preset Value Is the value of a dollar received today the same as received a year from today? A dollar today is worth more tha a dollar tomorrow because of iflatio, opportuity cost, ad risk Brigig
More informationDepartment of Economics Working Paper 2011:6
Deparme of Ecoomics Workig Paper 211:6 The Norwegia Shareholder Tax Recosidered Ja Söderse ad Tobias idhe Deparme of Ecoomics Workig paper 211:6 Uppsala Uiversiy April 211 P.O. Box 513 ISSN 1653-6975 SE-751
More informationCALCULATION OF OMX TALLINN
CALCULATION OF OMX TALLINN CALCULATION OF OMX TALLINN 1. OMX Tallinn index...3 2. Terms in use...3 3. Comuaion rules of OMX Tallinn...3 3.1. Oening, real-ime and closing value of he Index...3 3.2. Index
More informationA closer look at Black Scholes option thetas
J Econ Finan (2008) 32:59 74 DOI 0.007/s297-007-9000-8 A closer look a Black Scholes oion heas Douglas R. Emery & Weiyu Guo & Tie Su Published online: Ocober 2007 # Sringer Science & Business Media, LLC
More informationFull-wave Bridge Rectifier Analysis
Full-wave Brige Recifier Analysis Jahan A. Feuch, Ocober, 00 his aer evelos aroximae equais for esigning or analyzing a full-wave brige recifier eak-eecor circui. his circui is commly use in A o D cverers,
More informationUsefulness of the Forward Curve in Forecasting Oil Prices
Usefulness of he Forward Curve in Forecasing Oil Prices Akira Yanagisawa Leader Energy Demand, Supply and Forecas Analysis Group The Energy Daa and Modelling Cener Summary When people analyse oil prices,
More informationA Way of Hedging Mortality Rate Risks in Life Insurance Product Development
A Way of Hegig Moraliy ae iss i Life Isurace Prouc Develome Chagi Kim Absrac Forecasig moraliy imrovemes i he fuure is imora a ecessary for isurace busiess. A ieresig observaio is ha moraliy raes for a
More informationFuzzy Task Assignment Model of Web Services Supplier
Advaed Siee ad Tehology eers Vol.78 (Mulrab 2014),.43-48 h://dx.doi.org/10.14257/asl.2014.78.08 Fuzzy Task Assige Model of Web Servies Sulier Su Jia 1,2,Peg Xiu-ya 1, *, Xu Yig 1,3, Wag Pei-lei 2, Ma Na-ji
More informationLesson 17 Pearson s Correlation Coefficient
Outlie Measures of Relatioships Pearso s Correlatio Coefficiet (r) -types of data -scatter plots -measure of directio -measure of stregth Computatio -covariatio of X ad Y -uique variatio i X ad Y -measurig
More informationAPPLIED STATISTICS. Economic statistics
APPLIED STATISTICS Ecoomic saisics Reu Kaul ad Sajoy Roy Chowdhury Reader, Deparme of Saisics, Lady Shri Ram College for Wome Lajpa Nagar, New Delhi 0024 04-Ja-2007 (Revised 20-Nov-2007) CONTENTS Time
More informationTheorems About Power Series
Physics 6A Witer 20 Theorems About Power Series Cosider a power series, f(x) = a x, () where the a are real coefficiets ad x is a real variable. There exists a real o-egative umber R, called the radius
More informationCHAPTER 7: Central Limit Theorem: CLT for Averages (Means)
CHAPTER 7: Cetral Limit Theorem: CLT for Averages (Meas) X = the umber obtaied whe rollig oe six sided die oce. If we roll a six sided die oce, the mea of the probability distributio is X P(X = x) Simulatio:
More informationChapter 7. Response of First-Order RL and RC Circuits
Chaper 7. esponse of Firs-Order L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural
More informationSAMPLE QUESTIONS FOR FINAL EXAM. (1) (2) (3) (4) Find the following using the definition of the Riemann integral: (2x + 1)dx
SAMPLE QUESTIONS FOR FINAL EXAM REAL ANALYSIS I FALL 006 3 4 Fid the followig usig the defiitio of the Riema itegral: a 0 x + dx 3 Cosider the partitio P x 0 3, x 3 +, x 3 +,......, x 3 3 + 3 of the iterval
More informationAbstract. 1. Introduction. 1.1 Notation. 1.2 Parameters
1 Mdels, Predici, ad Esimai f Oubreaks f Ifecius Disease Peer J. Csa James P. Duyak Mjdeh Mhashemi {pjcsa@mire.rg, jduyak@mire.rg, mjdeh@mire.rg} he MIRE Crprai 202 Burlig Rad Bedfrd, MA 01730 1420 Absrac
More informationDerivative Securities: Lecture 7 Further applications of Black-Scholes and Arbitrage Pricing Theory. Sources: J. Hull Avellaneda and Laurence
Deivaive ecuiies: Lecue 7 uhe applicaios o Black-choles ad Abiage Picig heoy ouces: J. Hull Avellaeda ad Lauece Black s omula omeimes is easie o hik i ems o owad pices. Recallig ha i Black-choles imilaly
More informationwhere: T = number of years of cash flow in investment's life n = the year in which the cash flow X n i = IRR = the internal rate of return
EVALUATING ALTERNATIVE CAPITAL INVESTMENT PROGRAMS By Ke D. Duft, Extesio Ecoomist I the March 98 issue of this publicatio we reviewed the procedure by which a capital ivestmet project was assessed. The
More information4.3. The Integral and Comparison Tests
4.3. THE INTEGRAL AND COMPARISON TESTS 9 4.3. The Itegral ad Compariso Tests 4.3.. The Itegral Test. Suppose f is a cotiuous, positive, decreasig fuctio o [, ), ad let a = f(). The the covergece or divergece
More informationExample 2 Find the square root of 0. The only square root of 0 is 0 (since 0 is not positive or negative, so those choices don t exist here).
BEGINNING ALGEBRA Roots ad Radicals (revised summer, 00 Olso) Packet to Supplemet the Curret Textbook - Part Review of Square Roots & Irratioals (This portio ca be ay time before Part ad should mostly
More informationRC (Resistor-Capacitor) Circuits. AP Physics C
(Resisor-Capacior Circuis AP Physics C Circui Iniial Condiions An circui is one where you have a capacior and resisor in he same circui. Suppose we have he following circui: Iniially, he capacior is UNCHARGED
More informationDistributed Containment Control with Multiple Dynamic Leaders for Double-Integrator Dynamics Using Only Position Measurements
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 57, NO. 6, JUNE 22 553 Disribued Coaime Corol wih Muliple Dyamic Leaders for Double-Iegraor Dyamics Usig Oly Posiio Measuremes Jiazhe Li, Wei Re, Member, IEEE,
More informationHypothesis testing. Null and alternative hypotheses
Hypothesis testig Aother importat use of samplig distributios is to test hypotheses about populatio parameters, e.g. mea, proportio, regressio coefficiets, etc. For example, it is possible to stipulate
More informationFull-wave rectification, bulk capacitor calculations Chris Basso January 2009
ull-wave recificaion, bulk capacior calculaions Chris Basso January 9 This shor paper shows how o calculae he bulk capacior value based on ripple specificaions and evaluae he rms curren ha crosses i. oal
More informationBuilding Blocks Problem Related to Harmonic Series
TMME, vol3, o, p.76 Buildig Blocks Problem Related to Harmoic Series Yutaka Nishiyama Osaka Uiversity of Ecoomics, Japa Abstract: I this discussio I give a eplaatio of the divergece ad covergece of ifiite
More informationA New Hybrid Network Traffic Prediction Method
This full ex paper was peer reviewed a he direcio of IEEE Couicaios Sociey subjec aer expers for publicaio i he IEEE Globeco proceedigs. A New Hybrid Nework Traffic Predicio Mehod Li Xiag, Xiao-Hu Ge,
More informationOn Motion of Robot End-effector Using The Curvature Theory of Timelike Ruled Surfaces With Timelike Ruling
O Moio of obo Ed-effecor Usig he Curvaure heory of imelike uled Surfaces Wih imelike ulig Cumali Ekici¹, Yasi Ülüürk¹, Musafa Dede¹ B. S. yuh² ¹ Eskişehir Osmagazi Uiversiy Deparme of Mahemaics, 6480-UKEY
More information3. Greatest Common Divisor - Least Common Multiple
3 Greatest Commo Divisor - Least Commo Multiple Defiitio 31: The greatest commo divisor of two atural umbers a ad b is the largest atural umber c which divides both a ad b We deote the greatest commo gcd
More informationBINOMIAL EXPANSIONS 12.5. In this section. Some Examples. Obtaining the Coefficients
652 (12-26) Chapter 12 Sequeces ad Series 12.5 BINOMIAL EXPANSIONS I this sectio Some Examples Otaiig the Coefficiets The Biomial Theorem I Chapter 5 you leared how to square a iomial. I this sectio you
More informationCombining Adaptive Filtering and IF Flows to Detect DDoS Attacks within a Router
KSII RANSAIONS ON INERNE AN INFORMAION SYSEMS VOL. 4, NO. 3, Jue 2 428 opyrigh c 2 KSII ombiig Adapive Filerig ad IF Flows o eec os Aacks wihi a Rouer Ruoyu Ya,2, Qighua Zheg ad Haifei Li 3 eparme of ompuer
More informationA Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation
A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion
More informationA Queuing Model of the N-design Multi-skill Call Center with Impatient Customers
Ieraioal Joural of u- ad e- ervice, ciece ad Techology Vol.8, o., pp.- hp://dx.doi.org/./ijuess..8.. A Queuig Model of he -desig Muli-skill Call Ceer wih Impaie Cusomers Chuya Li, ad Deua Yue Yasha Uiversiy,
More information