A Research on Supplier Selection Method for CALS

Size: px
Start display at page:

Download "A Research on Supplier Selection Method for CALS"

Transcription

1 A Reserch o Suppler Selecto Method for CALS Xoyg X d Ll Jg School of Mechcl d Electroc Egeerg, Gugdog Uversty of Techology, Gugzhou , P.R. Ch ygxox@126.com jg_ll@21c.com Abstrct. Bsed o the chrcterstcs of suppler selecto for CALS(Cotuous Acqusto d Lfe-cycle Support), tht compes wth CALS hve my supplers d supplers re lwys strtegc supplers, suppler selecto process s dvded to two phses: pre-selecto d mkg decso. At suppler pre-selecto stge, polychromtc sets theory from Russ s troduced s the soluto scheme. Accordg to the propertes of supplers themselves d pre-selecto evlutg dctors, pre-selecto cotour Boole mtrx s creted utomtclly. Bsed o t, suppler pre-selecto model s set up. At decso-mkg stge, populr fuzzy lytc herrchy process s dopted to set up suppler selecto model. O the bss of evlutg dctors of the decso-mkg stge, the best suppler c be chose quckly. I the ed, pplcto exmple of motor compy s gve to testfy the fesblty d effectveess of the proposed method. Keywords: CALS, Suppler selecto, Pre-selecto, Polychromtc sets, Fuzzy lytc herrchy process 1. INTRODUCTION Sce CALS ws proposed 1985 by the Amerc Deprtmet of Defese, ts pplcto hs bee commo dy by dy, d t hs become the strtegy of the eterprse s full-scle formto developmet. Now my coutres d orgztos, such s Amerc, Jp, Eglsh, Sgpore d Tw re, re studyg d populrzg CALS ctvely. But our coutry, CALS s oly o theoretc dscusso stge, d cocrete reserch job just begs. As mportt step for CALS purchsg, suppler selecto s lso oe of mportt decso-mkg questos for eterprse. Suppler flueces the product qulty, delvery dte d competto of eterprse. Especlly whe the eterprse plces ts m eergy more d more o ts core busess, cotrctg o-core busess wth the suppler, suppler selecto ppers more mporttly. 2. CHARACTERS OF SUPPLIER SELECTION FOR CALS Selecto of cotrctors, sub-cotrctors d supplers c ll be cosdered s suppler selecto. Chrcters of suppler selecto for CALS re s follows:

2 1474 Xoyg X d Ll Jg (1) Meetg product lfecycle support Sce CALS s defed s cotuous cqusto d lfecycle support, suppler selecto for CALS must meet the demd of product lfecycle support. Tht s to sy product formto from brth to deth must be followed d quered, for exmple, we c qure the prt s suppler eve t ts mtece stge. To cheve the purpose, the formto betwee compy d suppler, suppler d suppler must be tegrted. Oly ths wy, formto shrg s reched deed d the demd of lfecycle support s met. (2) Suppler s strtegc coopertve comte Compes CALS geerlly purchse mterl d mche prts other compes, supplers re very mportt for ths kd of compy, d belog to strtegc supplers. So suppler selecto method d ssessmet dex must ccord wth strtegc suppler selecto. (3) Suppler pre-selecto occupes mportt posto I order to cooperte wth best suppler, compy serches supplers the whole world; therefore, my supplers c be chose. If ot pre-selectg but mkg decso drectly o supplers, decso-mkg wll fce my dffcultes. Now, compes lwys pre-select supplers rtfclly by some ssessmet dexes. But t s effcet d ccurte by ths rtfcl wy. Up to ow, reserch o suppler pre-selecto s lttle. Lterture [1] dopts fuzzy cluster lyss s pre-selecto method, d uses lytc herrchy process to cout the weghts of evlutg dctors. The defect of ths method s complcted model d huge computtol complexty, especlly whe there re my pre-selecto evlutg dctors compy. Lterture [2] pre-selects supplers by fuzzy serch method, mely uses formto retrevl method to pre-select potetl supplers. Ths method mybe led too my supplers stsfed the codtos, thereby gves my jobs to decso-mkg stge. Lterture [3] cosders the m jobs of suppler pre-selecto re the defto of eed, revew purchse requsto d setup of evlutg dctors whch s subjectve; therefore the pre-selecto stge should be left to hums rther th mches. Although the defto of eed, revew purchse requsto d setup of evlutg dctors must be cosdered pre-selecto stge, f compy hs my supplers, good pre-selecto method s lso requred. So ths pper, suppler selecto process s dvded to two phses: Pre-selecto d mkg decso. At suppler pre-selecto stge, polychromtc sets theory from Russ good t smulto o herrchcl structure s troduced s the soluto scheme. At decso-mkg stge, populr fuzzy lytc herrchy process s dopted to set up suppler selecto model. 3. SUPPLIER PRE-SELECTION BASED ON POLYCHROMATIC SETS CONTOUR BOOLEAN MATRIX 3.1 Advtges of Polychromtc Sets Polychromtc sets theory, whch s ew system theory d tool o delg wth formto, s put forwrd by Russ Professor V. V. Pvlov [4-5]. It uses the formlly sme mthemtcs model to emulte dfferet objects, whch mkes

3 A Reserch o Suppler Selecto Method for CALS 1475 emultg system more flexble. Moreover, t fts to solve the problems wth herrchcl structure, d suppler selecto s just ths kd of problem. Added to ths, polychromtc set hs the dvtge of lgorthmc dptblty, eve f suppler mout chges, suppler selecto lgorthm does t eed to lter. 3.2 Polychromtc Sets Cotour Boole Mtrx For the covetol set B = (b 1, b 2,, b ), elemet b ( = 1, 2,, ) s dstgushed from other elemets by ts me oly, d other propertes of the elemet re ot expressed ths expresso. From lterture [6-7], we c see the theory of polychromtc sets, suppose A = ( 1, 2,, ) s elemet set, elemet ( = 1, 2,, ) A c be dstgushed from other elemets by ot oly ts me but lso other propertes of the elemet. Suppose F(A)=(F 1, F 2,, F m ) s the ggregto of propertes. Cotour Boole mtrx [A F(A)] represets the reltoshp betwee elemet d F j. I ths Boole expresso, f d F j s relted, the j =1otherwse j =0, d F j (A) = ( 1(j), 2(j),, (j) ). The estblshmet of ths cotour Boole mtrx s ccordg to the formto or experece of rel world. As for suppler pre-selecto, cotour Boole mtrx s set up bsed o pre-selecto dexes d supplers ow propertes. C [ A F( )] ( j) A A, F ( A) F 1(1) (1) (1) 1 F j 1( j) ( j) ( j) Fm 1( m) ( m) ( m) 1 (1) 3.3 Pre-selecto Model bsed o Cotour Mtrx As for suppler pre-selecto, most compes estblsh the pre-selecto dexes ccordg to ther ctul stutos. e c pre-select supplers ccordce wth pre-selecto dexes d supplers ow propertes. The vrbles d steps of ths model re s follows: (1) Vrbles of Pre-selecto e suppose { 1 2, m } s the ggregto of supplers; { O 1 O 2, O } s the pre-selecto dexes sort d O j s No. j property of pre-selecto dex O (=1,2,, j=1,2, m ); { S represets the ggregto of pre-selecto dexes chose d S {O 1, O 2,. O m }( =1,2, ). (2) Steps of Pre-selecto

4 1476 Xoyg X d Ll Jg 1) The ggregto of supplers s regrded s A, d Aggregto of pre-selecto dexes {O j } s F(A). 2) Bsed o supplers formto d formul (1), settg up cotour mtrx [A F(A)] betwee supplers { 1 2, m } d pre-selecto dexes {O j }. 3) Suppose equls 1, ccordg to cotour mtrx [AF(A)], we c obt the vlue ggregto of Fs 1( A). 4) Repetg step 3) utl =. The Fs 1( A ) Fs 2 ( A ) Fs (A) s obted. 5) Usg F P (A) to express the result of Fs1 ( A) Fs2 ( A) Fs ( A). 6) If the elemet F P ( ) F P (A) equls 1, suppler s the suppler meets the requremets. 7) Ed. SUPPLIER DECISION-MAKING BASED ON FUZZY ANALYTIC HIERARCHY PROCESS At decso-mkg stge, lytc herrchy process s ofte dopted s evlutg method. But t hs some defects, such s dffculty cosstecy checkout. So we tke fuzzy lytc herrchy process s suppler decso-mkg method. Usg ths method, there re sx steps: Step 1 Settg up herrchcl structure e c crete evlutg dex herrchcl structure by topmost level, some medum levels d lowest level. Step 2 Costructg fuzzy judgmet mtrx Fuzzy judgmet mtrx F expresses the comprso of mportce o elemets the sme level reltve to elemet of ext hgher lyer. Accordg to mportce metrc vlue comprg to j, fuzzy judgmet mtrx s follows c be obted: F= (2) Propertes of mtrx F re: (1) 0< j <1d the vlue must be 0.1, 0.2,, 0.9; (2) =0.5, =1,2,, ; (3) j =1- j,, j=1, 2,,. Step 3 Checkoutg the cosstecy Cosstecy stdrd s D-vlue of correspodg elemets of rows s costt. Step 4 Clcultg moolyer weght Moolyer weght s the mportce order of elemets reltve to the elemet of ext hgher lyer. From lterture [8], clcultg formul of moolyer weght s s formul (3)

5 A Reserch o Suppler Selecto Method for CALS ( 1) k k 1 2 (3) Step 5 Clcultg composg weght The weght of the elemet of lowest level reltve to topmost level s the composg weght. Recurrece method uses commoly. Suppose there re k elemets o kth level, d the weght vector ggregto relto to topmost level s 1 k. Bsed o recurso rule, the composg weght of the elemet o lowest level s s formul (4): (4) Step 6 Assessg d computg the score of supplers Geerlly spekg, ssessg perso mrks the dexes of lowest level. If score ggregto of sub dexes s X=(x 1, x 2,, x ) T d ther composg weght ggregto s =(w 1, w 2,, w )the formul of suppler s score s s formul (5). Suppler who gets the topmost score s the best suppler. S T X 1 w x 2 (5) 5. EXAMPLES Now, we tke motor compy s our exmple. It hs my supplers, d suppler pre-selecto d decso-mkg system hs set up. Step 1 Suppler pre-selecto Suppose pre-selecto dexes of the compy re s follows: (1) Owershp: stte eterprse (e cosder t s F 1 ) d prvte eterprse (mely F 2 ) (2) Compy Address: Gugdog provce (mely F 3 ) d other re (mely F 4 ) (3) Totl Assets: below 5 mllos (mely F 5 ) d bove 5 mllos (mely F 6 ) Suppose the compy hs four supplers, d the propertes of supplers re s follows: Suppler A (e cosder t s 1 of A): stte eterprse; Gugdog Provce; 3.8 mllo; Suppler B (mely 2 ): stte eterprse; Gugdog Provce; 8 mllo; Suppler C (mely 3 ): prvte eterprse; Shdog Provce; 1 mllo; Suppler D (mely 4 ): stte eterprse; Gugdog Provce; 4.5 mllo; Now, the pre-selecto dexes chose re: Stte eterprse, Gugdog provce, Totl ssets below 5 mllo. Accordg to step 1) 2) of pre-selecto, cotour Boole mtrx s Tble 1. c be obted:

6 1478 Xoyg X d Ll Jg Propertes Suppler Tble 1. A Cotour Mtrx F 1 F 2 F 3 F 4 F 5 F Now, the pre-selecto dexes chose re Stte eterprse, Gugdog provce d Totl ssets below 5 mllo, mely {S }=(F 1, F 3, F 5 ). From bove cotour Boole mtrx, we c see F 1 (A)=(1,1,0,1), F 3 (A)=(1,1,0,1), F 5 (A)=(1,0,1,1), the F P (A)= F 1 (A)F 3 (A)F 5 (A)=(1,0,0,1). Becuse F P ( 1 )=1 d F P ( 4 )=1, suppler A d Suppler D s the supplers meet pre-selecto dexes chose. Step 2 Choose the best suppler bsed o fuzzy lytc herrchy process I step 1, we hve pre-selected suppler A d Suppler D. Suppose evlutg dexes d the herrchcl structure of the motor compy re s Fgure 1: Suppler evlutg dexes Product qulty Mgemet Qulty Apperce Fle Mgemet Drwg Mgemet Fgure 1. Suppler Evlutg Idexes Accordg to dex mportce degree d formul (3), moolyer weght of ll dexes c be obted. Suppose t s s Fgure 2. Usg formul (4), we c get composg weght of dexes o lowest level s Tble 2. From Tble 2, we c see composg weght of qulty s 0.42( ), composg weght of pperce s 0.28, composg weght of fle mgemet s 0.15, composg weght of drwg mgemet s 0.15.

7 A Reserch o Suppler Selecto Method for CALS 1479 Suppler evlutg dctor system Product qulty(0.7) Mgemet(0.3) Qulty(0.6) Apperce(0.4) Fle Mgemet(0.5) Drwg Mgemet(0.5) Fgure 2. Moolyer eght of ll Idexes Tble 2. Composg eght of Idexes o Lowest Level composg weght Qulty Apperce Fle Mgemet Drwg Mgemet Mgers of the compy mrk the dexes of lowest level ccordg to supplers behvor. Now we suppose tht the lowest level dexes score re s Tble 3. Tble 3. The Score of Lowest Level Idexes of Suppler A d D Qulty Apperce Fle Mgemet Drwg Mgemet Suppler A Suppler D Bsed o composg weght of Tble 2 d the score of Tble 3, usg formul (5), the score of suppler A d D c be obted. The totl score of suppler A s 86.3 ( ) d the totl score of suppler D s ( ), so suppler D s the best suppler. 6. CONCLUSIONS I ths pper, we brg forwrd suppler selecto method for CALS, d use polychromtc sets cotour Boole mtrx to suppler pre-selecto, the use fuzzy lytc herrchy process t decso-mkg stge. Usg ths method c choose supplers ccurtely d quckly, thus brg gret ecoomc beeft for eterprse.

8 1480 Xoyg X d Ll Jg REFERENCES 1. C. J, Z. J, d Y. L, Strtegy o Suppler Selecto of Shpbuldg Eterprses, CIMS. Volume 9, Number 10, pp , (2003). 2. X. L, C. u, d L. Lu, Reserch o Vedor Selecto Vertcl Busess-to-Busess Mrketplce, CIMS. Volume 9, Number 4, pp , (2003). 3. R. Dvdrjuh, Automtg Suppler Selecto Procedures. Ph. D Thess, Norweg Uversty of Scece d Techology (2001). 4. V.V. Pvlov, Polychromtc sets the systems theory: chges the composto of Ssets, Iformtsoye Tekholog. Number 1, pp.4-8, (1998). 5. Z. L, Polychromtc Sets d ts Applcto Smulto of Complex Object d System, Iformto d Cotrol. Volume 30, Number 3, pp , (2001). 6. L. Jg, X. X, M. L, d Z. L, Reserch o coceptul desg of jg d fxture bsed o polychromtc sets, Ch Mechcl Egeerg. Volume 17, Number 8, pp , (2006). 7. S. L, Z. L, d F. Tg, Coceptul desg of mchg ceter by usg polychromtc sets theory, Chese Jourl of Mechcl Egeerg. Volume 40, Number 6, pp , (2004). 8. J. Zhg, Fuzzy Alytc Herrchy Process, Fuzzy System d Mthemtcs. Volume 14, Number 2, pp.80-85, (2000).

A Technique for Constructing Odd-order Magic Squares Using Basic Latin Squares

A Technique for Constructing Odd-order Magic Squares Using Basic Latin Squares Itertol Jourl of Scetfc d Reserch Publctos, Volume, Issue, My 0 ISSN 0- A Techque for Costructg Odd-order Mgc Squres Usg Bsc Lt Squres Tomb I. Deprtmet of Mthemtcs, Mpur Uversty, Imphl, Mpur (INDIA) tombrom@gml.com

More information

A Method to Analysis Maintenance Support Capability of Aircraft Based on QFD

A Method to Analysis Maintenance Support Capability of Aircraft Based on QFD A Method to Alyss Mtece Support Cpblty of Arcrft Bsed o QFD WEN Jg-Q School of Mechcl Egeerg & Automto Behg Uversty Bejg, Ch wejq@me.bu.edu.c LI Qg School of Mechcl Egeerg & Automto Behg Uversty Bejg,

More information

Sequences and summations

Sequences and summations Lecture 0 Sequeces d summtos Istructor: Kgl Km CSE) E-ml: kkm0@kokuk.c.kr Tel. : 0-0-9 Room : New Mleum Bldg. 0 Lb : New Egeerg Bldg. 0 All sldes re bsed o CS Dscrete Mthemtcs for Computer Scece course

More information

EVALUATING COMPARISON BETWEEN CONSISTENCY IMPROVING METHOD AND RESURVEY IN AHP

EVALUATING COMPARISON BETWEEN CONSISTENCY IMPROVING METHOD AND RESURVEY IN AHP ISAHP 00, Bere, Stzerld, August -4, 00 EVALUATING COMPARISON BETWEEN CONSISTENCY IMPROVING METHOD AND RESURVEY IN AHP J Rhro, S Hlm d Set Wto Petr Chrst Uversty, Surby, Idoes @peter.petr.c.d sh@peter.petr.c.d

More information

Differential Method of Thin Layer for Retaining Wall Active Earth Pressure and Its Distribution under Seismic Condition Li-Min XU, Yong SUN

Differential Method of Thin Layer for Retaining Wall Active Earth Pressure and Its Distribution under Seismic Condition Li-Min XU, Yong SUN Itertol Coferece o Mechcs d Cvl Egeerg (ICMCE 014) Dfferetl Method of Th Lyer for Retg Wll Actve Erth Pressure d Its Dstrbuto uder Sesmc Codto L-M XU, Yog SUN Key Lbortory of Krst Evromet d Geologcl Hzrd

More information

Available online through

Available online through Avlble ole through wwwmfo FIXED POINTS FOR NON-SELF MAPPINGS ON CONEX ECTOR METRIC SPACES Susht Kumr Moht* Deprtmet of Mthemtcs West Begl Stte Uverst Brst 4 PrgsNorth) Kolt 76 West Begl Id E-ml: smwbes@yhoo

More information

Chapter 7. Bounds for weighted sums of Random Variables

Chapter 7. Bounds for weighted sums of Random Variables Chpter 7. Bouds for weghted sums of Rdom Vrbles 7. Itroducto Let d 2 be two depedet rdom vrbles hvg commo dstrbuto fucto. Htczeko (998 d Hu d L (2000 vestgted the Rylegh dstrbuto d obted some results bout

More information

Analytical Approach for the Solution of Thermodynamic Identities with Relativistic General Equation of State in a Mixture of Gases

Analytical Approach for the Solution of Thermodynamic Identities with Relativistic General Equation of State in a Mixture of Gases Itertol Jourl of Advced Reserch Physcl Scece (IJARPS) Volume, Issue 5, September 204, PP 6-0 ISSN 2349-7874 (Prt) & ISSN 2349-7882 (Ole) www.rcourls.org Alytcl Approch for the Soluto of Thermodymc Idettes

More information

MTH 146 Class 7 Notes

MTH 146 Class 7 Notes 7.7- Approxmte Itegrto Motvto: MTH 46 Clss 7 Notes I secto 7.5 we lered tht some defte tegrls, lke x e dx, cot e wrtte terms of elemetry fuctos. So, good questo to sk would e: How c oe clculte somethg

More information

DISCRETE TIME MODELS OF FORWARD CONTRACTS INSURANCE

DISCRETE TIME MODELS OF FORWARD CONTRACTS INSURANCE G Tstsshvl DSCRETE TME MODELS OF FORWARD CONTRACTS NSURANCE (Vol) 008 September DSCRETE TME MODELS OF FORWARD CONTRACTS NSURANCE GSh Tstsshvl e-ml: gurm@mdvoru 69004 Vldvosto Rdo str 7 sttute for Appled

More information

--Manuscript Draft-- application in multiple attribute group decision making

--Manuscript Draft-- application in multiple attribute group decision making tertol Jourl of Mche Lerg d Cyberetcs he eutrosophc umber geerlzed weghted power vergg opertor d ts pplcto multple ttrbute group decso mg --Muscrpt Drft-- Muscrpt umber: Full tle: Artcle ype: Abstrct:

More information

Chapter Unary Matrix Operations

Chapter Unary Matrix Operations Chpter 04.04 Ury trx Opertos After redg ths chpter, you should be ble to:. kow wht ury opertos mes,. fd the trspose of squre mtrx d t s reltoshp to symmetrc mtrces,. fd the trce of mtrx, d 4. fd the ermt

More information

On a class of analytic functions defined by Ruscheweyh derivative

On a class of analytic functions defined by Ruscheweyh derivative Lfe Scece Jourl ;9( http://wwwlfescecestecom O clss of lytc fuctos defed by Ruscheweyh dervtve S N Ml M Arf K I Noor 3 d M Rz Deprtmet of Mthemtcs GC Uversty Fslbd Pujb Pst Deprtmet of Mthemtcs Abdul Wl

More information

Acoustooptic Cell Array (AOCA) System for DWDM Application in Optical Communication

Acoustooptic Cell Array (AOCA) System for DWDM Application in Optical Communication 596 Acoustooptc Cell Arry (AOCA) System for DWDM Applcto Optcl Commucto ml S. Rwt*, Mocef. Tyh, Sumth R. Ktkur d Vdy Nll Deprtmet of Electrcl Egeerg Uversty of Nevd, Reo, NV 89557, U.S.A. Tel: -775-78-57;

More information

Single Valued Neutrosophic Similarity Measures for Multiple Attribute Decision-Making

Single Valued Neutrosophic Similarity Measures for Multiple Attribute Decision-Making 48 Neutrosophc ets d ystems Vol. 2 204 gle Vlued Neutrosophc mlrty Mesures for Multple ttrbute Decso-Mkg Ju Ye d Qsheg Zhg 2 Deprtmet of Electrcl d formto Egeerg hog Uversty 508 Hucheg West Rod hog Zheg

More information

Analytic hierarchy process-based Chinese sports industry structure scheme optimization selection and adjustment research

Analytic hierarchy process-based Chinese sports industry structure scheme optimization selection and adjustment research Avlble ole www.ocpr.co Jourl of hecl d Phrceutcl Reserch, 204, 6(6):2406-24 Reserch Artcle ISSN : 0975-7384 ODEN(USA) : JPR5 Alytc herrchy process-bsed hese sports dustry structure schee optzto selecto

More information

The definite Riemann integral

The definite Riemann integral Roberto s Notes o Itegrl Clculus Chpter 4: Defte tegrls d the FTC Secto 4 The defte Rem tegrl Wht you eed to kow lredy: How to ppromte the re uder curve by usg Rem sums. Wht you c ler here: How to use

More information

CURVE FITTING LEAST SQUARES METHOD

CURVE FITTING LEAST SQUARES METHOD Nuercl Alss for Egeers Ger Jord Uverst CURVE FITTING Although, the for of fucto represetg phscl sste s kow, the fucto tself ot be kow. Therefore, t s frequetl desred to ft curve to set of dt pots the ssued

More information

DERIVATIVES OF KRONECKER PRODUCTS THEMSELVES BASED ON KRONECKER PRODUCT AND MATRIX CALCULUS

DERIVATIVES OF KRONECKER PRODUCTS THEMSELVES BASED ON KRONECKER PRODUCT AND MATRIX CALCULUS Jourl of heoretcl d ppled Iformto echology th Februry 3. Vol. 48 No. 5-3 JI & S. ll rghts reserved. ISSN: 99-8645 www.jtt.org E-ISSN: 87-395 DERIVIVES OF KRONECKER PRODUCS HEMSEVES SED ON KRONECKER PRODUC

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

SUM PROPERTIES FOR THE K-LUCAS NUMBERS WITH ARITHMETIC INDEXES

SUM PROPERTIES FOR THE K-LUCAS NUMBERS WITH ARITHMETIC INDEXES Avlble ole t http://sc.org J. Mth. Comput. Sc. 4 (04) No. 05-7 ISSN: 97-507 SUM PROPERTIES OR THE K-UCAS NUMBERS WITH ARITHMETIC INDEXES BIJENDRA SINGH POOJA BHADOURIA AND OMPRAKASH SIKHWA * School of

More information

MATH2999 Directed Studies in Mathematics Matrix Theory and Its Applications

MATH2999 Directed Studies in Mathematics Matrix Theory and Its Applications MATH999 Drected Studes Mthemtcs Mtr Theory d Its Applctos Reserch Topc Sttory Probblty Vector of Hgher-order Mrkov Ch By Zhg Sho Supervsors: Prof. L Ch-Kwog d Dr. Ch Jor-Tg Cotets Abstrct. Itroducto: Bckgroud.

More information

Chapter 2 Intro to Math Techniques for Quantum Mechanics

Chapter 2 Intro to Math Techniques for Quantum Mechanics Wter 3 Chem 356: Itroductory Qutum Mechcs Chpter Itro to Mth Techques for Qutum Mechcs... Itro to dfferetl equtos... Boudry Codtos... 5 Prtl dfferetl equtos d seprto of vrbles... 5 Itroducto to Sttstcs...

More information

DESIGN OPTIMIZATION OF A DISC BRAKE BASED ON A MULTI- OBJECTIVE OPTIMIZATION ALGORITHM AND ANALYTIC HIERARCHY PROCESS METHOD

DESIGN OPTIMIZATION OF A DISC BRAKE BASED ON A MULTI- OBJECTIVE OPTIMIZATION ALGORITHM AND ANALYTIC HIERARCHY PROCESS METHOD Jucho Zhou Je Go Kzhu Wg Yghu Lo https://do.org/0.78/tof.4403 ISSN 333-4 eissn 849-39 DESIGN OPTIMIZATION OF A DISC BRAKE BASED ON A MULTI- OBJECTIVE OPTIMIZATION ALGORITHM AND ANALYTIC HIERARCHY PROCESS

More information

MATRIX AND VECTOR NORMS

MATRIX AND VECTOR NORMS Numercl lyss for Egeers Germ Jord Uversty MTRIX ND VECTOR NORMS vector orm s mesure of the mgtude of vector. Smlrly, mtr orm s mesure of the mgtude of mtr. For sgle comoet etty such s ordry umers, the

More information

Research on green machine product design evaluate system based on AHP

Research on green machine product design evaluate system based on AHP ppled Mechcs d Mterls Sutted: 04-07-0 ISSN: 66-748 Vol. 680 pp 47-44 ccepted: 04-07-4 do:0.408/.scetfc.et/mm.680.47 Ole: 04-0-0 04 rs ech Pulctos Stzerld Reserch o gree che product desg evlute syste sed

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

Area and the Definite Integral. Area under Curve. The Partition. y f (x) We want to find the area under f (x) on [ a, b ]

Area and the Definite Integral. Area under Curve. The Partition. y f (x) We want to find the area under f (x) on [ a, b ] Are d the Defte Itegrl 1 Are uder Curve We wt to fd the re uder f (x) o [, ] y f (x) x The Prtto We eg y prttog the tervl [, ] to smller su-tervls x 0 x 1 x x - x -1 x 1 The Bsc Ide We the crete rectgles

More information

Chapter 3 Supplemental Text Material

Chapter 3 Supplemental Text Material S3-. The Defto of Fctor Effects Chpter 3 Supplemetl Text Mterl As oted Sectos 3- d 3-3, there re two wys to wrte the model for sglefctor expermet, the mes model d the effects model. We wll geerlly use

More information

ICS141: Discrete Mathematics for Computer Science I

ICS141: Discrete Mathematics for Computer Science I Uversty o Hw ICS: Dscrete Mthemtcs or Computer Scece I Dept. Iormto & Computer Sc., Uversty o Hw J Stelovsy bsed o sldes by Dr. Be d Dr. Stll Orgls by Dr. M. P. Fr d Dr. J.L. Gross Provded by McGrw-Hll

More information

On Several Inequalities Deduced Using a Power Series Approach

On Several Inequalities Deduced Using a Power Series Approach It J Cotemp Mth Sceces, Vol 8, 203, o 8, 855-864 HIKARI Ltd, wwwm-hrcom http://dxdoorg/02988/jcms2033896 O Severl Iequltes Deduced Usg Power Seres Approch Lored Curdru Deprtmet of Mthemtcs Poltehc Uversty

More information

1 4 6 is symmetric 3 SPECIAL MATRICES 3.1 SYMMETRIC MATRICES. Defn: A matrix A is symmetric if and only if A = A, i.e., a ij =a ji i, j. Example 3.1.

1 4 6 is symmetric 3 SPECIAL MATRICES 3.1 SYMMETRIC MATRICES. Defn: A matrix A is symmetric if and only if A = A, i.e., a ij =a ji i, j. Example 3.1. SPECIAL MATRICES SYMMETRIC MATRICES Def: A mtr A s symmetr f d oly f A A, e,, Emple A s symmetr Def: A mtr A s skew symmetr f d oly f A A, e,, Emple A s skew symmetr Remrks: If A s symmetr or skew symmetr,

More information

Optimality of Strategies for Collapsing Expanded Random Variables In a Simple Random Sample Ed Stanek

Optimality of Strategies for Collapsing Expanded Random Variables In a Simple Random Sample Ed Stanek Optmlt of Strteges for Collpsg Expe Rom Vrles Smple Rom Smple E Stek troucto We revew the propertes of prectors of ler comtos of rom vrles se o rom vrles su-spce of the orgl rom vrles prtculr, we ttempt

More information

Union, Intersection, Product and Direct Product of Prime Ideals

Union, Intersection, Product and Direct Product of Prime Ideals Globl Jourl of Pure d Appled Mthemtcs. ISSN 0973-1768 Volume 11, Number 3 (2015), pp. 1663-1667 Reserch Id Publctos http://www.rpublcto.com Uo, Itersecto, Product d Drect Product of Prme Idels Bdu.P (1),

More information

POWERS OF COMPLEX PERSYMMETRIC ANTI-TRIDIAGONAL MATRICES WITH CONSTANT ANTI-DIAGONALS

POWERS OF COMPLEX PERSYMMETRIC ANTI-TRIDIAGONAL MATRICES WITH CONSTANT ANTI-DIAGONALS IRRS 9 y 04 wwwrppresscom/volumes/vol9issue/irrs_9 05pdf OWERS OF COLE ERSERIC I-RIIGOL RICES WIH COS I-IGOLS Wg usu * Q e Wg Hbo & ue College of Scece versty of Shgh for Scece d echology Shgh Ch 00093

More information

Evaluation of the Singular Stress Field. of the Crack Tip of the Infinite Elastic Plate

Evaluation of the Singular Stress Field. of the Crack Tip of the Infinite Elastic Plate ICCM05, 4-7 th July, Auckld, NZ Evluto of the Sgulr Stress Feld of the Crck Tp of the Ifte Elstc lte * J.Y. Lu,, G. L, Z.C.Su 3,. Zhg d Y.Y. Wg Fculty of Ifrstructure Egeerg, Dl Uversty of Techology, Dl

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

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

Advanced Algorithmic Problem Solving Le 3 Arithmetic. Fredrik Heintz Dept of Computer and Information Science Linköping University

Advanced Algorithmic Problem Solving Le 3 Arithmetic. Fredrik Heintz Dept of Computer and Information Science Linköping University Advced Algorthmc Prolem Solvg Le Arthmetc Fredrk Hetz Dept of Computer d Iformto Scece Lköpg Uversty Overvew Arthmetc Iteger multplcto Krtsu s lgorthm Multplcto of polyomls Fst Fourer Trsform Systems of

More information

Discrete Mathematics and Probability Theory Fall 2016 Seshia and Walrand DIS 10b

Discrete Mathematics and Probability Theory Fall 2016 Seshia and Walrand DIS 10b CS 70 Dscrete Mathematcs ad Probablty Theory Fall 206 Sesha ad Walrad DIS 0b. Wll I Get My Package? Seaky delvery guy of some compay s out delverg packages to customers. Not oly does he had a radom package

More information

Roberto s Notes on Integral Calculus Chapter 4: Definite integrals and the FTC Section 2. Riemann sums

Roberto s Notes on Integral Calculus Chapter 4: Definite integrals and the FTC Section 2. Riemann sums Roerto s Notes o Itegrl Clculus Chpter 4: Defte tegrls d the FTC Secto 2 Rem sums Wht you eed to kow lredy: The defto of re for rectgle. Rememer tht our curret prolem s how to compute the re of ple rego

More information

PubH 7405: REGRESSION ANALYSIS REGRESSION IN MATRIX TERMS

PubH 7405: REGRESSION ANALYSIS REGRESSION IN MATRIX TERMS PubH 745: REGRESSION ANALSIS REGRESSION IN MATRIX TERMS A mtr s dspl of umbers or umercl quttes ld out rectgulr rr of rows d colums. The rr, or two-w tble of umbers, could be rectgulr or squre could be

More information

Rendering Equation. Linear equation Spatial homogeneous Both ray tracing and radiosity can be considered special case of this general eq.

Rendering Equation. Linear equation Spatial homogeneous Both ray tracing and radiosity can be considered special case of this general eq. Rederg quto Ler equto Sptl homogeeous oth ry trcg d rdosty c be cosdered specl cse of ths geerl eq. Relty ctul photogrph Rdosty Mus Rdosty Rederg quls the dfferece or error mge http://www.grphcs.corell.edu/ole/box/compre.html

More information

The use of Analytic Hierarchy Process for the life extension analysis of Air Defense Integrated Systems

The use of Analytic Hierarchy Process for the life extension analysis of Air Defense Integrated Systems The use of Alytc Herrchy Process for the lfe exteso lyss of Ar Defese Itegrted Systems VASILE ŞANDRU, Fculty of Aeroutc Mgemet Her Codă Ar Force Acdemy 0 Mh Vtezul Street, Brşov ROMANIA e-ml svsle@yhoo.com

More information

For combinatorial problems we might need to generate all permutations, combinations, or subsets of a set.

For combinatorial problems we might need to generate all permutations, combinations, or subsets of a set. Addtoal Decrease ad Coquer Algorthms For combatoral problems we mght eed to geerate all permutatos, combatos, or subsets of a set. Geeratg Permutatos If we have a set f elemets: { a 1, a 2, a 3, a } the

More information

Regression. By Jugal Kalita Based on Chapter 17 of Chapra and Canale, Numerical Methods for Engineers

Regression. By Jugal Kalita Based on Chapter 17 of Chapra and Canale, Numerical Methods for Engineers Regresso By Jugl Klt Bsed o Chpter 7 of Chpr d Cle, Numercl Methods for Egeers Regresso Descrbes techques to ft curves (curve fttg) to dscrete dt to obt termedte estmtes. There re two geerl pproches two

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

St John s College. UPPER V Mathematics: Paper 1 Learning Outcome 1 and 2. Examiner: GE Marks: 150 Moderator: BT / SLS INSTRUCTIONS AND INFORMATION

St John s College. UPPER V Mathematics: Paper 1 Learning Outcome 1 and 2. Examiner: GE Marks: 150 Moderator: BT / SLS INSTRUCTIONS AND INFORMATION St Joh s College UPPER V Mthemtcs: Pper Lerg Outcome d ugust 00 Tme: 3 hours Emer: GE Mrks: 50 Modertor: BT / SLS INSTRUCTIONS ND INFORMTION Red the followg structos crefull. Ths questo pper cossts of

More information

Linear Open Loop Systems

Linear Open Loop Systems Colordo School of Me CHEN43 Trfer Fucto Ler Ope Loop Sytem Ler Ope Loop Sytem... Trfer Fucto for Smple Proce... Exmple Trfer Fucto Mercury Thermometer... 2 Derblty of Devto Vrble... 3 Trfer Fucto for Proce

More information

A Brief Introduction to Olympiad Inequalities

A Brief Introduction to Olympiad Inequalities Ev Che Aprl 0, 04 The gol of ths documet s to provde eser troducto to olympd equltes th the stdrd exposto Olympd Iequltes, by Thoms Mldorf I ws motvted to wrte t by feelg gulty for gettg free 7 s o problems

More information

Systems of second order ordinary differential equations

Systems of second order ordinary differential equations Ffth order dgolly mplct Ruge-Kutt Nystrom geerl method solvg secod Order IVPs Fudzh Isml Astrct A dgolly mplct Ruge-Kutt-Nystróm Geerl (SDIRKNG) method of ffth order wth explct frst stge for the tegrto

More information

Chapter 4: Distributions

Chapter 4: Distributions Chpter 4: Dstrbutos Prerequste: Chpter 4. The Algebr of Expecttos d Vrces I ths secto we wll mke use of the followg symbols: s rdom vrble b s rdom vrble c s costt vector md s costt mtrx, d F m s costt

More information

Generalized Hybrid Grey Relation Method for Multiple Attribute Mixed Type Decision Making*

Generalized Hybrid Grey Relation Method for Multiple Attribute Mixed Type Decision Making* Geerlzed Hybrd Grey Relto Method for Multple Attrbute Med Type Decso Mkg Gol K Yuchol Jog Sfeg u b Ceter of Nturl Scece versty of Sceces Pyogyg DPR Kore b College of Ecoocs d Mgeet Ng versty of Aeroutcs

More information

Introduction to local (nonparametric) density estimation. methods

Introduction to local (nonparametric) density estimation. methods Itroducto to local (oparametrc) desty estmato methods A slecture by Yu Lu for ECE 66 Sprg 014 1. Itroducto Ths slecture troduces two local desty estmato methods whch are Parze desty estmato ad k-earest

More information

Hopf Bifurcation of Maglev System with Coupled Elastic Guideway

Hopf Bifurcation of Maglev System with Coupled Elastic Guideway Hopf Bfurcto of Mglev System wth Coupled Elstc udewy No Loghu She, Ho Wg, Dogsheg Zou, Zhzhou Zhg* d Wese Chg Egeerg Reserch Ceter of Mglev Techology, Chgsh Isttute of Techology, Chgsh 7, Hu, PRCh sheloghu@yhoocomc,

More information

An Alternative Method to Find the Solution of Zero One Integer Linear Fractional Programming Problem with the Help of -Matrix

An Alternative Method to Find the Solution of Zero One Integer Linear Fractional Programming Problem with the Help of -Matrix Itertol Jourl of Scetfc d Reserch Pulctos, Volue 3, Issue 6, Jue 3 ISSN 5-353 A Altertve Method to Fd the Soluto of Zero Oe Iteger Ler Frctol Progrg Prole wth the Help of -Mtr VSeeregsy *, DrKJeyr ** *

More information

GEOMETRIC MEAN METHOD FOR JUDGEMENT MATRICES: FORMULAS FOR ERRORS

GEOMETRIC MEAN METHOD FOR JUDGEMENT MATRICES: FORMULAS FOR ERRORS GEOMETRIC MEAN METHOD FOR JUDGEMENT MATRICES: FORMULAS FOR ERRORS I.L. Tomshevs Isttute of Mthemtcs, Iformto d Spce Techologes, Norther (Arctc) Federl Uversty, Arhgels 63000, Russ E-ml: tomshevl@gml.com

More information

The Selection Problem - Variable Size Decrease/Conquer (Practice with algorithm analysis)

The Selection Problem - Variable Size Decrease/Conquer (Practice with algorithm analysis) We have covered: Selecto, Iserto, Mergesort, Bubblesort, Heapsort Next: Selecto the Qucksort The Selecto Problem - Varable Sze Decrease/Coquer (Practce wth algorthm aalyss) Cosder the problem of fdg the

More information

Random variables and sampling theory

Random variables and sampling theory Revew Rdom vrbles d smplg theory [Note: Beg your study of ths chpter by redg the Overvew secto below. The red the correspodg chpter the textbook, vew the correspodg sldeshows o the webste, d do the strred

More information

The z-transform. LTI System description. Prof. Siripong Potisuk

The z-transform. LTI System description. Prof. Siripong Potisuk The -Trsform Prof. Srpog Potsuk LTI System descrpto Prevous bss fucto: ut smple or DT mpulse The put sequece s represeted s ler combto of shfted DT mpulses. The respose s gve by covoluto sum of the put

More information

L5 Polynomial / Spline Curves

L5 Polynomial / Spline Curves L5 Polyomal / Sple Curves Cotets Coc sectos Polyomal Curves Hermte Curves Bezer Curves B-Sples No-Uform Ratoal B-Sples (NURBS) Mapulato ad Represetato of Curves Types of Curve Equatos Implct: Descrbe a

More information

1 Onto functions and bijections Applications to Counting

1 Onto functions and bijections Applications to Counting 1 Oto fuctos ad bectos Applcatos to Coutg Now we move o to a ew topc. Defto 1.1 (Surecto. A fucto f : A B s sad to be surectve or oto f for each b B there s some a A so that f(a B. What are examples of

More information

ITERATIVE METHODS FOR SOLVING SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS

ITERATIVE METHODS FOR SOLVING SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS Numercl Alyss for Egeers Germ Jord Uversty ITERATIVE METHODS FOR SOLVING SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS Numercl soluto of lrge systems of ler lgerc equtos usg drect methods such s Mtr Iverse, Guss

More information

Analysis of Disassembly Systems in Remanufacturing using Kanban Control

Analysis of Disassembly Systems in Remanufacturing using Kanban Control 007-0344 lyss of Dsssembly Systems Remufcturg usg Kb Cotrol ybek Korug, Keml Dcer Dgec Bogzc Uversty, Deprtmet of Idustrl Egeerg, 34342 Bebek, Istbul, Turkey E-ml: ybek.korug@bou.edu.tr hoe: +90 212 359

More information

this is the indefinite integral Since integration is the reverse of differentiation we can check the previous by [ ]

this is the indefinite integral Since integration is the reverse of differentiation we can check the previous by [ ] Atervtves The Itegrl Atervtves Ojectve: Use efte tegrl otto for tervtves. Use sc tegrto rules to f tervtves. Aother mportt questo clculus s gve ervtve f the fucto tht t cme from. Ths s the process kow

More information

Solving Constrained Flow-Shop Scheduling. Problems with Three Machines

Solving Constrained Flow-Shop Scheduling. Problems with Three Machines It J Cotemp Math Sceces, Vol 5, 2010, o 19, 921-929 Solvg Costraed Flow-Shop Schedulg Problems wth Three Maches P Pada ad P Rajedra Departmet of Mathematcs, School of Advaced Sceces, VIT Uversty, Vellore-632

More information

DATA FITTING. Intensive Computation 2013/2014. Annalisa Massini

DATA FITTING. Intensive Computation 2013/2014. Annalisa Massini DATA FITTING Itesve Computto 3/4 Als Mss Dt fttg Dt fttg cocers the problem of fttg dscrete dt to obt termedte estmtes. There re two geerl pproches two curve fttg: Iterpolto Dt s ver precse. The strteg

More information

ON NILPOTENCY IN NONASSOCIATIVE ALGEBRAS

ON NILPOTENCY IN NONASSOCIATIVE ALGEBRAS Jourl of Algebr Nuber Theory: Advces d Applctos Volue 6 Nuber 6 ges 85- Avlble t http://scetfcdvces.co. DOI: http://dx.do.org/.864/t_779 ON NILOTENCY IN NONASSOCIATIVE ALGERAS C. J. A. ÉRÉ M. F. OUEDRAOGO

More information

Chapter 2 Intro to Math Techniques for Quantum Mechanics

Chapter 2 Intro to Math Techniques for Quantum Mechanics Fll 4 Chem 356: Itroductory Qutum Mechcs Chpter Itro to Mth Techques for Qutum Mechcs... Itro to dfferetl equtos... Boudry Codtos... 5 Prtl dfferetl equtos d seprto of vrbles... 5 Itroducto to Sttstcs...

More information

Bond Additive Modeling 5. Mathematical Properties of the Variable Sum Exdeg Index

Bond Additive Modeling 5. Mathematical Properties of the Variable Sum Exdeg Index CROATICA CHEMICA ACTA CCACAA ISSN 00-6 e-issn -7X Crot. Chem. Act 8 () (0) 9 0. CCA-5 Orgl Scetfc Artcle Bod Addtve Modelg 5. Mthemtcl Propertes of the Vrble Sum Edeg Ide Dmr Vukčevć Fculty of Nturl Sceces

More information

On Solution of Min-Max Composition Fuzzy Relational Equation

On Solution of Min-Max Composition Fuzzy Relational Equation U-Sl Scece Jourl Vol.4()7 O Soluto of M-Mx Coposto Fuzzy eltol Equto N.M. N* Dte of cceptce /5/7 Abstrct I ths pper, M-Mx coposto fuzzy relto equto re studed. hs study s geerlzto of the works of Ohsto

More information

OPTIMIZATION OF EAST JAVA ECONOMY BY APPLYING GOVERNMENT POLICY TO MAXIMIZE EMPLOYMENT ABSORPTION (Linear Programming Input-Output Model)

OPTIMIZATION OF EAST JAVA ECONOMY BY APPLYING GOVERNMENT POLICY TO MAXIMIZE EMPLOYMENT ABSORPTION (Linear Programming Input-Output Model) OPTIMIZATION OF EAST JAVA ECONOM B APPLING GOVERNMENT POLIC TO MAIMIZE EMPLOMENT ABSORPTION (Ler Progrmmg Iput-Output Model) Moses L Sggh e-ml: moses@etscd Idustrl Egeerg Deprtmet Isttut Tekolog Sepuluh

More information

Numerical Solution of Higher Order Linear Fredholm Integro Differential Equations.

Numerical Solution of Higher Order Linear Fredholm Integro Differential Equations. Amerc Jorl of Egeerg Reserch (AJER) 04 Amerc Jorl of Egeerg Reserch (AJER) e-iss : 30-0847 p-iss : 30-0936 Volme-03, Isse-08, pp-43-47 www.jer.org Reserch Pper Ope Access mercl Solto of Hgher Order Ler

More information

1.3 Continuous Functions and Riemann Sums

1.3 Continuous Functions and Riemann Sums mth riem sums, prt 0 Cotiuous Fuctios d Riem Sums I Exmple we sw tht lim Lower() = lim Upper() for the fuctio!! f (x) = + x o [0, ] This is o ccidet It is exmple of the followig theorem THEOREM Let f be

More information

Decision Science Letters

Decision Science Letters Decso Scece Letters 4 (205) 49 62 Cotets lsts vlble t GrowgScece Decso Scece Letters homepge: www.growgscece.com/dsl A hybrd pproch bsed o SERVQUAL d fuzzy TOPSIS for evlutg bg servce qulty Mhd Krm, Mld

More information

Design of Bayesian MDS Sampling Plan Based on the Process Capability Index

Design of Bayesian MDS Sampling Plan Based on the Process Capability Index World Acdey of Scece, Egeerg d Techology Vol:, No:0, 07 Desg of Byes MDS Splg Pl Bsed o the Process pblty Idex Dvood Shshebor, Mohd Sber Fllh Nezhd, S Sef Itertol Scece Idex, Idustrl d Mufcturg Egeerg

More information

An Indian Journal FULL PAPER ABSTRACT KEYWORDS. Trade Science Inc. Research on scheme evaluation method of automation mechatronic systems

An Indian Journal FULL PAPER ABSTRACT KEYWORDS. Trade Science Inc. Research on scheme evaluation method of automation mechatronic systems [ype text] [ype text] [ype text] ISSN : 0974-7435 Volume 0 Issue 6 Boechology 204 Ida Joural FULL PPER BIJ, 0(6, 204 [927-9275] Research o scheme evaluato method of automato mechatroc systems BSRC Che

More information

( ) k ( ) 1 T n 1 x = xk. Geometric series obtained directly from the definition. = 1 1 x. See also Scalars 9.1 ADV-1: lim n.

( ) k ( ) 1 T n 1 x = xk. Geometric series obtained directly from the definition. = 1 1 x. See also Scalars 9.1 ADV-1: lim n. Sclrs-9.0-ADV- Algebric Tricks d Where Tylor Polyomils Come From 207.04.07 A.docx Pge of Algebric tricks ivolvig x. You c use lgebric tricks to simplify workig with the Tylor polyomils of certi fuctios..

More information

Supporting Web-Based Instructional Design with Fuzzy Approaches for Assessing Attitude Surveys

Supporting Web-Based Instructional Design with Fuzzy Approaches for Assessing Attitude Surveys Supportg Web-Bsed Istructol Desg wth Fuzzy Approches for Assessg Atttude Surveys Cheg-Chg Jeg Deprtmet of Elemetry Educto, Ntol Ttug Uversty cjeg@cc.ttu.edu.tw Abstrct Durg the developmet process of structol

More information

The Computation of Common Infinity-norm Lyapunov Functions for Linear Switched Systems

The Computation of Common Infinity-norm Lyapunov Functions for Linear Switched Systems ISS 746-7659 Egd UK Jour of Iformto d Comutg Scece Vo. 6 o. 4. 6-68 The Comutto of Commo Ifty-orm yuov Fuctos for er Swtched Systems Zheg Che Y Go Busess Schoo Uversty of Shgh for Scece d Techoogy Shgh

More information

Least Squares Method For Solving Integral Equations With Multiple Time Lags

Least Squares Method For Solving Integral Equations With Multiple Time Lags Eg. & Tech. Jourl, Vol.8, No., Lest Squres Method For Solvg Itegrl Equtos Wth Multple Tme Lgs Dr.Suh N. Sheh*, Hyt Adel Al* & Hl Mohmmed Ysee* Receved o:6//9 Accepted o:// Astrct The m purpose of ths work

More information

Computational Issue of Fuzzy Rule-based System

Computational Issue of Fuzzy Rule-based System IJCSNS Itertol Jourl of Computer Scece d Networ Securty, VOL.6 No.A, Februry 6 Computtol Issue of Fuzzy Rule-bsed System Chushe L Deprtmet of Computer Scece d Iformto Egeerg, Ntol Uversty of T 33, Sec.,

More information

Modeling uncertainty using probabilities

Modeling uncertainty using probabilities S 1571 Itroduto to I Leture 23 Modelg uertty usg probbltes Mlos Huskreht mlos@s.ptt.edu 5329 Seott Squre dmstrto Fl exm: Deember 11 2006 12:00-1:50pm 5129 Seott Squre Uertty To mke dgost feree possble

More information

2.28 The Wall Street Journal is probably referring to the average number of cubes used per glass measured for some population that they have chosen.

2.28 The Wall Street Journal is probably referring to the average number of cubes used per glass measured for some population that they have chosen. .5 x 54.5 a. x 7. 786 7 b. The raked observatos are: 7.4, 7.5, 7.7, 7.8, 7.9, 8.0, 8.. Sce the sample sze 7 s odd, the meda s the (+)/ 4 th raked observato, or meda 7.8 c. The cosumer would more lkely

More information

The Exponential Function

The Exponential Function The Epoetil Fuctio Defiitio: A epoetil fuctio with bse is defied s P for some costt P where 0 d. The most frequetly used bse for epoetil fuctio is the fmous umber e.788... E.: It hs bee foud tht oyge cosumptio

More information

A New Method for Decision Making Based on Soft Matrix Theory

A New Method for Decision Making Based on Soft Matrix Theory Joural of Scetfc esearch & eports 3(5): 0-7, 04; rtcle o. JS.04.5.00 SCIENCEDOMIN teratoal www.scecedoma.org New Method for Decso Mag Based o Soft Matrx Theory Zhmg Zhag * College of Mathematcs ad Computer

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

10.2 Series. , we get. which is called an infinite series ( or just a series) and is denoted, for short, by the symbol. i i n

10.2 Series. , we get. which is called an infinite series ( or just a series) and is denoted, for short, by the symbol. i i n 0. Sere I th ecto, we wll troduce ere tht wll be dcug for the ret of th chpter. Wht ere? If we dd ll term of equece, we get whch clled fte ere ( or jut ere) d deoted, for hort, by the ymbol or Doe t mke

More information

To use adaptive cluster sampling we must first make some definitions of the sampling universe:

To use adaptive cluster sampling we must first make some definitions of the sampling universe: 8.3 ADAPTIVE SAMPLING Most of the methods dscussed samplg theory are lmted to samplg desgs hch the selecto of the samples ca be doe before the survey, so that oe of the decsos about samplg deped ay ay

More information

Schrödinger Equation Via Laplace-Beltrami Operator

Schrödinger Equation Via Laplace-Beltrami Operator IOSR Jourl of Mthemtics (IOSR-JM) e-issn: 78-578, p-issn: 39-765X. Volume 3, Issue 6 Ver. III (Nov. - Dec. 7), PP 9-95 www.iosrjourls.org Schrödiger Equtio Vi Lplce-Beltrmi Opertor Esi İ Eskitşçioğlu,

More information

Lecture 3-4 Solutions of System of Linear Equations

Lecture 3-4 Solutions of System of Linear Equations Lecture - Solutos of System of Ler Equtos Numerc Ler Alger Revew of vectorsd mtrces System of Ler Equtos Guss Elmto (drect solver) LU Decomposto Guss-Sedel method (tertve solver) VECTORS,,, colum vector

More information

COMPLEX NUMBERS AND DE MOIVRE S THEOREM

COMPLEX NUMBERS AND DE MOIVRE S THEOREM COMPLEX NUMBERS AND DE MOIVRE S THEOREM OBJECTIVE PROBLEMS. s equl to b d. 9 9 b 9 9 d. The mgr prt of s 5 5 b 5. If m, the the lest tegrl vlue of m s b 8 5. The vlue of 5... s f s eve, f s odd b f s eve,

More information

Chapter 3 Sampling For Proportions and Percentages

Chapter 3 Sampling For Proportions and Percentages Chapter 3 Samplg For Proportos ad Percetages I may stuatos, the characterstc uder study o whch the observatos are collected are qualtatve ature For example, the resposes of customers may marketg surveys

More information

Section 6.3: Geometric Sequences

Section 6.3: Geometric Sequences 40 Chpter 6 Sectio 6.: Geometric Sequeces My jobs offer ul cost-of-livig icrese to keep slries cosistet with ifltio. Suppose, for exmple, recet college grdute fids positio s sles mger erig ul slry of $6,000.

More information

International Journal of Scientific and Research Publications, Volume 3, Issue 5, May ISSN

International Journal of Scientific and Research Publications, Volume 3, Issue 5, May ISSN Itertol Jourl of Scetfc d Reserch Pulctos, Volue 3, Issue 5, My 13 1 A Effcet Method for Esy Coputto y Usg - Mtr y Cosderg the Iteger Vlues for Solvg Iteger Ler Frctol Progrg Proles VSeeregsy *, DrKJeyr

More information

CS473-Algorithms I. Lecture 3. Solving Recurrences. Cevdet Aykanat - Bilkent University Computer Engineering Department

CS473-Algorithms I. Lecture 3. Solving Recurrences. Cevdet Aykanat - Bilkent University Computer Engineering Department CS473-Algorthms I Lecture 3 Solvg Recurreces Cevdet Aykt - Blket Uversty Computer Egeerg Deprtmet Solvg Recurreces The lyss of merge sort Lecture requred us to solve recurrece. Recurreces re lke solvg

More information

Functions of Random Variables

Functions of Random Variables Fuctos of Radom Varables Chapter Fve Fuctos of Radom Varables 5. Itroducto A geeral egeerg aalyss model s show Fg. 5.. The model output (respose) cotas the performaces of a system or product, such as weght,

More information

CHAPTER 4 RADICAL EXPRESSIONS

CHAPTER 4 RADICAL EXPRESSIONS 6 CHAPTER RADICAL EXPRESSIONS. The th Root of a Real Number A real umber a s called the th root of a real umber b f Thus, for example: s a square root of sce. s also a square root of sce ( ). s a cube

More information

PROGRESSIONS AND SERIES

PROGRESSIONS AND SERIES PROGRESSIONS AND SERIES A sequece is lso clled progressio. We ow study three importt types of sequeces: () The Arithmetic Progressio, () The Geometric Progressio, () The Hrmoic Progressio. Arithmetic Progressio.

More information

Patterns of Continued Fractions with a Positive Integer as a Gap

Patterns of Continued Fractions with a Positive Integer as a Gap IOSR Jourl of Mthemtcs (IOSR-JM) e-issn: 78-578, -ISSN: 39-765X Volume, Issue 3 Ver III (My - Ju 6), PP -5 wwwosrjourlsorg Ptters of Cotued Frctos wth Postve Iteger s G A Gm, S Krth (Mthemtcs, Govermet

More information