COMPLETELY RANDOM DESIGN (CRD) -Design can be used when experimental units are essentially homogeneous.

Size: px
Start display at page:

Download "COMPLETELY RANDOM DESIGN (CRD) -Design can be used when experimental units are essentially homogeneous."

Transcription

1 COMPLETEL RANDOM DESIGN CRD Descpon of he Desgn -Smples desgn o use. -Desgn can be used when expemenal uns ae essenally homogeneous. -Because of he homogeney equemen, may be dffcul o use hs desgn fo feld expemens. -The CRD s bes sued fo expemens wh a small numbe of eamens. Randomzaon Pocedue -Teamens ae assgned o expemenal uns compleely a andom. -Evey expemenal un has he same pobably of ecevng any eamen. -Randomzaon s pefomed usng a andom numbe able, compue, pogam, ec. Example of Randomzaon -Gven you have eamens A, B, C, and D and 5 eplcaes, how many expemenal uns would you have? D C D B B 3 3 A C B D 5 5 C C 6 6 B A 7 7 C A 8 8 D B 9 9 A D 0 0 A -Noe ha hee s no blockng of expemenal uns no eplcaes. -Evey expemenal un has he same pobably of ecevng any eamen.

2 Advanages of a CRD. Vey flexble desgn.e. numbe of eamens and eplcaes s only lmed by he avalable numbe of expemenal uns.. Sascal analyss s smple compaed o ohe desgns. 3. Loss of nfomaon due o mssng daa s small compaed o ohe desgns due o he lage numbe of degees of feedom fo he eo souce of vaaon. Dsadvanages. If expemenal uns ae no homogeneous and you fal o mnmze hs vaaon usng blockng, hee may be a loss of pecson.. Usually he leas effcen desgn unless expemenal uns ae homogeneous. 3. No sued fo a lage numbe of eamens. Fxed vs. Random Effecs -The choce of labelng a faco as a fxed o andom effec wll affec how you wll make he F-es. -Ths wll become moe mpoan lae n he couse when we dscuss neacons. Fxed Effec -All eamens of nees ae ncluded n you expemen. -ou canno make nfeences o a lage expemen. Example : An expemen s conduced a Fago and Gand Foks, ND. If locaon s consdeed a fxed effec, you canno make nfeences owad a lage aea e.g. he cenal Red Rve Valley. Example : An expemen s conduced usng fou aes e.g. ½ X, X,.5 X, X of a hebcde o deemne s effcacy o conol weeds. If ae s consdeed a fxed effec, you canno make nfeences abou wha may have occued a any aes no used n he expemen e.g. ¼ x,.5 X, ec.. Random Effec -Teamens ae a sample of he populaon o whch you can make nfeences. -ou can make nfeences owad a lage populaon usng he nfomaon fom he

3 analyses. Example : An expemen s conduced a Fago and Gand Foks, ND. If locaon s consdeed a andom effec, you can make nfeences owad a lage aea e.g. you could use he esuls o sae wha mgh be expeced o occu n he cenal Red Rve Valley. Example : An expemen s conduced usng fou aes e.g. ½ X, X,.5 X, X of an hebcde o deemne s effcacy o conol weeds. If ae s consdeed a andom effec, you can make nfeences abou wha may have occued a aes no used n he expemen e.g. ¼ x,.5 X, ec.. Analyss of he Fxed Effecs Model Noaon Sascal noaon can be confusng, bu use of he -do noaon can help smplfy hngs. The do n he -do noaon mples summaon acoss ove he subscp eplaces. Fo example, y y y y.. n y y. a y Teamen oal, whee n n Teamen mean n N y Expemen oal, whee a Expemen mean, whee N numbe of obsevaons n a eamen numbe of eamens oal numbe of obsevaons n he expemen. Lnea Addve Model fo he CRD τ ε whee: s he h obsevaon of he h eamen, s he populaon mean, τ s he eamen effec of he h eamen, and ε s he andom eo. 3

4 -Usng hs model we can esmae τ o Example ε fo any obsevaon f we ae gven and. Teamen Teamen Teamen We can now we he lnea model fo each obsevaon. -We n fo each obsevaon. Teamen Teamen Teamen We n he especve τ fo each obsevaon whee τ. Teamen Teamen Teamen

5 -We n he ε fo each obsevaon. Teamen Teamen Teamen Noe fo each eamen ε 0. -If you ae asked o solve fo τ 3, wha s he answe? -If you ae asked o solve fo ε 3, wha s he answe? -Queson: If you ae gven us he eamen oals. s, how would you fll n he values fo each of he obsevaons such ha he Eo SS 0. Example Answe: Remembe ha he Expemenal Eo s he falue of obsevaons eaed alke o be he same. Theefoe, f all eamens have he same value n each eplcae, he Expemenal Eo SS 0. Gven he followng nfomaon, fll n he values fo all Eo SS 0. Teamen Teamen Teamen 3 s such ha he Expemenal

6 Answe Teamen Teamen Teamen Noe n he pevous wo examples ha τ 0. Ths s ue fo all suaons. Gven H :. H 0 A : fo a leas one pa of eamens,' '.e., he sum of he eamen means dvded by he numbe of eamens equals he expemen mean. Ths defnon mples ha τ 0.. The hypohess wen above can be ewen n ems of he eamen effecs τ as: H H 0 : A τ τ. τ 0 : τ 0 fo a leas. a Thus, when we ae esng he null hypohess ha all eamens means ae he same, we ae esng a he same me he null hypohess ha all eamen effecs, τ, ae zeo. Paonng he Toal Sum of Squaes Remembe ha: τ. ε. Thus, τ ε can be ewen as:... The Analyss of Vaance s deved fom he paonng of he coeced Toal Sum of Squaes. 6

7 ] [ Squaes Sum of Toal..... a n and The las em of he equaon equals zeo because 0. ε. Thus,., whch s Toal Sum of Squaes Teamen Sum of Squaes Eo Sum of Squaes ANOVA fo Any Numbe of Teamens wh Equal Replcaon Gven he followng daa: Teamen Replcae A B C ,875 5,805 7,8 Sep. We he hypoheses o be esed : : o o H H A o H o : All hee means ae equal. H A : A leas one of he means s dffeen fom he ohe means. 7

8 Sep. Calculae he Coecon Faco. CF *3 6,8.0 Sep 3. Calculae he Toal SS ToalSS CF CF 7,08 6, Sep. Calculae he Teamen SS TRT SS. TRTSS CF , Sep 5. Calculae he Eo SS Eo SS Toal SS Teamen SS

9 Sep 6. Complee he ANOVA able Souces of vaaon Df SS MS F Teamen NS Eo Toal Sep 7. Look up Table F-values. F 0.05;,9.6 F 0.0;,9 8.0 Sep 8. Make conclusons. -Snce F-calc <.6 we fal o eec Ho: 3 a he 95% level of confdence. -Snce F-calc < 8.0 we fal o eec Ho: 3 a he 99% level of confdence Sep 9. Calculae Coeffcen of Vaaon CV. s % CV *00 Remembe ha he Eo MS s. % CV.67 *00 *3 6.9 / % *00 9

10 ANOVA fo Any Numbe of Teamens wh Unequal Replcaon Gven he followng daa: Teamen Replcae A B C D Sep. We he hypoheses o be esed. H o : 3 H A : A leas one of he means s dffeen fom one of he ohe means. Sep. Calculae he Coecon Faco CF 7 Sep 3. Calculae he Toal SS ToalSS CF CF

11 Sep. Calculae he Teamen SS TRT SS. TRTSS CF Sep 5. Calculae he Eo SS Eo SS Toal SS Teamen SS Sep 6. Complee he ANOVA able Souces of vaaon Df SS MS F Teamen ** Eo By subacon Toal Toal numbe of obsevaons Sep 7. Look up Table F-values. F 0.05;3,3 3. F 0.0;3,3 5.7 Sep 8. Make conclusons. Snce F-calc 6.39 > 3. we eec Ho: 3 a he 95% level of confdence. Snce F-calc 6.39 > 5.7 we eec Ho: 3 a he 99% level of confdence

12 Sep 9. Calculae Coeffcen of Vaaon CV. s % CV *00 Remembe ha he Eo MS s. % CV 0.05 * /.088 *00 0.8% ANOVA wh Samplng Equal Numbe of Samples Pe Expemenal Un Lnea Model k τ ε δ k Whee: k s he k h sample of he h obsevaon of he h eamen, s he populaon mean, τ s he eamen effec of he h eamen, ε s he andom eo, and δ k s he samplng eo. ANOVA able SOV Df F Teamen - Teamen MS/Expemenal Eo MS Expemenal eo Samplng Eo s- - - Toal s-

13 Facs abou ANOVA wh Samplng -Thee ae wo souces of vaaon ha conbue o he vaance appopae o compasons among eamen means.. Samplng Eo vaaon among samplng uns eaed alke σ s.. Expemenal Eo vaaon among expemenal uns eaed alke σ. s σ E -The Expemenal Eo MS s expeced o be lage han he Samplng Eo MS. -If he Expemenal Eo vaance componen s no mpoan, he Samplng Eo MS and he Expemenal Eo MS wll be of he same ode of magnude. -If he Expemenal Eo vaance componen s mpoan, he Expemenal Eo MS wll be much lage han he Samplng Eo MS. Example Tempeaue 8 o o 6 o Po numbe Po numbe Po numbe Plan Noe eamen, eplcae, and k sample. Sep. Calculae coecon faco:. s

14 Sep. Calculae he Toal SS: ToalSS k CF CF 36.5 Sep 3. Calculae he Teamen SS: TeamenSS CF s Sep. Calculae he SS Among Expemenal Uns Toal SSAEUT. SSAEUT CF s

15 Sep 5. Calculae he Expemenal Eo SS: Expemenal Eo SS SSAEUT SS TRT Sep 6. Calculae he Samplng Eo SS: Samplng Eo SS Toal SS SSAEUT Sep 7. Complee he ANOVA Table: SOV Df SS MS F Teamen * Expemenal Eo Samplng Eo s Toal s Sep 8 Look up Table F-values. F 0.05;,6 5. F 0.0;,6 0.9 Sep 8. Make conclusons. Snce F-calc 5.98 > 5. we eec Ho: a he 95% level of confdence. Snce F-calc 5.98 < 0.9 we fal o eec Ho: a he 99% level of confdence

16 ANOVA When he Numbe of Subsamples ae No Equal. ToalSS k oal# ofobsevaons df #obsevaons. TeamenSS df # eamens s oal# ofobs. k SSAEUT.. s oal# ofobs. k df # Expemenal uns SS Expemenal Eo SSAEUT SS TRT SS Samplng Eo Toal SS SSAEUT df SSAEUT df TRT df df Toal df SSAEUT df Assumpons Undelyng ANOVA Expemenal eos ae andom, ndependenly, and nomally dsbued abou a mean of zeo and wh a common vaance.e. eamen vaances ae homogenous. The above assumpon can be expess as NID0, σ. Depaue fom hs assumpon can affec boh he level of sgnfcance and he sensvy of F- o -ess o eal depaues fom H o : Ths esuls n he eecon of Ho when s ue.e. a Type I Eo moe ofen han α calls fo. The powe of he es also s educed f he assumpon of NID0, σ s volaed. Volaon of he assumpon NID0, σ wh he fxed model s usually of lle consequence because ANOVA s a vey obus echnque. Volaon of he basc assumpons of ANOVA can be nvesgaed by obsevng plos of he esduals. Resduals wll be dscussed n moe deal when Tansfomaons ae dscussed lae n he semese. 6

LATIN SQUARE DESIGN (LS) -With the Latin Square design you are able to control variation in two directions.

LATIN SQUARE DESIGN (LS) -With the Latin Square design you are able to control variation in two directions. Facts about the LS Design LATIN SQUARE DESIGN (LS) -With the Latin Squae design you ae able to contol vaiation in two diections. -Teatments ae aanged in ows and columns -Each ow contains evey teatment.

More information

3 Autocorrelation. 3.1 Time series plot. 3.2 Lagged scatterplot

3 Autocorrelation. 3.1 Time series plot. 3.2 Lagged scatterplot 3 Auocoelaon Auocoelaon efes o he coelaon of a me sees wh s own pas and fuue values. Auocoelaon s also somemes called lagged coelaon o seal coelaon, whch efes o he coelaon beween membes of a sees of numbes

More information

Modeling the Yield Curve Dynamics

Modeling the Yield Curve Dynamics FIXED-INCOME SECURITIES Chape 2 Modeling he Yield Cuve Dynamics Ouline Moivaion Inees Rae Tees Single-Faco Coninuous-Time Models Muli-Faco Coninuous-Time Models Abiage Models Moivaion Why do we Cae? Picing

More information

Valuing Long-Lived Assets

Valuing Long-Lived Assets Valuing Long-Lived Asses Olive Tabalski, 008-09-0 This chape explains how you can calculae he pesen value of cash flow. Some vey useful shocu mehods will be shown. These shocus povide a good oppouniy fo

More information

HFCC Math Lab Intermediate Algebra - 13 SOLVING RATE-TIME-DISTANCE PROBLEMS

HFCC Math Lab Intermediate Algebra - 13 SOLVING RATE-TIME-DISTANCE PROBLEMS HFCC Mah Lab Inemeiae Algeba - 3 SOLVING RATE-TIME-DISTANCE PROBLEMS The vaiables involve in a moion poblem ae isance (), ae (), an ime (). These vaiables ae elae by he equaion, which can be solve fo any

More information

An Algorithm For Factoring Integers

An Algorithm For Factoring Integers An Algothm Fo Factong Integes Yngpu Deng and Yanbn Pan Key Laboatoy of Mathematcs Mechanzaton, Academy of Mathematcs and Systems Scence, Chnese Academy of Scences, Bejng 100190, People s Republc of Chna

More information

Gravitation. Definition of Weight Revisited. Newton s Law of Universal Gravitation. Newton s Law of Universal Gravitation. Gravitational Field

Gravitation. Definition of Weight Revisited. Newton s Law of Universal Gravitation. Newton s Law of Universal Gravitation. Gravitational Field Defnton of Weght evsted Gavtaton The weght of an object on o above the eath s the gavtatonal foce that the eath exets on the object. The weght always ponts towad the cente of mass of the eath. On o above

More information

PCA vs. Varimax rotation

PCA vs. Varimax rotation PCA vs. Vamax otaton The goal of the otaton/tansfomaton n PCA s to maxmze the vaance of the new SNP (egensnp), whle mnmzng the vaance aound the egensnp. Theefoe the dffeence between the vaances captued

More information

Transformations. Computer Graphics. Types of Transformations. 2D Scaling from the origin. 2D Translations. 9/22/2011. Geometric Transformation

Transformations. Computer Graphics. Types of Transformations. 2D Scaling from the origin. 2D Translations. 9/22/2011. Geometric Transformation 9// anfomaion. Compue Gaphic Lecue anfomaion Wha i a anfomaion? Wha oe i o? anfom he cooinae / nomal veco of objec Wh ue hem? Moelling -Moving he objec o he eie locaion in he envionmen -Muliple inance

More information

Semipartial (Part) and Partial Correlation

Semipartial (Part) and Partial Correlation Semipatial (Pat) and Patial Coelation his discussion boows heavily fom Applied Multiple egession/coelation Analysis fo the Behavioal Sciences, by Jacob and Paticia Cohen (975 edition; thee is also an updated

More information

HUT, TUT, LUT, OU, ÅAU / Engineering departments Entrance examination in mathematics May 25, 2004

HUT, TUT, LUT, OU, ÅAU / Engineering departments Entrance examination in mathematics May 25, 2004 HUT, TUT, LUT, OU, ÅAU / Engineeing depamens Enane examinaion in mahemais May 5, 4 Insuions. Reseve a sepaae page fo eah poblem. Give you soluions in a lea fom inluding inemediae seps. Wie a lean opy of

More information

The Fresnel Equations and Brewster's Law

The Fresnel Equations and Brewster's Law The Fesnel Equaons and Bewse's Law Equpmen Opcal bench pvo, wo 1 mee opcal benches, geen lase a 543.5 nm, 10cm damee polazes, ecangula polaze, LX-0 phoo-deeco n opcal moun, hck acylc block, hck glass block,

More information

12/7/2011. Procedures to be Covered. Time Series Analysis Using Statgraphics Centurion. Time Series Analysis. Example #1 U.S.

12/7/2011. Procedures to be Covered. Time Series Analysis Using Statgraphics Centurion. Time Series Analysis. Example #1 U.S. Tme Seres Analyss Usng Sagraphcs Cenuron Nel W. Polhemus, CTO, SaPon Technologes, Inc. Procedures o be Covered Descrpve Mehods (me sequence plos, auocorrelaon funcons, perodograms) Smoohng Seasonal Decomposon

More information

Bending Stresses for Simple Shapes

Bending Stresses for Simple Shapes -6 Bendng Stesses fo Smple Sapes In bendng, te maxmum stess and amount of deflecton can be calculated n eac of te followng stuatons. Addtonal examples ae avalable n an engneeng andbook. Secton Modulus

More information

Continuous Compounding and Annualization

Continuous Compounding and Annualization Continuous Compounding and Annualization Philip A. Viton Januay 11, 2006 Contents 1 Intoduction 1 2 Continuous Compounding 2 3 Pesent Value with Continuous Compounding 4 4 Annualization 5 5 A Special Poblem

More information

(Semi)Parametric Models vs Nonparametric Models

(Semi)Parametric Models vs Nonparametric Models buay, 2003 Pobablty Models (Sem)Paametc Models vs Nonpaametc Models I defne paametc, sempaametc, and nonpaametc models n the two sample settng My defnton of sempaametc models s a lttle stonge than some

More information

PHYSICS 161 EXAM III: Thursday December 04, 2003 11:00 a.m.

PHYSICS 161 EXAM III: Thursday December 04, 2003 11:00 a.m. PHYS 6: Eam III Fall 003 PHYSICS 6 EXAM III: Thusda Decembe 04, 003 :00 a.m. Po. N. S. Chan. Please pn ou name and ene ou sea numbe o den ou and ou eamnaon. Suden s Pned Name: Recaon Secon Numbe: Sea Numbe:.

More information

ú Ó Á É é ú ú É ú Á Á ú É É É ú É Ó É ó É Á ú ú ó Á Á ú Ó ú Ó ú É Á ú Á ú ó ú Á ú Á É Á Á Ó É Á ú ú é ú ú ú ú Á ú ó ú Ó Á Á Á Á ú ú ú é É ó é ó ú ú ú É é ú ú ú óú ú ú Ó Á ú ö é É ú ú ú úé ú ú É É Á É

More information

Analyzing Energy Use with Decomposition Methods

Analyzing Energy Use with Decomposition Methods nalyzng nergy Use wh Decomposon Mehods eve HNN nergy Technology Polcy Dvson eve.henen@ea.org nergy Tranng Week Pars 1 h prl 213 OCD/ 213 Dscusson nergy consumpon and energy effcency? How can energy consumpon

More information

FOREIGN EXCHANGE EXPOSURE AND PRICING IN THE AUSTRALIAN EQUITIES MARKET: A FAMA AND FRENCH FRAMEWORK. Amalia Di Iorio* Robert Faff

FOREIGN EXCHANGE EXPOSURE AND PRICING IN THE AUSTRALIAN EQUITIES MARKET: A FAMA AND FRENCH FRAMEWORK. Amalia Di Iorio* Robert Faff 1 FOREIGN EXCHANGE EXPOSURE AN PRICING IN THE AUSTRALIAN EQUITIES MARKET: A FAMA AN FRENCH FRAMEWORK Amala Ioo* Robe Faff * Coespondng Auho: School of Economcs and Fnance RMIT Unvesy GPO Box 2476V Melboune,

More information

Degrees of freedom in HLM models

Degrees of freedom in HLM models Degees o eedom n HLM models The vaous degees o eedom n a HLM2/HLM3 model can be calculated accodng to Table 1 and Table 2. Table 1: Degees o Feedom o HLM2 Models Paamete/Test Statstc Degees o Feedom Gammas

More information

Electric Potential. otherwise to move the object from initial point i to final point f

Electric Potential. otherwise to move the object from initial point i to final point f PHY2061 Enched Physcs 2 Lectue Notes Electc Potental Electc Potental Dsclame: These lectue notes ae not meant to eplace the couse textbook. The content may be ncomplete. Some topcs may be unclea. These

More information

Experiment #1: Reflection, Refraction, and Dispersion

Experiment #1: Reflection, Refraction, and Dispersion Expeimen #1: Reflecion, Refacion, and Dispesion Pupose: To sudy eflecion and efacion of ligh a plane and cuved sufaces, as well as he phenomenon of dispesion. Equipmen: Ray Box wih Slis Opical Accessoies

More information

Symmetric polynomials and partitions Eugene Mukhin

Symmetric polynomials and partitions Eugene Mukhin Symmetic polynomials and patitions Eugene Mukhin. Symmetic polynomials.. Definition. We will conside polynomials in n vaiables x,..., x n and use the shotcut p(x) instead of p(x,..., x n ). A pemutation

More information

Spline. Computer Graphics. B-splines. B-Splines (for basis splines) Generating a curve. Basis Functions. Lecture 14 Curves and Surfaces II

Spline. Computer Graphics. B-splines. B-Splines (for basis splines) Generating a curve. Basis Functions. Lecture 14 Curves and Surfaces II Lecure 4 Curves and Surfaces II Splne A long flexble srps of meal used by drafspersons o lay ou he surfaces of arplanes, cars and shps Ducks weghs aached o he splnes were used o pull he splne n dfferen

More information

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,

More information

How To Change V1 Programming

How To Change V1 Programming REPORT # HOW TO REPROGRAM V1 RADAR DETECTORS IF YOU REALLY WANT TO How To ange V1 Pogamming WARNING: Impotant ada alets may be blocked by changes in factoy settings es that ae Essential To Full Potection

More information

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow

More information

Episode 401: Newton s law of universal gravitation

Episode 401: Newton s law of universal gravitation Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce

More information

An Introduction to Omega

An Introduction to Omega An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei isk-ewad chaacteistics? The Finance Development Cente 2002 1 Fom

More information

MORE ON TVM, "SIX FUNCTIONS OF A DOLLAR", FINANCIAL MECHANICS. Copyright 2004, S. Malpezzi

MORE ON TVM, SIX FUNCTIONS OF A DOLLAR, FINANCIAL MECHANICS. Copyright 2004, S. Malpezzi MORE ON VM, "SIX FUNCIONS OF A DOLLAR", FINANCIAL MECHANICS Copyrgh 2004, S. Malpezz I wan everyone o be very clear on boh he "rees" (our basc fnancal funcons) and he "fores" (he dea of he cash flow model).

More information

1. Time Value of Money 3 2. Discounted Cash Flow 35 3. Statistics and Market Returns 49 4. Probabilities 81 5. Key Formulas 109

1. Time Value of Money 3 2. Discounted Cash Flow 35 3. Statistics and Market Returns 49 4. Probabilities 81 5. Key Formulas 109 1. Time Value of Money 3 2. Discouned Cash Flow 35 3. Saisics and Make Reuns 49 4. Pobabiliies 81 5. Key Fomulas 109 Candidae Noe: This is a lenghy Sudy Session ha, along wih Sudy Session 3, you should

More information

Capacity Planning. Operations Planning

Capacity Planning. Operations Planning Operaons Plannng Capacy Plannng Sales and Operaons Plannng Forecasng Capacy plannng Invenory opmzaon How much capacy assgned o each producon un? Realsc capacy esmaes Sraegc level Moderaely long me horzon

More information

The Binomial Distribution

The Binomial Distribution The Binomial Distibution A. It would be vey tedious if, evey time we had a slightly diffeent poblem, we had to detemine the pobability distibutions fom scatch. Luckily, thee ae enough similaities between

More information

AREA COVERAGE SIMULATIONS FOR MILLIMETER POINT-TO-MULTIPOINT SYSTEMS USING STATISTICAL MODEL OF BUILDING BLOCKAGE

AREA COVERAGE SIMULATIONS FOR MILLIMETER POINT-TO-MULTIPOINT SYSTEMS USING STATISTICAL MODEL OF BUILDING BLOCKAGE Radoengneeng Aea Coveage Smulatons fo Mllmete Pont-to-Multpont Systems Usng Buldng Blockage 43 Vol. 11, No. 4, Decembe AREA COVERAGE SIMULATIONS FOR MILLIMETER POINT-TO-MULTIPOINT SYSTEMS USING STATISTICAL

More information

Skills Needed for Success in Calculus 1

Skills Needed for Success in Calculus 1 Skills Needed fo Success in Calculus Thee is much appehension fom students taking Calculus. It seems that fo man people, "Calculus" is snonmous with "difficult." Howeve, an teache of Calculus will tell

More information

Supplementary Material for EpiDiff

Supplementary Material for EpiDiff Supplementay Mateial fo EpiDiff Supplementay Text S1. Pocessing of aw chomatin modification data In ode to obtain the chomatin modification levels in each of the egions submitted by the use QDCMR module

More information

Selected Financial Formulae. Basic Time Value Formulae PV A FV A. FV Ad

Selected Financial Formulae. Basic Time Value Formulae PV A FV A. FV Ad Basc Tme Value e Fuure Value of a Sngle Sum PV( + Presen Value of a Sngle Sum PV ------------------ ( + Solve for for a Sngle Sum ln ------ PV -------------------- ln( + Solve for for a Sngle Sum ------

More information

Additional File 1 - A model-based circular binary segmentation algorithm for the analysis of array CGH data

Additional File 1 - A model-based circular binary segmentation algorithm for the analysis of array CGH data 1 Addtonal Fle 1 - A model-based ccula bnay segmentaton algothm fo the analyss of aay CGH data Fang-Han Hsu 1, Hung-I H Chen, Mong-Hsun Tsa, Lang-Chuan La 5, Ch-Cheng Huang 1,6, Shh-Hsn Tu 6, Ec Y Chuang*

More information

PRODUCTION AND INVENTORY CONTROL IN A MULTISTAGE NETWORK

PRODUCTION AND INVENTORY CONTROL IN A MULTISTAGE NETWORK MITIP6, - Sepembe, Bdape PRDUCTIN AND INVENTRY CNTR IN A MUTISTAGE NETWRK Jean-Clade Henne CNRS, ISA, 6 avene Noe Dame d ac 49 Ange, Fance E-mal: henne@laaf Abac: The dy analye a newok of enepe ha coopeae

More information

2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,

2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses, 3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects

More information

The LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero.

The LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero. Poject Decision Metics: Levelized Cost of Enegy (LCOE) Let s etun to ou wind powe and natual gas powe plant example fom ealie in this lesson. Suppose that both powe plants wee selling electicity into the

More information

Estimation and Comparison of Chained CPI-U Standard Errors With Regular CPI-U Results (2000-2001)

Estimation and Comparison of Chained CPI-U Standard Errors With Regular CPI-U Results (2000-2001) 2003 Join Saisical Meeings - Secion on Suvey eseach Mehods Esimaion and ompaison of hained PI-U Sandad Eos Wih egula PI-U esuls (2000-2001) Owen J. Shoemake U.S. Bueau of Labo Saisics, 2 Mass Ave., NE,

More information

Figure 2. So it is very likely that the Babylonians attributed 60 units to each side of the hexagon. Its resulting perimeter would then be 360!

Figure 2. So it is very likely that the Babylonians attributed 60 units to each side of the hexagon. Its resulting perimeter would then be 360! 1. What ae angles? Last time, we looked at how the Geeks intepeted measument of lengths. Howeve, as fascinated as they wee with geomety, thee was a shape that was much moe enticing than any othe : the

More information

Lecture 16: Color and Intensity. and he made him a coat of many colours. Genesis 37:3

Lecture 16: Color and Intensity. and he made him a coat of many colours. Genesis 37:3 Lectue 16: Colo and Intensity and he made him a coat of many colous. Genesis 37:3 1. Intoduction To display a pictue using Compute Gaphics, we need to compute the colo and intensity of the light at each

More information

Experiment 6: Centripetal Force

Experiment 6: Centripetal Force Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee

More information

Questions for Review. By buying bonds This period you save s, next period you get s(1+r)

Questions for Review. By buying bonds This period you save s, next period you get s(1+r) MACROECONOMICS 2006 Week 5 Semina Questions Questions fo Review 1. How do consumes save in the two-peiod model? By buying bonds This peiod you save s, next peiod you get s() 2. What is the slope of a consume

More information

Stock market performance and pension fund investment policy: rebalancing, free float, or market timing?

Stock market performance and pension fund investment policy: rebalancing, free float, or market timing? Fnal veson IJCB Sock make pefomance and penson fund nvesmen polcy: ebalancng fee floa o make mng? Jacob A. Bkke ab Dk W.G.A. Boedes a and Jan de Deu c Ocobe 27 2008 Absac hs acle examnes he mpac of sock

More information

Calculation of Sampling Weights

Calculation of Sampling Weights Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a two-stage stratfed cluster desgn. 1 The frst stage conssted of a sample

More information

SIMPLE LINEAR CORRELATION

SIMPLE LINEAR CORRELATION SIMPLE LINEAR CORRELATION Smple lnear correlaton s a measure of the degree to whch two varables vary together, or a measure of the ntensty of the assocaton between two varables. Correlaton often s abused.

More information

4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first non-zero digit to

4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first non-zero digit to . Simplify: 0 4 ( 8) 0 64 ( 8) 0 ( 8) = (Ode of opeations fom left to ight: Paenthesis, Exponents, Multiplication, Division, Addition Subtaction). Simplify: (a 4) + (a ) (a+) = a 4 + a 0 a = a 7. Evaluate

More information

Generalized Difference Sequence Space On Seminormed Space By Orlicz Function

Generalized Difference Sequence Space On Seminormed Space By Orlicz Function Ieaoa Joa of Scece ad Eee Reeach IJSER Vo Ie Decembe -4 5687 568X Geeazed Dffeece Seece Sace O Semomed Sace B Ocz Fco A.Sahaaa Aa ofeo G Ie of TechooCombaoeIda. Abac I h aewe defe he eece ace o emomed

More information

Ultraconservative Online Algorithms for Multiclass Problems

Ultraconservative Online Algorithms for Multiclass Problems Jounal of Machine Leaning Reseach 3 (2003) 951-991 Submied 2/02; Published 1/03 Ulaconsevaive Online Algoihms fo Muliclass Poblems Koby Camme Yoam Singe School of Compue Science & Engineeing Hebew Univesiy,

More information

est using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.

est using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years. 9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,

More information

BIOS American Megatrends Inc (AMI) v02.61 BIOS setup guide and manual for AM2/AM2+/AM3 motherboards

BIOS American Megatrends Inc (AMI) v02.61 BIOS setup guide and manual for AM2/AM2+/AM3 motherboards BIOS Ameican Megatends Inc (AMI) v02.61 BIOS setup guide and manual fo AM2/AM2+/AM3 motheboads The BIOS setup, also called CMOS setup, is a cucial pat of the pope setting up of a PC the BIOS (Basic Input

More information

Kalman filtering as a performance monitoring technique for a propensity scorecard

Kalman filtering as a performance monitoring technique for a propensity scorecard Kalman flerng as a performance monorng echnque for a propensy scorecard Kaarzyna Bjak * Unversy of Souhampon, Souhampon, UK, and Buro Informacj Kredyowej S.A., Warsaw, Poland Absrac Propensy scorecards

More information

Robotics and Autonomous Systems. Cross-spectral visual simultaneous localization and mapping (SLAM) with sensor handover

Robotics and Autonomous Systems. Cross-spectral visual simultaneous localization and mapping (SLAM) with sensor handover Robocs and Auonomous Sysems 61 (213) 19 28 Conens lss avalable a ScVese ScenceDec Robocs and Auonomous Sysems jounal homepage: www.elseve.com/locae/obo Coss-specal vsual smulaneous localzaon and mappng

More information

Model Question Paper Mathematics Class XII

Model Question Paper Mathematics Class XII Model Question Pape Mathematics Class XII Time Allowed : 3 hous Maks: 100 Ma: Geneal Instuctions (i) The question pape consists of thee pats A, B and C. Each question of each pat is compulsoy. (ii) Pat

More information

Gauss Law. Physics 231 Lecture 2-1

Gauss Law. Physics 231 Lecture 2-1 Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing

More information

I = Prt. = P(1+i) n. A = Pe rt

I = Prt. = P(1+i) n. A = Pe rt 11 Chapte 6 Matheatcs of Fnance We wll look at the atheatcs of fnance. 6.1 Sple and Copound Inteest We wll look at two ways nteest calculated on oney. If pncpal pesent value) aount P nvested at nteest

More information

Usefulness of the Forward Curve in Forecasting Oil Prices

Usefulness 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 information

Revision: June 12, 2010 215 E Main Suite D Pullman, WA 99163 (509) 334 6306 Voice and Fax

Revision: June 12, 2010 215 E Main Suite D Pullman, WA 99163 (509) 334 6306 Voice and Fax .3: Inucors Reson: June, 5 E Man Sue D Pullman, WA 9963 59 334 636 Voce an Fax Oerew We connue our suy of energy sorage elemens wh a scusson of nucors. Inucors, lke ressors an capacors, are passe wo-ermnal

More information

Chapter 30: Magnetic Fields Due to Currents

Chapter 30: Magnetic Fields Due to Currents d Chapte 3: Magnetic Field Due to Cuent A moving electic chage ceate a magnetic field. One of the moe pactical way of geneating a lage magnetic field (.1-1 T) i to ue a lage cuent flowing though a wie.

More information

Functions of a Random Variable: Density. Math 425 Intro to Probability Lecture 30. Definition Nice Transformations. Problem

Functions of a Random Variable: Density. Math 425 Intro to Probability Lecture 30. Definition Nice Transformations. Problem Intoduction One Function of Random Vaiables Functions of a Random Vaiable: Density Math 45 Into to Pobability Lectue 30 Let gx) = y be a one-to-one function whose deiatie is nonzeo on some egion A of the

More information

SELF-INDUCTANCE AND INDUCTORS

SELF-INDUCTANCE AND INDUCTORS MISN-0-144 SELF-INDUCTANCE AND INDUCTORS SELF-INDUCTANCE AND INDUCTORS by Pete Signell Michigan State Univesity 1. Intoduction.............................................. 1 A 2. Self-Inductance L.........................................

More information

APPLYING LINGUISTIC PROMETHEE METHOD IN INVESTMENT PORTFOLIO DECISION-MAKING

APPLYING LINGUISTIC PROMETHEE METHOD IN INVESTMENT PORTFOLIO DECISION-MAKING Inenaonal Jounal of Eleconc Bune Managemen, Vol. 9, No., pp. 39-48 (0 39 PPLYING LINGUISTI PROMETHEE METHOD IN INVESTMENT PORTFOLIO DEISION-MKING hen-tung hen *, We-Zhan Hung and Hu-Lng heng 3 Depamen

More information

Vector Algebra. Lecture programme. Engineering Maths 1.2

Vector Algebra. Lecture programme. Engineering Maths 1.2 Leue pogmme Engneeng Mh. Veo lge Conen of leue. Genel noduon. Sl nd veo. Cen omponen. Deon one. Geome epeenon. Modulu of veo. Un veo. Pllel veo.. ddon of veo: pllelogm ule; ngle lw; polgon lw; veo lw fo

More information

An iterative wave-front sensing algorithm for high-contrast imaging systems *

An iterative wave-front sensing algorithm for high-contrast imaging systems * An ieaive wave-fon sensing algoihm fo high-conas imaging sysems * Jiangpei Dou,, Deqing Ren,,,3 and Yongian Zhu, aional Asonomical Obsevaoies / anjing Insiue of Asonomical Opics & Technology, Chinese Academy

More information

Determining solar characteristics using planetary data

Determining solar characteristics using planetary data Detemining sola chaacteistics using planetay data Intoduction The Sun is a G type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this inestigation

More information

The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C

The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C Geneal Physics - PH Winte 6 Bjoen Seipel The Electic Potential, Electic Potential Enegy and Enegy Consevation Electic Potential Enegy U is the enegy of a chaged object in an extenal electic field (Unit

More information

Thank you for participating in Teach It First!

Thank you for participating in Teach It First! Thank you fo paticipating in Teach It Fist! This Teach It Fist Kit contains a Common Coe Suppot Coach, Foundational Mathematics teache lesson followed by the coesponding student lesson. We ae confident

More information

Physics HSC Course Stage 6. Space. Part 1: Earth s gravitational field

Physics HSC Course Stage 6. Space. Part 1: Earth s gravitational field Physics HSC Couse Stage 6 Space Pat 1: Eath s gavitational field Contents Intoduction... Weight... 4 The value of g... 7 Measuing g...8 Vaiations in g...11 Calculating g and W...13 You weight on othe

More information

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it. Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing

More information

Week 3-4: Permutations and Combinations

Week 3-4: Permutations and Combinations Week 3-4: Pemutations and Combinations Febuay 24, 2016 1 Two Counting Pinciples Addition Pinciple Let S 1, S 2,, S m be disjoint subsets of a finite set S If S S 1 S 2 S m, then S S 1 + S 2 + + S m Multiplication

More information

Module Availability at Regent s School of Drama, Film and Media Autumn 2016 and Spring 2017 *subject to change*

Module Availability at Regent s School of Drama, Film and Media Autumn 2016 and Spring 2017 *subject to change* Availability at Regent s School of Dama, Film and Media Autumn 2016 and Sping 2017 *subject to change* 1. Choose you modules caefully You must discuss the module options available with you academic adviso/

More information

The Role of Stock Markets in Current Account Dynamics: a Time-Series Approach

The Role of Stock Markets in Current Account Dynamics: a Time-Series Approach WP/04/50 The Role of Sock Make n Cuen Accoun Dynamc: a Tme-See Appoach Benoî Meceeau 2004 Inenaonal Moneay Fund WP/04/50 IMF Wokng Pape Aa and Pacfc Depamen The Role of Sock Make n Cuen Accoun Dynamc:

More information

Derivative Securities: Lecture 7 Further applications of Black-Scholes and Arbitrage Pricing Theory. Sources: J. Hull Avellaneda and Laurence

Derivative 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 information

Converting knowledge Into Practice

Converting knowledge Into Practice Conveting knowledge Into Pactice Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 2 0 1 0 C o p y i g h t s V l a d i m i R i b a k o v 1 Disclaime and Risk Wanings Tading

More information

MEAN SEPARATION TESTS (LSD AND Tukey s Procedure) is rejected, we need a method to determine which means are significantly different from the others.

MEAN SEPARATION TESTS (LSD AND Tukey s Procedure) is rejected, we need a method to determine which means are significantly different from the others. MEAN SEPARATION TESTS (LSD AND Tukey s Procedure) If Ho 1 2... n is rejected, we need a method to determine which means are significantly different from the others. We ll look at three separation tests

More information

Pedro M. Castro Iiro Harjunkoski Ignacio E. Grossmann. Lisbon, Portugal Ladenburg, Germany Pittsburgh, USA

Pedro M. Castro Iiro Harjunkoski Ignacio E. Grossmann. Lisbon, Portugal Ladenburg, Germany Pittsburgh, USA Pedro M. Casro Iro Harjunkosk Ignaco E. Grossmann Lsbon Porugal Ladenburg Germany Psburgh USA 1 Process operaons are ofen subjec o energy consrans Heang and coolng ules elecrcal power Avalably Prce Challengng

More information

Daily Correlation and Volatility Dynamics between National Stock Markets with Non-overlapping Trading Hours

Daily Correlation and Volatility Dynamics between National Stock Markets with Non-overlapping Trading Hours Daly Coelaon and Volaly Dynamcs beween Naonal Sock Makes w Non-ovelang adng Hous Yguo Sun Deamen of Economcs Unvesy of Guel Guel ON NG2W Canada Febuay 2008 (Pelmnay Daf) bsac s ae sudes e daly coelaon

More information

Problem Set # 9 Solutions

Problem Set # 9 Solutions Poblem Set # 9 Solutions Chapte 12 #2 a. The invention of the new high-speed chip inceases investment demand, which shifts the cuve out. That is, at evey inteest ate, fims want to invest moe. The incease

More information

Define What Type of Trader Are you?

Define What Type of Trader Are you? Define What Type of Tade Ae you? Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 1 Disclaime and Risk Wanings Tading any financial maket involves isk. The content of this

More information

Multiple criteria network models for project management

Multiple criteria network models for project management Mulple cea newo model fo pojec managemen Víceeální í oé modely pojeoém øízení T. ŠUBRT Czech Uney of Agculue, Pague, Czech Republc Abac: The am of he pape o peen one pobly of how o model and ole a eouce

More information

Fixed Income Attribution. Remco van Eeuwijk, Managing Director Wilshire Associates Incorporated 15 February 2006

Fixed Income Attribution. Remco van Eeuwijk, Managing Director Wilshire Associates Incorporated 15 February 2006 Fxed Incoe Arbuon eco van Eeuwk Managng Drecor Wlshre Assocaes Incorporaed 5 February 2006 Agenda Inroducon Goal of Perforance Arbuon Invesen Processes and Arbuon Mehodologes Facor-based Perforance Arbuon

More information

PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 12

PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 12 14 The Ch-squared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed

More information

Financing Terms in the EOQ Model

Financing Terms in the EOQ Model Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad

More information

PY1052 Problem Set 8 Autumn 2004 Solutions

PY1052 Problem Set 8 Autumn 2004 Solutions PY052 Poblem Set 8 Autumn 2004 Solutions H h () A solid ball stats fom est at the uppe end of the tack shown and olls without slipping until it olls off the ight-hand end. If H 6.0 m and h 2.0 m, what

More information

- Models: - Classical: : Mastermodel (clay( Curves. - Example: - Independent variable t

- Models: - Classical: : Mastermodel (clay( Curves. - Example: - Independent variable t Compue Gaphcs Geomec Moelg Iouco - Geomec Moelg (GM) sce e of 96 - Compue asssace fo - Desg: CAD - Maufacug: : CAM - Moels: - Classcal: : Masemoel (cla( cla, poopes,, Mock-up) - GM: mahemacal escpo fo

More information

Saturated and weakly saturated hypergraphs

Saturated and weakly saturated hypergraphs Satuated and weakly satuated hypegaphs Algebaic Methods in Combinatoics, Lectues 6-7 Satuated hypegaphs Recall the following Definition. A family A P([n]) is said to be an antichain if we neve have A B

More information

Signal Rectification

Signal Rectification 9/3/25 Signal Recificaion.doc / Signal Recificaion n imporan applicaion of juncion diodes is signal recificaion. here are wo ypes of signal recifiers, half-wae and fullwae. Le s firs consider he ideal

More information

Estimating intrinsic currency values

Estimating intrinsic currency values Cung edge Foregn exchange Esmang nrnsc currency values Forex marke praconers consanly alk abou he srenghenng or weakenng of ndvdual currences. In hs arcle, Jan Chen and Paul Dous presen a new mehodology

More information

What Explains Superior Retail Performance?

What Explains Superior Retail Performance? Wha Explans Superor Real Performance? Vshal Gaur, Marshall Fsher, Ananh Raman The Wharon School, Unversy of Pennsylvana vshal@grace.wharon.upenn.edu fsher@wharon.upenn.edu Harvard Busness School araman@hbs.edu

More information

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur Module 4 Single-phase A circuis ersion EE T, Kharagpur esson 5 Soluion of urren in A Series and Parallel ircuis ersion EE T, Kharagpur n he las lesson, wo poins were described:. How o solve for he impedance,

More information

The force between electric charges. Comparing gravity and the interaction between charges. Coulomb s Law. Forces between two charges

The force between electric charges. Comparing gravity and the interaction between charges. Coulomb s Law. Forces between two charges The foce between electic chages Coulomb s Law Two chaged objects, of chage q and Q, sepaated by a distance, exet a foce on one anothe. The magnitude of this foce is given by: kqq Coulomb s Law: F whee

More information

Reduced Pattern Training Based on Task Decomposition Using Pattern Distributor

Reduced Pattern Training Based on Task Decomposition Using Pattern Distributor > PNN05-P762 < Reduced Patten Taining Based on Task Decomposition Using Patten Distibuto Sheng-Uei Guan, Chunyu Bao, and TseNgee Neo Abstact Task Decomposition with Patten Distibuto (PD) is a new task

More information

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 Voltage ( = Electic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage is

More information

Najat El-Mekkaoui de Freitas and Joaquim Oliveira Martins Health, Pension Benefits and Longevity How They Affect Household Savings?

Najat El-Mekkaoui de Freitas and Joaquim Oliveira Martins Health, Pension Benefits and Longevity How They Affect Household Savings? Naja El-Mekkaou de Feas and Joaqum Olvea Mans Healh, Penson Benefs and Longevy How They Affec Household Savngs? DP 0/203-046 HEALTH, PENSION BENEFITS AND LONGEVITY: HOW THEY AFFECT HOUSEHOLD SAVINGS? Naja

More information

12.1. FÖRSTER RESONANCE ENERGY TRANSFER

12.1. FÖRSTER RESONANCE ENERGY TRANSFER ndei Tokmakoff, MIT epatment of Chemisty, 3/5/8 1-1 1.1. FÖRSTER RESONNCE ENERGY TRNSFER Föste esonance enegy tansfe (FR) efes to the nonadiative tansfe of an electonic excitation fom a dono molecule to

More information

How To Calculate Backup From A Backup From An Oal To A Daa

How To Calculate Backup From A Backup From An Oal To A Daa 6 IJCSNS Inernaonal Journal of Compuer Scence and Nework Secury, VOL.4 No.7, July 04 Mahemacal Model of Daa Backup and Recovery Karel Burda The Faculy of Elecrcal Engneerng and Communcaon Brno Unversy

More information