An Analysis of Brand Selection

Size: px
Start display at page:

Download "An Analysis of Brand Selection"

Transcription

1 (IJCS) Itetol Joul of dvced Comute Scece d lctos Vol. o. 8 lss of Bd Selecto Kuho Tkesu College of Busess dmstto Tokoh Uvest 5 Oouch Fuj Ct Shuok -8 J uk Hguch Fcult of Busess dmstto Setsu Uvest -8 Iked-kmch eg Osk J stct It s ofte oseved tht cosumes select ue clss d he the u et tme. Suose tht fome ug dt d cuet ug dt e gtheed. lso suose tht ue d s locted ue the vle. The the tsto mt ecomes ue tgul mt ude the suosto tht fome ug vles e set ut d cuet ug vles e set outut. Tkesu et l. led the d selecto d ts mt stuctue efoe. I tht e oducts of oe gee e led. I ths e d selecto mog multle gee d ts mt stuctue e led. Tkg utomole fo emle custome d selecto fom com to B o com to C c e mde cle utlg ove stted method. We c cofm ot ol the efeece shft mog ds ut lso the efeece shft mog comes. Ths eles uldg mketg stteg fo utomole com much ese. lg such stuctue ovdes useful lctos. Thus ths oosed och eles to mke effectve mketg l d/o estlshg e d. Keods d selecto; mt stuctue; d osto I. ITODUCTIO Mketg lss s oe of the eve edg themes ecuse thee se lots of evets d e ted the mket d socet. Thee e m themes to e vestgted d the lses m e utled fo mketg l etc. I ths e e focus o the d selecto cosumes. It s ofte oseved tht cosumes select ue clss d he the u et tme fte the e oed to use cuet d. Suose tht fome ug dt d cuet ug dt e gtheed. lso suose tht ue d s locted ue the vle. The the tsto mt ecomes ue tgul mt ude the suosto tht fome ug vles e set ut d cuet ug vles e set outut. The lss of the d selecto the sme d gou s led Tkesu et l. [6]. I ths e e ed ths scheme to oducts of multle gees. Fo emle e cosde the cse of ecklce. If she s ccustomed to use ecklce she ould u hghe ced ecklce. O the othe hd she m u celet o eg fo he totl coodto fsho. Heg fom the etle oth c e see selectg ue clss d d selectg othe gee oduct. Theefoe ths lss s ve megful fo the ctcl use hch occus ctull. If tsto mt s detfed e c mke vous lses usg t d s-ste foecstg c e eecuted. Uless les fo oducts otce ts d osto hethe t s ue o loe th othe oducts mt stuctue mkes t ossle to detf those clcultg cosumes ctvtes fo d selecto. Thus ths oosed och mkes t effectve to eecute mketg l d/o estlsh e d. Qutttve lss coceg d selecto hs ee eecuted mk [5] Tkhsh et l.[]. mk[5] emed uchsg ocess Mkov Tsto Polt th the ut of dvetsg eese. Tkhsh et l.[] mde lss the Bd Selecto Polt model usg logstcs dstuto. Tkesu et l.[6] led the efeece shft of custome d selecto the cse of utomole. Tkesu et l.[] led the efeece shft of custome d selecto fo sgle d gou. I ths e e t to ed ths scheme to oducts of multle gees d vous lses s eecuted. ctull ths scheme c ofte e see. Such esech s ute e oe. Heefte mt stuctue fo sgle d gou s clfed fo the selecto of d secto. Eso to multle d selecto s eecuted d led secto. s-ste foecstg s stted secto. umecl clculto s eecuted secto 5. lcto of ths method s eteded secto 6. II. BD SELECTIO D ITS MTI STUCTUE. Ue shft of Bd selecto o suose tht s the most ue clss d s the secod ue clss d d s the loest clss d. Cosume s ehvo of selectg d mght e etc. mght e fe. Suose tht s cuet ug vle d s evous ug vle. Shft to s eecuted fom o. Theefoe s stted the follog euto. j eesets the tsto olt fom j -th to -th d. Smll d.jcs.thes.og 8 P g e

2 (IJCS) Itetol Joul of dvced Comute Scece d lctos Vol. o. 8 8 P g e.jcs.thes.og These e e-tte s follos. () Set The s eeseted s follos. () Hee s ue tgul mt. To eme ths geetg the follog dt hch ll cosst of the dt hch the tsto s mde fom loe d to ue d () () Pmete c e estmted usg lest sue method. Suose ε (5) Whee d mme follog J M J T ε ε (6)  Whch estmted vlue s of s oted s follos. ˆ T T () I the dt gou hch ll cosst of the dt hch the tsto s mde fom loe d to ue d estmted vlue  should e ue tgul mt. If the follog dt hch shft to loe d e dded ol fe euto () d ()  ould cot mute tems the loe t of tgle. B. Sotg d kg e-gg o I geel dt vles m ot e ode s. I tht cse lge d smll vlue le sctteed Â. But e-gg ths e c set ode shftg o. The lge vlue ts e gtheed the ue tgul mt d the smll vlue ts e gtheed the loe tgul mt.   (8) C. Mt stuctue ude the cse skg temedte clss d s sked It s ofte oseved tht some cosumes select the most ue clss d fom the most loe clss d d sk selectg the temedte clss d. We suose v ds (suose the e ld fom ue osto to loe osto s v ). I the ove cse selecto shfts ould e: v v Suose the do ot shft to fom to fom d to fom the Mt stuctue ould e s follos. Shftg o

3 (IJCS) Itetol Joul of dvced Comute Scece d lctos Vol. o. 8 8 P g e.jcs.thes.og v v 55 5 () We cofm ths the umecl emle secto. III. EPSIO OF THE MODEL TO MULTIPLE GEE PODUCTS Edg E.() to multle gee oducts e ot the follog eutos. Fst of ll e stte the geeled model of E.(). () Whee () () Hee If the d selecto s eecuted tods ue clss the ecomes s follos. () Edg ove eutos to oducts of gees e ot the follog eutos. Whee () (5) (6)

4 (IJCS) Itetol Joul of dvced Comute Scece d lctos Vol. o. 8 e-tg E.() s : W W () The the tsto mt s deved s follos the sme th E.(). T T ˆ W W W W (8) W W Hee W () () W ε () ε () If the d selecto s eecuted tods ue clss d the sme gee the tsto mt fo emle ecome ue tgul mt s c e see. Suose s celet s eg d s ecklce. If e ol see e c eme hethe thee s ue d shft. But thee s cse tht d selecto s eecuted tods othe gee oducts. Thee occus d selecto shft fom cet d level of to cet d level of o. Fo emle suose thee e fve levels ech d the levels clude fom ottom to to d level. I tht cse f thee s d selecto shft fom the mddle d level to othe gee oduct e c ot teestg esult emg ho the d selecto shft s eecuted tod the sme level o ue level of othe gee oduct. If e c see the ted of d selecto shft e c foesee the d selecto shft tods othe gee d. etle c utle the esult of ths to mke effectve mketg l. We cofm ths the smle umecl emle 5. et e eme the cse d gous. Mtces e comosed Block Mt. IV. S-STEP FOECSTIG o e see E.() tme sees. Set t tme s : () The E.() c e e-stted s : ().jcs.thes.og 85 P g e

5 (IJCS) Itetol Joul of dvced Comute Scece d lctos Vol. o. 8 Whee suff s tte the loe t of ght hd sde ecuse thee ses multle the euto of foecstg. s -ste foecstg s eecuted the follog euto. s s s s V. UMEICL EMPLE (5) We cosde the cse of. Suose thee e follog custome efeece shfts. Fom the loe level of to mddle o ue level of Fom the loe level of to loe mddle o ue level of Fom the mddle level of to mddle o ue level of Fom the ue level of to ue level of Fom the loe level of to loe mddle o ue level of Fom the mddle level of to mddle o ue level of Fom the ue level of to ue level of d lso suose tht thee e efeece shfts hch st t the sme level. Fo smlct efeece shft of sts t the sme level th d. I these cses e c ssume tht ech lock mt of E.() ecomes s follos. :Dgol mt : :Ue tgul mt o e suose custome efeece shfts s follos.. Jum fom th to d k of : evets. Jum fom th to d k of : evet. Jum fom d to st k of : evets. St t th k of : evets 5. St t d k of : evets 6. St t d k of : evets. St t st k of : evets 8. Jum fom th k of to d k of : evet. Jum fom th k of to d k of : evet. Jum fom d k of to st k of : evet. St t th k of : evets. St t d k of : evets. St t d k of : evet. St t st k of : evets 5. Jum fom th k of to d k of : evets 6. Jum fom d k of to st k of : evets. St t th k of : evets 8. St t d k of : evets. St t d k of : evets. St t st k of : evet. Jum fom th k of to th k of : evets. Jum fom th k of to d k of : evets. Jum fom d k of to d k of : evets. Jum fom st k of to st k of : evet 5. Jum fom st k of to st k of : evet 6. Jum fom d k of to d k of : evets. Jum fom d k of to d k of : evet 8. Jum fom d k of to d k of : evets. Jum fom d k of to st k of : evet The the vecto W W fo cse - fo emle e eessed s follos.. W W. W W Susttutg these to E.(8) e c ot E.(6)..jcs.thes.og 86 P g e

6 (IJCS) Itetol Joul of dvced Comute Scece d lctos Vol. o. 8 8 P g e.jcs.thes.og (6) Wtchg ths e c cofm follog fetues s stted efoe. of E.() ecme s follos. :Dgol mt : :Ue tgul mt Tkg utomole fo emle custome d selecto fom com to B o com to C c e mde cle utlg ove stted method. We c cofm ot ol the efeece shft mog ds ut lso the efeece shft mog comes. Ths eles uldg mketg stteg fo utomole com much ese. VI. COCLUSIO Cosumes ofte u hghe gde d oducts s the e ccustomed o oed to use cuet d oducts the hve. I ths e mt stuctue s clfed he d selecto s eecuted tod hghe gde d. Edg d selecto fom sgle d gou to multle gee d gou e could mke much moe euste d multdmesol lss. d fomulto of eteso to the d gous s eecuted usg Block Mt. s -ste foecst model s lso fomulted. I umecl emle mt stuctue s hothess s vefed coceg d selecto mog multle ds. If e c see the ted of d selecto shft e c foesee the d selecto shft tods othe gee d. etle c utle the esult of ths to mke effectve mketg l. Such esech s

7 uestoe vestgto of cosumes ctvt utomole uchsg should e eecuted the e futue to vef oted esults. EFEECES [] ked. Mgemet Bds Eut Smo & Schuste US. [] KthH. Mketg Scece (I Jese) Toko Uvest Pess 8. [] KthH.Sugt. Cuet movemet of Mketg Scece (I Jese) Oetos esech ; : 8-88 [] Tkhsh. T.Tkhsh Buldg Bd Selecto Model Cosdeg Cosumes olt to Bd (I Jese) J Idustl Mgemet ssocto ; 5(5): - [5] mkh. Qutttve esech Coceg dvetsg d Bd Shft (I Jese) Mketg Scece Chk-Shoo Pulshg 8. [6] TkesuK..Hguch lss of the Pefeece Shft of Custome Bd Selecto mog Multle Gees of utomole d Its Mt Stuctue Joul of Commucto d Comute ; (): - 5 [] TkesuK..Hguch lss of the Pefeece Shft of Custome Bd Selecto Itetol Joul of Comuttol Scece ; (): - (IJCS) Itetol Joul of dvced Comute Scece d lctos Vol. o. 8.jcs.thes.og 88 P g e

Summary: Binomial Expansion...! r. where

Summary: Binomial Expansion...! r. where Summy: Biomil Epsio 009 M Teo www.techmejcmth-sg.wes.com ) Re-cp of Additiol Mthemtics Biomil Theoem... whee )!!(! () The fomul is ville i MF so studets do ot eed to memoise it. () The fomul pplies oly

More information

Difference Sets of Null Density Subsets of

Difference Sets of Null Density Subsets of dvces Pue Mthetcs 95-99 http://ddoog/436/p37 Pulshed Ole M (http://wwwscrpog/oul/p) Dffeece Sets of Null Dest Susets of Dwoud hd Dsted M Hosse Deptet of Mthetcs Uvest of Gul Rsht I El: hd@gulc h@googlelco

More information

Chapter Linear Regression

Chapter Linear Regression Chpte 6.3 Le Regesso Afte edg ths chpte, ou should be ble to. defe egesso,. use sevel mmzg of esdul cte to choose the ght cteo, 3. deve the costts of le egesso model bsed o lest sques method cteo,. use

More information

Studying the Problems of Multiple Integrals with Maple Chii-Huei Yu

Studying the Problems of Multiple Integrals with Maple Chii-Huei Yu Itetol Joul of Resech (IJR) e-issn: 2348-6848, - ISSN: 2348-795X Volume 3, Issue 5, Mch 26 Avlble t htt://tetoljoulofesechog Studyg the Poblems of Multle Itegls wth Mle Ch-Hue Yu Detmet of Ifomto Techology,

More information

Chapter 17. Least Square Regression

Chapter 17. Least Square Regression The Islmc Uvest of Gz Fcult of Egeeg Cvl Egeeg Deptmet Numecl Alss ECIV 336 Chpte 7 Lest que Regesso Assocte Pof. Mze Abultef Cvl Egeeg Deptmet, The Islmc Uvest of Gz Pt 5 - CURVE FITTING Descbes techques

More information

Parametric Methods. Autoregressive (AR) Moving Average (MA) Autoregressive - Moving Average (ARMA) LO-2.5, P-13.3 to 13.4 (skip

Parametric Methods. Autoregressive (AR) Moving Average (MA) Autoregressive - Moving Average (ARMA) LO-2.5, P-13.3 to 13.4 (skip Pmeti Methods Autoegessive AR) Movig Avege MA) Autoegessive - Movig Avege ARMA) LO-.5, P-3.3 to 3.4 si 3.4.3 3.4.5) / Time Seies Modes Time Seies DT Rdom Sig / Motivtio fo Time Seies Modes Re the esut

More information

SEPTIC B-SPLINE COLLOCATION METHOD FOR SIXTH ORDER BOUNDARY VALUE PROBLEMS

SEPTIC B-SPLINE COLLOCATION METHOD FOR SIXTH ORDER BOUNDARY VALUE PROBLEMS VOL. 5 NO. JULY ISSN 89-8 RN Joul of Egeeg d ppled Sceces - s Resech ulshg Netok RN. ll ghts eseved..pouls.com SETIC -SLINE COLLOCTION METHOD FOR SIXTH ORDER OUNDRY VLUE ROLEMS K.N.S. Ks Vsdhm d. Mul Ksh

More information

SOME REMARKS ON HORIZONTAL, SLANT, PARABOLIC AND POLYNOMIAL ASYMPTOTE

SOME REMARKS ON HORIZONTAL, SLANT, PARABOLIC AND POLYNOMIAL ASYMPTOTE D I D A C T I C S O F A T H E A T I C S No (4) 3 SOE REARKS ON HORIZONTAL, SLANT, PARABOLIC AND POLYNOIAL ASYPTOTE Tdeusz Jszk Abstct I the techg o clculus, we cosde hozotl d slt symptote I ths ppe the

More information

CBSE , ˆj. cos CBSE_2015_SET-1. SECTION A 1. Given that a 2iˆ ˆj. We need to find. 3. Consider the vector equation of the plane.

CBSE , ˆj. cos CBSE_2015_SET-1. SECTION A 1. Given that a 2iˆ ˆj. We need to find. 3. Consider the vector equation of the plane. CBSE CBSE SET- SECTION. Gv tht d W d to fd 7 7 Hc, 7 7 7. Lt,. W ow tht.. Thus,. Cosd th vcto quto of th pl.. z. - + z = - + z = Thus th Cts quto of th pl s - + z = Lt d th dstc tw th pot,, - to th pl.

More information

Describes techniques to fit curves (curve fitting) to discrete data to obtain intermediate estimates.

Describes techniques to fit curves (curve fitting) to discrete data to obtain intermediate estimates. CURVE FITTING Descbes techques to ft cuves (cuve fttg) to dscete dt to obt temedte estmtes. Thee e two geel ppoches fo cuve fttg: Regesso: Dt ehbt sgfct degee of sctte. The stteg s to deve sgle cuve tht

More information

Chapter 7. Kleene s Theorem. 7.1 Kleene s Theorem. The following theorem is the most important and fundamental result in the theory of FA s:

Chapter 7. Kleene s Theorem. 7.1 Kleene s Theorem. The following theorem is the most important and fundamental result in the theory of FA s: Chpte 7 Kleene s Theoem 7.1 Kleene s Theoem The following theoem is the most impotnt nd fundmentl esult in the theoy of FA s: Theoem 6 Any lnguge tht cn e defined y eithe egul expession, o finite utomt,

More information

GCE AS and A Level MATHEMATICS FORMULA BOOKLET. From September Issued WJEC CBAC Ltd.

GCE AS and A Level MATHEMATICS FORMULA BOOKLET. From September Issued WJEC CBAC Ltd. GCE AS d A Level MATHEMATICS FORMULA BOOKLET Fom Septeme 07 Issued 07 Pue Mthemtcs Mesuto Suce e o sphee = 4 Ae o cuved suce o coe = heght slt Athmetc Sees S = + l = [ + d] Geometc Sees S = S = o < Summtos

More information

BINOMIAL THEOREM SOLUTION. 1. (D) n. = (C 0 + C 1 x +C 2 x C n x n ) (1+ x+ x 2 +.)

BINOMIAL THEOREM SOLUTION. 1. (D) n. = (C 0 + C 1 x +C 2 x C n x n ) (1+ x+ x 2 +.) BINOMIAL THEOREM SOLUTION. (D) ( + + +... + ) (+ + +.) The coefficiet of + + + +... + fo. Moeove coefficiet of is + + + +... + if >. So. (B)... e!!!! The equied coefficiet coefficiet of i e -.!...!. (A),

More information

CBSE SAMPLE PAPER SOLUTIONS CLASS-XII MATHS SET-2 CBSE , ˆj. cos. SECTION A 1. Given that a 2iˆ ˆj. We need to find

CBSE SAMPLE PAPER SOLUTIONS CLASS-XII MATHS SET-2 CBSE , ˆj. cos. SECTION A 1. Given that a 2iˆ ˆj. We need to find BSE SMLE ER SOLUTONS LSS-X MTHS SET- BSE SETON Gv tht d W d to fd 7 7 Hc, 7 7 7 Lt, W ow tht Thus, osd th vcto quto of th pl z - + z = - + z = Thus th ts quto of th pl s - + z = Lt d th dstc tw th pot,,

More information

The formulae in this booklet have been arranged according to the unit in which they are first

The formulae in this booklet have been arranged according to the unit in which they are first Fomule Booklet Fomule Booklet The fomule ths ooklet hve ee ge og to the ut whh the e fst toue. Thus te sttg ut m e eque to use the fomule tht wee toue peeg ut e.g. tes sttg C mght e epete to use fomule

More information

Fredholm Type Integral Equations with Aleph-Function. and General Polynomials

Fredholm Type Integral Equations with Aleph-Function. and General Polynomials Iteto Mthetc Fou Vo. 8 3 o. 989-999 HIKI Ltd.-h.co Fedho Te Iteg uto th eh-fucto d Gee Poo u J K.J. o Ittute o Mgeet tude & eech Mu Id u5@g.co Kt e K.J. o Ittute o Mgeet tude & eech Mu Id dehuh_3@hoo.co

More information

Certain Expansion Formulae Involving a Basic Analogue of Fox s H-Function

Certain Expansion Formulae Involving a Basic Analogue of Fox s H-Function vlle t htt:vu.edu l. l. Mth. ISSN: 93-9466 Vol. 3 Iue Jue 8. 8 36 Pevouly Vol. 3 No. lcto d led Mthetc: Itetol Joul M Cet Exo Foule Ivolvg c logue o Fox -Fucto S.. Puoht etet o c-scece Mthetc College o

More information

Generalisation on the Zeros of a Family of Complex Polynomials

Generalisation on the Zeros of a Family of Complex Polynomials Ieol Joul of hemcs esech. ISSN 976-584 Volume 6 Numbe 4. 93-97 Ieol esech Publco House h://www.house.com Geelso o he Zeos of Fmly of Comlex Polyomls Aee sgh Neh d S.K.Shu Deme of hemcs Lgys Uvesy Fdbd-

More information

Advanced Higher Maths: Formulae

Advanced Higher Maths: Formulae Advced Highe Mths: Fomule Advced Highe Mthemtics Gee (G): Fomule you solutely must memoise i ode to pss Advced Highe mths. Rememe you get o fomul sheet t ll i the em! Ame (A): You do t hve to memoise these

More information

A Primer on Portfolio Theory

A Primer on Portfolio Theory Pt I: Some Bscs A Pme on Potolo Theoy The ottom lne th otolo constucton s lenng ho to del th uncetnty. To egn, let s stt th some dentons: A ndom vle s nume ssocted th n outcome tht s uncetn. Fo exmle,

More information

7.5-Determinants in Two Variables

7.5-Determinants in Two Variables 7.-eteminnts in Two Vibles efinition of eteminnt The deteminnt of sque mti is el numbe ssocited with the mti. Eve sque mti hs deteminnt. The deteminnt of mti is the single ent of the mti. The deteminnt

More information

Week 8. Topic 2 Properties of Logarithms

Week 8. Topic 2 Properties of Logarithms Week 8 Topic 2 Popeties of Logithms 1 Week 8 Topic 2 Popeties of Logithms Intoduction Since the esult of ithm is n eponent, we hve mny popeties of ithms tht e elted to the popeties of eponents. They e

More information

Elastic-Plastic Transition of Transversely. Isotropic Thin Rotating Disc

Elastic-Plastic Transition of Transversely. Isotropic Thin Rotating Disc otempoy Egeeg Sceces, Vol., 9, o. 9, 4-44 Elstc-Plstc sto o svesely Isotopc h ottg Dsc Sjeev Shm d Moj Sh Deptmet o Mthemtcs JII Uvesty, -, Secto 6 Nod-7, UP, Id sjt@edml.com, moj_sh7@edml.com stct Elstc-plstc

More information

The formulae in this booklet have been arranged according to the unit in which they are first

The formulae in this booklet have been arranged according to the unit in which they are first Fomule Booklet Fomule Booklet The fomule ths ooklet hve ee ge ccog to the ut whch the e fst touce. Thus cte sttg ut m e eque to use the fomule tht wee touce peceg ut e.g. ctes sttg C mght e epecte to use

More information

EXERCISE - 01 CHECK YOUR GRASP

EXERCISE - 01 CHECK YOUR GRASP EXERISE - 0 HEK YOUR GRASP 3. ( + Fo sum of coefficiets put ( + 4 ( + Fo sum of coefficiets put ; ( + ( 4. Give epessio c e ewitte s 7 4 7 7 3 7 7 ( 4 3( 4... 7( 4 7 7 7 3 ( 4... 7( 4 Lst tem ecomes (4

More information

( ) D x ( s) if r s (3) ( ) (6) ( r) = d dr D x

( ) D x ( s) if r s (3) ( ) (6) ( r) = d dr D x SIO 22B, Rudnick dpted fom Dvis III. Single vile sttistics The next few lectues e intended s eview of fundmentl sttistics. The gol is to hve us ll speking the sme lnguge s we move to moe dvnced topics.

More information

Mathematical Statistics

Mathematical Statistics 7 75 Ode Sttistics The ode sttistics e the items o the dom smple ed o odeed i mitude om the smllest to the lest Recetl the impotce o ode sttistics hs icesed owi to the moe equet use o opmetic ieeces d

More information

Keywords: Heptic non-homogeneous equation, Pyramidal numbers, Pronic numbers, fourth dimensional figurate numbers.

Keywords: Heptic non-homogeneous equation, Pyramidal numbers, Pronic numbers, fourth dimensional figurate numbers. [Gol 5: M 0] ISSN: 77-9655 IJEST INTENTIONL JOUNL OF ENGINEEING SCIENCES & ESECH TECHNOLOGY O the Hetc No-Hoogeeous Euto th Four Ukos z 6 0 M..Gol * G.Suth S.Vdhlksh * Dertet of MthetcsShrt Idr Gdh CollegeTrch

More information

5 - Determinants. r r. r r. r r. r s r = + det det det

5 - Determinants. r r. r r. r r. r s r = + det det det 5 - Detemts Assote wth y sque mtx A thee s ume lle the etemt of A eote A o et A. Oe wy to efe the etemt, ths futo fom the set of ll mtes to the set of el umes, s y the followg thee popetes. All mtes elow

More information

Class Summary. be functions and f( D) , we define the composition of f with g, denoted g f by

Class Summary. be functions and f( D) , we define the composition of f with g, denoted g f by Clss Summy.5 Eponentil Functions.6 Invese Functions nd Logithms A function f is ule tht ssigns to ech element D ectly one element, clled f( ), in. Fo emple : function not function Given functions f, g:

More information

EECE 260 Electrical Circuits Prof. Mark Fowler

EECE 260 Electrical Circuits Prof. Mark Fowler EECE 60 Electicl Cicuits Pof. Mk Fowle Complex Numbe Review /6 Complex Numbes Complex numbes ise s oots of polynomils. Definition of imginy # nd some esulting popeties: ( ( )( ) )( ) Recll tht the solution

More information

Advanced Higher Maths: Formulae

Advanced Higher Maths: Formulae : Fomule Gee (G): Fomule you bsolutely must memoise i ode to pss Advced Highe mths. Remembe you get o fomul sheet t ll i the em! Ambe (A): You do t hve to memoise these fomule, s it is possible to deive

More information

Mark Scheme (Results) January 2008

Mark Scheme (Results) January 2008 Mk Scheme (Results) Jnuy 00 GCE GCE Mthemtics (6679/0) Edecel Limited. Registeed in Englnd nd Wles No. 4496750 Registeed Office: One90 High Holbon, London WCV 7BH Jnuy 00 6679 Mechnics M Mk Scheme Question

More information

Language Processors F29LP2, Lecture 5

Language Processors F29LP2, Lecture 5 Lnguge Pocessos F29LP2, Lectue 5 Jmie Gy Feuy 2, 2014 1 / 1 Nondeteministic Finite Automt (NFA) NFA genelise deteministic finite utomt (DFA). They llow sevel (0, 1, o moe thn 1) outgoing tnsitions with

More information

10 Statistical Distributions Solutions

10 Statistical Distributions Solutions Communictions Engineeing MSc - Peliminy Reding 1 Sttisticl Distiutions Solutions 1) Pove tht the vince of unifom distiution with minimum vlue nd mximum vlue ( is ) 1. The vince is the men of the sques

More information

PROGRESSION AND SERIES

PROGRESSION AND SERIES INTRODUCTION PROGRESSION AND SERIES A gemet of umbes {,,,,, } ccodig to some well defied ule o set of ules is clled sequece Moe pecisely, we my defie sequece s fuctio whose domi is some subset of set of

More information

2. Elementary Linear Algebra Problems

2. Elementary Linear Algebra Problems . Eleety e lge Pole. BS: B e lge Suoute (Pog pge wth PCK) Su of veto opoet:. Coputto y f- poe: () () () (3) N 3 4 5 3 6 4 7 8 Full y tee Depth te tep log()n Veto updte the f- poe wth N : ) ( ) ( ) ( )

More information

= y and Normed Linear Spaces

= y and Normed Linear Spaces 304-50 LINER SYSTEMS Lectue 8: Solutos to = ad Nomed Lea Spaces 73 Fdg N To fd N, we eed to chaacteze all solutos to = 0 Recall that ow opeatos peseve N, so that = 0 = 0 We ca solve = 0 ecusvel backwads

More information

In Calculus I you learned an approximation method using a Riemann sum. Recall that the Riemann sum is

In Calculus I you learned an approximation method using a Riemann sum. Recall that the Riemann sum is Mth Sprg 08 L Approxmtg Dete Itegrls I Itroducto We hve studed severl methods tht llow us to d the exct vlues o dete tegrls However, there re some cses whch t s ot possle to evlute dete tegrl exctly I

More information

Reflection from a surface depends on the quality of the surface and how much light is absorbed during the process. Rays

Reflection from a surface depends on the quality of the surface and how much light is absorbed during the process. Rays Geometc Otcs I bem o lgt s ow d s sot wvelegt comso to te dmeso o y obstcle o etue ts t, te ts bem my be teted s stgt-le y o lgt d ts wve oetes o te momet goed. I ts oxmto, lgt ys e tced toug ec otcs elemet

More information

Electronic Companion for Optimal Design of Co-Productive Services: Interaction and Work Allocation

Electronic Companion for Optimal Design of Co-Productive Services: Interaction and Work Allocation Submitted to Mnufctuing & Sevice Oetions Mngement mnuscit Electonic Comnion fo Otiml Design of Co-Poductive Sevices: Intection nd Wok Alloction Guillume Roels UCLA Andeson School of Mngement, 110 Westwood

More information

Physics 604 Problem Set 1 Due Sept 16, 2010

Physics 604 Problem Set 1 Due Sept 16, 2010 Physics 64 Polem et 1 Due ept 16 1 1) ) Inside good conducto the electic field is eo (electons in the conducto ecuse they e fee to move move in wy to cncel ny electic field impessed on the conducto inside

More information

( m is the length of columns of A ) spanned by the columns of A : . Select those columns of B that contain a pivot; say those are Bi

( m is the length of columns of A ) spanned by the columns of A : . Select those columns of B that contain a pivot; say those are Bi Assgmet /MATH 47/Wte Due: Thusday Jauay The poblems to solve ae umbeed [] to [] below Fst some explaatoy otes Fdg a bass of the colum-space of a max ad povg that the colum ak (dmeso of the colum space)

More information

Technical Appendix for Inventory Management for an Assembly System with Product or Component Returns, DeCroix and Zipkin, Management Science 2005.

Technical Appendix for Inventory Management for an Assembly System with Product or Component Returns, DeCroix and Zipkin, Management Science 2005. Techc Appedx fo Iveoy geme fo Assemy Sysem wh Poduc o Compoe eus ecox d Zp geme Scece 2005 Lemm µ µ s c Poof If J d µ > µ he ˆ 0 µ µ µ µ µ µ µ µ Sm gumes essh he esu f µ ˆ > µ > µ > µ o K ˆ If J he so

More information

SOLVING SYSTEMS OF EQUATIONS, DIRECT METHODS

SOLVING SYSTEMS OF EQUATIONS, DIRECT METHODS ELM Numecl Alyss D Muhem Mecmek SOLVING SYSTEMS OF EQUATIONS DIRECT METHODS ELM Numecl Alyss Some of the cotets e dopted fom Luee V. Fusett Appled Numecl Alyss usg MATLAB. Petce Hll Ic. 999 ELM Numecl

More information

VECTOR MECHANICS FOR ENGINEERS: Vector Mechanics for Engineers: Dynamics. In the current chapter, you will study the motion of systems of particles.

VECTOR MECHANICS FOR ENGINEERS: Vector Mechanics for Engineers: Dynamics. In the current chapter, you will study the motion of systems of particles. Seeth Edto CHPTER 4 VECTOR MECHNICS FOR ENINEERS: DYNMICS Fedad P. ee E. Russell Johsto, J. Systems of Patcles Lectue Notes: J. Walt Ole Texas Tech Uesty 003 The Mcaw-Hll Compaes, Ic. ll ghts eseed. Seeth

More information

π,π is the angle FROM a! TO b

π,π is the angle FROM a! TO b Mth 151: 1.2 The Dot Poduct We hve scled vectos (o, multiplied vectos y el nume clled scl) nd dded vectos (in ectngul component fom). Cn we multiply vectos togethe? The nswe is YES! In fct, thee e two

More information

Electric Potential. and Equipotentials

Electric Potential. and Equipotentials Electic Potentil nd Euipotentils U Electicl Potentil Review: W wok done y foce in going fom to long pth. l d E dl F W dl F θ Δ l d E W U U U Δ Δ l d E W U U U U potentil enegy electic potentil Potentil

More information

Soo King Lim Figure 1: Figure 2: Figure 3: Figure 4: Figure 5: Figure 6: Figure 7: Figure 8: Figure 9: Figure 10: Figure 11:

Soo King Lim Figure 1: Figure 2: Figure 3: Figure 4: Figure 5: Figure 6: Figure 7: Figure 8: Figure 9: Figure 10: Figure 11: Soo Kg Lm 1.0 Nested Fctorl Desg... 1.1 Two-Fctor Nested Desg... 1.1.1 Alss of Vrce... Exmple 1... 5 1.1. Stggered Nested Desg for Equlzg Degree of Freedom... 7 1.1. Three-Fctor Nested Desg... 8 1.1..1

More information

BINOMIAL THEOREM OBJECTIVE PROBLEMS in the expansion of ( 3 +kx ) are equal. Then k =

BINOMIAL THEOREM OBJECTIVE PROBLEMS in the expansion of ( 3 +kx ) are equal. Then k = wwwskshieduciocom BINOMIAL HEOREM OBJEIVE PROBLEMS he coefficies of, i e esio of k e equl he k /7 If e coefficie of, d ems i e i AP, e e vlue of is he coefficies i e,, 7 ems i e esio of e i AP he 7 7 em

More information

I. Exponential Function

I. Exponential Function MATH & STAT Ch. Eoetil Fuctios JCCSS I. Eoetil Fuctio A. Defiitio f () =, whee ( > 0 ) d is the bse d the ideedet vible is the eoet. [ = 1 4 4 4L 4 ] ties (Resf () = is owe fuctio i which the bse is the

More information

Chapter Gauss-Seidel Method

Chapter Gauss-Seidel Method Chpter 04.08 Guss-Sedel Method After redg ths hpter, you should be ble to:. solve set of equtos usg the Guss-Sedel method,. reogze the dvtges d ptflls of the Guss-Sedel method, d. determe uder wht odtos

More information

Homework 3 MAE 118C Problems 2, 5, 7, 10, 14, 15, 18, 23, 30, 31 from Chapter 5, Lamarsh & Baratta. The flux for a point source is:

Homework 3 MAE 118C Problems 2, 5, 7, 10, 14, 15, 18, 23, 30, 31 from Chapter 5, Lamarsh & Baratta. The flux for a point source is: . Homewok 3 MAE 8C Poblems, 5, 7, 0, 4, 5, 8, 3, 30, 3 fom Chpte 5, msh & Btt Point souces emit nuetons/sec t points,,, n 3 fin the flux cuent hlf wy between one sie of the tingle (blck ot). The flux fo

More information

SOLUTIONS ( ) ( )! ( ) ( ) ( ) ( )! ( ) ( ) ( ) ( ) n r. r ( Pascal s equation ). n 1. Stepanov Dalpiaz

SOLUTIONS ( ) ( )! ( ) ( ) ( ) ( )! ( ) ( ) ( ) ( ) n r. r ( Pascal s equation ). n 1. Stepanov Dalpiaz STAT UIU Pctice Poblems # SOLUTIONS Stepov Dlpiz The followig e umbe of pctice poblems tht my be helpful fo completig the homewo, d will liely be vey useful fo studyig fo ems...-.-.- Pove (show) tht. (

More information

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING FLUID MECHANICS III Solutions to Problem Sheet 3

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING FLUID MECHANICS III Solutions to Problem Sheet 3 DEPATMENT OF CIVIL AND ENVIONMENTAL ENGINEEING FLID MECHANICS III Solutions to Poblem Sheet 3 1. An tmospheic vote is moelle s combintion of viscous coe otting s soli boy with ngul velocity Ω n n iottionl

More information

Solutions Manual for Polymer Science and Technology Third Edition

Solutions Manual for Polymer Science and Technology Third Edition Solutos ul for Polymer Scece d Techology Thrd Edto Joel R. Fred Uer Sddle Rver, NJ Bosto Idols S Frcsco New York Toroto otrel Lodo uch Prs drd Cetow Sydey Tokyo Sgore exco Cty Ths text s ssocted wth Fred/Polymer

More information

A Dynamical Quasi-Boolean System

A Dynamical Quasi-Boolean System ULETNUL Uestăţ Petol Gze Ploeşt Vol LX No / - 9 Se Mtetă - otă - Fză l Qs-oole Sste Gel Mose Petole-Gs Uest o Ploest ots etet est 39 Ploest 68 o el: ose@-loesto stt Ths e oes the esto o ol theoetl oet:

More information

Chapter I Vector Analysis

Chapter I Vector Analysis . Chpte I Vecto nlss . Vecto lgeb j It s well-nown tht n vecto cn be wtten s Vectos obe the followng lgebc ules: scl s ) ( j v v cos ) ( e Commuttv ) ( ssoctve C C ) ( ) ( v j ) ( ) ( ) ( ) ( (v) he lw

More information

Course Updates. Reminders: 1) Assignment #8 available. 2) Chapter 28 this week.

Course Updates. Reminders: 1) Assignment #8 available. 2) Chapter 28 this week. Couse Updtes http://www.phys.hwii.edu/~vne/phys7-sp1/physics7.html Remindes: 1) Assignment #8 vilble ) Chpte 8 this week Lectue 3 iot-svt s Lw (Continued) θ d θ P R R θ R d θ d Mgnetic Fields fom long

More information

Radial geodesics in Schwarzschild spacetime

Radial geodesics in Schwarzschild spacetime Rdil geodesics in Schwzschild spcetime Spheiclly symmetic solutions to the Einstein eqution tke the fom ds dt d dθ sin θdϕ whee is constnt. We lso hve the connection components, which now tke the fom using

More information

Answers to test yourself questions

Answers to test yourself questions Answes to test youself questions opic Descibing fields Gm Gm Gm Gm he net field t is: g ( d / ) ( 4d / ) d d Gm Gm Gm Gm Gm Gm b he net potentil t is: V d / 4d / d 4d d d V e 4 7 9 49 J kg 7 7 Gm d b E

More information

XII. Addition of many identical spins

XII. Addition of many identical spins XII. Addto of may detcal sps XII.. ymmetc goup ymmetc goup s the goup of all possble pemutatos of obects. I total! elemets cludg detty opeato. Each pemutato s a poduct of a ceta fte umbe of pawse taspostos.

More information

5.4. The Fundamental Theorem of Calculus. 356 Chapter 5: Integration. Mean Value Theorem for Definite Integrals

5.4. The Fundamental Theorem of Calculus. 356 Chapter 5: Integration. Mean Value Theorem for Definite Integrals 56 Chter 5: Integrtion 5.4 The Fundmentl Theorem of Clculus HISTORICA BIOGRAPHY Sir Isc Newton (64 77) In this section we resent the Fundmentl Theorem of Clculus, which is the centrl theorem of integrl

More information

COMP 465: Data Mining More on PageRank

COMP 465: Data Mining More on PageRank COMP 465: Dt Mnng Moe on PgeRnk Sldes Adpted Fo: www.ds.og (Mnng Mssve Dtsets) Powe Iteton: Set = 1/ 1: = 2: = Goto 1 Exple: d 1/3 1/3 5/12 9/24 6/15 = 1/3 3/6 1/3 11/24 6/15 1/3 1/6 3/12 1/6 3/15 Iteton

More information

School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007

School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007 School of Electicl nd Compute Engineeing, Conell Univesity ECE 303: Electomgnetic Fields nd Wves Fll 007 Homewok 3 Due on Sep. 14, 007 by 5:00 PM Reding Assignments: i) Review the lectue notes. ii) Relevnt

More information

Chapter 5: Your Program Asks for Advice.

Chapter 5: Your Program Asks for Advice. Chte 5: You Pogm Asks fo Advce. Pge 63 Chte 5: You Pogm Asks fo Advce. Ths chte ntoduces new tye of ves (stng ves) nd how to get text nd numec esonses fom the use. Anothe Tye of Ve The Stng Ve: In Chte

More information

6.6 The Marquardt Algorithm

6.6 The Marquardt Algorithm 6.6 The Mqudt Algothm lmttons of the gdent nd Tylo expnson methods ecstng the Tylo expnson n tems of ch-sque devtves ecstng the gdent sech nto n tetve mtx fomlsm Mqudt's lgothm utomtclly combnes the gdent

More information

Density estimation II

Density estimation II CS 750 Mche Lerg Lecture 6 esty estmto II Mlos Husrecht mlos@tt.edu 539 Seott Squre t: esty estmto {.. } vector of ttrute vlues Ojectve: estmte the model of the uderlyg rolty dstruto over vrles X X usg

More information

Discrete Model Parametrization

Discrete Model Parametrization Poceedings of Intentionl cientific Confeence of FME ession 4: Automtion Contol nd Applied Infomtics Ppe 9 Discete Model Pmetition NOKIEVIČ, Pet Doc,Ing,Cc Deptment of Contol ystems nd Instumenttion, Fculty

More information

Convert the NFA into DFA

Convert the NFA into DFA Convert the NF into F For ech NF we cn find F ccepting the sme lnguge. The numer of sttes of the F could e exponentil in the numer of sttes of the NF, ut in prctice this worst cse occurs rrely. lgorithm:

More information

9.4 The response of equilibrium to temperature (continued)

9.4 The response of equilibrium to temperature (continued) 9.4 The esponse of equilibium to tempetue (continued) In the lst lectue, we studied how the chemicl equilibium esponds to the vition of pessue nd tempetue. At the end, we deived the vn t off eqution: d

More information

THEORY OF EQUATIONS OBJECTIVE PROBLEMS. If the eqution x 6x 0 0 ) - ) 4) -. If the sum of two oots of the eqution k is -48 ) 6 ) 48 4) 4. If the poduct of two oots of 4 ) -4 ) 4) - 4. If one oot of is

More information

3.1 Magnetic Fields. Oersted and Ampere

3.1 Magnetic Fields. Oersted and Ampere 3.1 Mgnetic Fields Oested nd Ampee The definition of mgnetic induction, B Fields of smll loop (dipole) Mgnetic fields in mtte: ) feomgnetism ) mgnetiztion, (M ) c) mgnetic susceptiility, m d) mgnetic field,

More information

African Journal of Science and Technology (AJST) Science and Engineering Series Vol. 4, No. 2, pp GENERALISED DELETION DESIGNS

African Journal of Science and Technology (AJST) Science and Engineering Series Vol. 4, No. 2, pp GENERALISED DELETION DESIGNS Af Joul of See Tehology (AJST) See Egeeg See Vol. 4, No.,. 7-79 GENERALISED DELETION DESIGNS Mhel Ku Gh Joh Wylff Ohbo Dee of Mhe, Uvey of Nob, P. O. Bo 3097, Nob, Key ABSTRACT:- I h e yel gle ele fol

More information

On Some Hadamard-Type Inequalıtıes for Convex Functıons

On Some Hadamard-Type Inequalıtıes for Convex Functıons Aville t htt://vuedu/ Al Al Mth ISSN: 93-9466 Vol 9, Issue June 4, 388-4 Alictions nd Alied Mthetics: An Intentionl Jounl AAM On Soe Hdd-Tye Inequlıtıes o, Convex Functıons M Ein Özdei Detent o Mthetics

More information

Analysis of Arithmetic. Analysis of Arithmetic. Analysis of Arithmetic Round-Off Errors. Analysis of Arithmetic. Analysis of Arithmetic

Analysis of Arithmetic. Analysis of Arithmetic. Analysis of Arithmetic Round-Off Errors. Analysis of Arithmetic. Analysis of Arithmetic In the fixed-oint imlementation of a digital filte only the esult of the multilication oeation is quantied The eesentation of a actical multilie with the quantie at its outut is shown below u v Q ^v The

More information

The Shape of the Pair Distribution Function.

The Shape of the Pair Distribution Function. The Shpe of the P Dstbuton Functon. Vlentn Levshov nd.f. Thope Deptment of Phscs & stonom nd Cente fo Fundmentl tels Resech chgn Stte Unvest Sgnfcnt pogess n hgh-esoluton dffcton epements on powde smples

More information

Name Ima Sample ASU ID

Name Ima Sample ASU ID Nme Im Smple ASU ID 2468024680 CSE 355 Test 1, Fll 2016 30 Septemer 2016, 8:35-9:25.m., LSA 191 Regrding of Midterms If you elieve tht your grde hs not een dded up correctly, return the entire pper to

More information

U>, and is negative. Electric Potential Energy

U>, and is negative. Electric Potential Energy Electic Potentil Enegy Think of gvittionl potentil enegy. When the lock is moved veticlly up ginst gvity, the gvittionl foce does negtive wok (you do positive wok), nd the potentil enegy (U) inceses. When

More information

Section 7.2 Two-way ANOVA with random effect(s)

Section 7.2 Two-way ANOVA with random effect(s) Secto 7. Two-wy ANOVA wth rdom effect(s) 1 1. Model wth Two Rdom ffects The fctors hgher-wy ANOVAs c g e cosdered fxed or rdom depedg o the cotext of the study. or ech fctor: Are the levels of tht fctor

More information

Section IV.6: The Master Method and Applications

Section IV.6: The Master Method and Applications Sectio IV.6: The Mster Method d Applictios Defiitio IV.6.1: A fuctio f is symptoticlly positive if d oly if there exists rel umer such tht f(x) > for ll x >. A cosequece of this defiitio is tht fuctio

More information

Analysis of the Preference Shift of Customer Brand. Selection among Multiple Genres of. Jewelry/Accessory and Its Matrix Structure

Analysis of the Preference Shift of Customer Brand. Selection among Multiple Genres of. Jewelry/Accessory and Its Matrix Structure Jourl of Comuttios & Modellig vol. o. 9- ISS: 9- (rit) 9-88 (olie) Scieress Ltd lysis of the Preferece Shift of Customer Brd Selectio mog Multile Geres of Jewelry/ccessory d Its Mtrix Structure Chie Ishio

More information

Some Unbiased Classes of Estimators of Finite Population Mean

Some Unbiased Classes of Estimators of Finite Population Mean Itertol Jourl O Mtemtcs Ad ttstcs Iveto (IJMI) E-IN: 3 4767 P-IN: 3-4759 Www.Ijms.Org Volume Issue 09 etember. 04 PP-3-37 ome Ubsed lsses o Estmtors o Fte Poulto Me Prvee Kumr Msr d s Bus. Dertmet o ttstcs,

More information

Introductions to ArithmeticGeometricMean

Introductions to ArithmeticGeometricMean Intoductions to AitheticGeoeticMen Intoduction to the Aithetic-Geoetic Men Genel The ithetic-geoetic en eed in the woks of J Lnden (77, 775) nd J-L Lgnge (784-785) who defined it though the following quite-ntul

More information

RECAPITULATION & CONDITIONAL PROBABILITY. Number of favourable events n E Total number of elementary events n S

RECAPITULATION & CONDITIONAL PROBABILITY. Number of favourable events n E Total number of elementary events n S Fomulae Fo u Pobablty By OP Gupta [Ida Awad We, +91-9650 350 480] Impotat Tems, Deftos & Fomulae 01 Bascs Of Pobablty: Let S ad E be the sample space ad a evet a expemet espectvely Numbe of favouable evets

More information

Lecture 5 Single factor design and analysis

Lecture 5 Single factor design and analysis Lectue 5 Sngle fcto desgn nd nlss Completel ndomzed desgn (CRD Completel ndomzed desgn In the desgn of expements, completel ndomzed desgns e fo studng the effects of one pm fcto wthout the need to tke

More information

Lecture 3 summary. C4 Lecture 3 - Jim Libby 1

Lecture 3 summary. C4 Lecture 3 - Jim Libby 1 Lecue su Fes of efeece Ivce ude sfoos oo of H wve fuco: d-fucos Eple: e e - µ µ - Agul oeu s oo geeo Eule gles Geec slos cosevo lws d Noehe s heoe C4 Lecue - Lbb Fes of efeece Cosde fe of efeece O whch

More information

Approximate Integration

Approximate Integration Study Sheet (7.7) Approimte Itegrtio I this sectio, we will ler: How to fid pproimte vlues of defiite itegrls. There re two situtios i which it is impossile to fid the ect vlue of defiite itegrl. Situtio:

More information

GRAPHING LINEAR EQUATIONS. Linear Equations. x l ( 3,1 ) _x-axis. Origin ( 0, 0 ) Slope = change in y change in x. Equation for l 1.

GRAPHING LINEAR EQUATIONS. Linear Equations. x l ( 3,1 ) _x-axis. Origin ( 0, 0 ) Slope = change in y change in x. Equation for l 1. GRAPHING LINEAR EQUATIONS Qudrt II Qudrt I ORDERED PAIR: The first umer i the ordered pir is the -coordite d the secod umer i the ordered pir is the y-coordite. (, ) Origi ( 0, 0 ) _-is Lier Equtios Qudrt

More information

PhysicsAndMathsTutor.com

PhysicsAndMathsTutor.com PhysicsAMthsTuto.com . M 6 0 7 0 Leve lk 6 () Show tht 7 is eigevlue of the mti M fi the othe two eigevlues of M. (5) () Fi eigevecto coespoig to the eigevlue 7. *M545A068* (4) Questio cotiue Leve lk *M545A078*

More information

2.Decision Theory of Dependence

2.Decision Theory of Dependence .Deciio Theoy of Depedece Theoy :I et of vecto if thee i uet which i liely depedet the whole et i liely depedet too. Coolly :If the et i liely idepedet y oepty uet of it i liely idepedet. Theoy : Give

More information

M A T H F A L L CORRECTION. Algebra I 2 1 / 0 9 / U N I V E R S I T Y O F T O R O N T O

M A T H F A L L CORRECTION. Algebra I 2 1 / 0 9 / U N I V E R S I T Y O F T O R O N T O M A T H 2 4 0 F A L L 2 0 1 4 HOMEWORK ASSIGNMENT #1 CORRECTION Alger I 2 1 / 0 9 / 2 0 1 4 U N I V E R S I T Y O F T O R O N T O 1. Suppose nd re nonzero elements of field F. Using only the field xioms,

More information

SULIT 3472/2. Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasa digunakan.

SULIT 3472/2. Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasa digunakan. SULT 347/ Rumus-umus eikut oleh memtu d mejw sol. Simol-simol yg diei dlh yg is diguk. LGER. 4c x 5. log m log m log 9. T d. m m m 6. log = log m log 0. S d m m 3. 7. log m log m. S, m m logc 4. 8. log.

More information

The Area of a Triangle

The Area of a Triangle The e of Tingle tkhlid June 1, 015 1 Intodution In this tile we will e disussing the vious methods used fo detemining the e of tingle. Let [X] denote the e of X. Using se nd Height To stt off, the simplest

More information

Parameter Estimation and Hypothesis Testing of Two Negative Binomial Distribution Population with Missing Data

Parameter Estimation and Hypothesis Testing of Two Negative Binomial Distribution Population with Missing Data Avlble ole wwwsceceeccom Physcs Poce 0 475 480 0 Ieol Cofeece o Mecl Physcs Bomecl ee Pmee smo Hyohess es of wo Neve Boml Dsbuo Poulo wh Mss D Zhwe Zho Collee of MhemcsJl Noml UvesyS Ch zhozhwe@6com Absc

More information

Physics 505 Fall 2005 Midterm Solutions. This midterm is a two hour open book, open notes exam. Do all three problems.

Physics 505 Fall 2005 Midterm Solutions. This midterm is a two hour open book, open notes exam. Do all three problems. Physics 55 Fll 5 Midtem Solutions This midtem is two hou open ook, open notes exm. Do ll thee polems. [35 pts] 1. A ectngul ox hs sides of lengths, nd c z x c [1] ) Fo the Diichlet polem in the inteio

More information

ME 501A Seminar in Engineering Analysis Page 1

ME 501A Seminar in Engineering Analysis Page 1 Mtr Trsformtos usg Egevectors September 8, Mtr Trsformtos Usg Egevectors Lrry Cretto Mechcl Egeerg A Semr Egeerg Alyss September 8, Outle Revew lst lecture Trsformtos wth mtr of egevectors: = - A ermt

More information

A Mobile Personalized RFID System

A Mobile Personalized RFID System A Moble Pesolzed RFID System Ruy-Shug hg Jh-Sheg hg d Jg-Hsg Ruey Detmet of omute Scece d Ifomto Egeeg Ntol Dog Hw Uvesty Hule TAIWAN {schgschg}@ml.dhu.edu.tw d9400@ems.dhu.edu.tw Abstct RFID s d-develog

More information

St Andrew s Academy Mathematics Department Higher Mathematics VECTORS

St Andrew s Academy Mathematics Department Higher Mathematics VECTORS St ndew s cdemy Mthemtics etment Highe Mthemtics VETORS St ndew's cdemy Mths et 0117 1 Vectos sics 1. = nd = () Sketch the vectos nd. () Sketch the vectos nd. (c) Given u = +, sketch the vecto u. (d) Given

More information

Section 35 SHM and Circular Motion

Section 35 SHM and Circular Motion Section 35 SHM nd Cicul Motion Phsics 204A Clss Notes Wht do objects do? nd Wh do the do it? Objects sometimes oscillte in simple hmonic motion. In the lst section we looed t mss ibting t the end of sping.

More information