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

Size: px
Start display at page:

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

Transcription

1 Avlble ole wwwsceceeccom Physcs Poce 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 Ou uose s o el wh he mee esmo hyohess es o he equly of wo eve boml sbuo oulos wh mss he cossecy symoc omly of he esmos e ove I o ssc o es equly of wo eve sbuos s lm sbuo e obe 0 0 Publshe by lseve by lseve BV Seleco L Seleco /o ee /o evew ee-evew ue esosbly ue esosbly of ICMPB Ieol of me Commee oze] Oe ccess ue CC BY-NC-ND lcese Keywos:mss mxmum lkelhoo esmo hyohess es Iouco he oblem of mss s vey commo my sues fel exemes see Lekowsk Ls & Sehouwe] Km & Cuy] Mss c bs mee esme A vey of mehos hve bee eveloe o esme he ukow mees of ffee moels whe hee exss mss Refeece ] els wh he mee esmo hyohess es o he equly of wo exoel sbuo ue ye ceso smle wh mss Refeece 4] cosee he esmo fo wo boml sbuos wh lly mss xc Lkelhoo Ifeece fo wo xoel Poulos ue Jo ye -II Ceso ws sue by Blksh Rsoul see 5] Moeove Refeece 6] vese he esmo es fo wo oml oulos wh lly mss I hs e Ou uose s o el wh he mee esmo hyohess es o he equly of wo eve boml sbuo oulos wh mss he cossecy symoc omly of he esmos e ove I o ssc o es equly of wo eve sbuos s lm sbuo e ve he es of hs e s oze s follows I Seco II we ouce ob he mee esmo I Seco III we e he lm sbuo of esmo he hyohess es Publshe by lseve BV Seleco /o ee evew ue esosbly of ICMPB Ieol Commee Oe ccess ue CC BY-NC-ND lcese o:006/jho0054

2 476 Zhwe Zho / Physcs Poce cofece evl bou he ffeece of mees wo oulos e scusse Seco IV Mxmum lkelhoo esmo I hs seco we cose he mxmum lkelhoo esmo fo he mee eve boml sbuo oulos wh mss Cose he follow wo eve boml sbuo oulos whose obbly fucos e f x; C x x- fo x 0 ohewse whee e ukow mees Fo hs sbuo we focus o he cse whee some vlues smle of sze my be mss h s we ob he follow comlee obsevos Y fom wo bove oulos Whe s mss Whe Y s mss Fuhemoe we ssume h P P I wh follows we cose he esmo of Bse o he obsevos he lkelhoo fuco c be we - C ] L Hece he lohm of he lkelhoo fuco s ve by Noe h l C l - l ] l L l L Solv he lo-lkelhoo equo we ob I sml wy we hve Y - ]

3 Zhwe Zho / Physcs Poce he lm oey of esmos I hs seco we cose he lm oey of esmos heoem : s s whee " " eoes coveece lmos suely Poof Noe h e eeely ecl sbue vble we hve s Afe smle clculo we e whch comb wh ves Fuhe by we hve s s s heoem : s s whee " " eoes coveece lmos suely By us he sme meho s we use o ove heoem we c ove heoem so we om he oof hee Lemm : Le k k k hs couous l evo If L N0 he k k ] N0 whee j eoe coveece sbuo j k k j heoem : N0 whee Poof Le W We hve { W } s eeely ecl sbue vble W Le W W W W

4 478 Zhwe Zho / Physcs Poce By mulve cel lm heoem we hve 0 N W W We whee Le We hve By smle clculo we hve By Lemm we hve 0 ] N whee heoem 4: 0 N whee By us he sme meho s we use o ove heoem we c ove heoem 4 so we om he oof hee

5 Zhwe Zho / Physcs Poce es he equly of wo oulos cofece evl fo I hs seco we cose he follow hyoheses: 0 : 0 : 0 H H Fs we esblsh es sscs scuss he lm sbuo of es sscs Le By he so le umbe lw we hve s s s heefoe we c ob he follow esul: heoem 5: 0 ] N Pcully ue he-ull hyohess 0 H we hve 0 ] N Poof By Slusky heoem heoem heoem we c ove heoem 4 Le wh follows we scuss he symoc cofece evl of Fo 0< <ssume h ssfes x e Fo ve cofece level by heoem we hve ] P heefoe we ob he cofece evl of :

6 480 Zhwe Zho / Physcs Poce Ackowleme hs wok s suoe by Nol Nul Scece Fouo of Ch No Refeeces ] J M Lekowsk J R L S A Sehouwe "Sees fo he lyss of mue fom smle suvey: he ol mecl ce ulzo exeue suvey" Mecl Ce vol ] JO Km J Cuy "he eme of mss mulve lyss" Socolocl Mehos & Resech vol ] ZW Zho SYW RW L L "Pmee esmo hyohess es of wo exoel oulos ue ye ceso smle wh msse " Joul of Jl Uvesy Scece o vol ] HY LI ZJOU "smo fo wo boml sbuos wh lly mss " Joul of Gsu Lhe Uvesy Nul Sceces vol ] N Blksh Abbs Rsoul "xc lkelhoo feece fo wo exoel oulos ue jo ye -II ceso" Comuol Sscs & D Alyss vol ] YP Lu "smo es fo wo oml oulos wh lly mss " Joul of Nohes Noml Uvesy Scece o vol

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

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

On Fractional Operational Calculus pertaining to the product of H- functions

On Fractional Operational Calculus pertaining to the product of H- functions nenonl eh ounl of Enneen n ehnolo RE e-ssn: 2395-56 Volume: 2 ue: 3 une-25 wwwene -SSN: 2395-72 On Fonl Oeonl Clulu enn o he ou of - funon D VBL Chu, C A 2 Demen of hem, Unve of Rhn, u-3255, n E-ml : vl@hooom

More information

Maximum likelihood estimate of phylogeny. BIOL 495S/ CS 490B/ MATH 490B/ STAT 490B Introduction to Bioinformatics April 24, 2002

Maximum likelihood estimate of phylogeny. BIOL 495S/ CS 490B/ MATH 490B/ STAT 490B Introduction to Bioinformatics April 24, 2002 Mmm lkelhood eme of phylogey BIO 9S/ S 90B/ MH 90B/ S 90B Iodco o Bofomc pl 00 Ovevew of he pobblc ppoch o phylogey o k ee ccodg o he lkelhood d ee whee d e e of eqece d ee by ee wh leve fo he eqece. he

More information

X-Ray Notes, Part III

X-Ray Notes, Part III oll 6 X-y oe 3: Pe X-Ry oe, P III oe Deeo Coe oupu o x-y ye h look lke h: We efe ue of que lhly ffee efo h ue y ovk: Co: C ΔS S Sl o oe Ro: SR S Co o oe Ro: CR ΔS C SR Pevouly, we ee he SR fo ye hv pxel

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

FRACTIONAL MELLIN INTEGRAL TRANSFORM IN (0, 1/a)

FRACTIONAL MELLIN INTEGRAL TRANSFORM IN (0, 1/a) Ieol Jol o Se Reeh Pblo Volme Ie 5 y ISSN 5-5 FRACTIONAL ELLIN INTEGRAL TRANSFOR IN / S.. Kh R..Pe* J.N.Slke** Deme o hem hh Aemy o Egeeg Al-45 Pe I oble No.: 98576F No.: -785759 Eml-mkh@gml.om Deme o

More information

T h e C S E T I P r o j e c t

T h e C S E T I P r o j e c t T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T

More information

-HYBRID LAPLACE TRANSFORM AND APPLICATIONS TO MULTIDIMENSIONAL HYBRID SYSTEMS. PART II: DETERMINING THE ORIGINAL

-HYBRID LAPLACE TRANSFORM AND APPLICATIONS TO MULTIDIMENSIONAL HYBRID SYSTEMS. PART II: DETERMINING THE ORIGINAL UPB Sc B See A Vo 72 I 3 2 ISSN 223-727 MUTIPE -HYBRID APACE TRANSORM AND APPICATIONS TO MUTIDIMENSIONA HYBRID SYSTEMS PART II: DETERMININ THE ORIINA Ve PREPEIŢĂ Te VASIACHE 2 Ace co copeeă oă - pce he

More information

P a g e 3 6 of R e p o r t P B 4 / 0 9

P a g e 3 6 of R e p o r t P B 4 / 0 9 P a g e 3 6 of R e p o r t P B 4 / 0 9 p r o t e c t h um a n h e a l t h a n d p r o p e r t y fr om t h e d a n g e rs i n h e r e n t i n m i n i n g o p e r a t i o n s s u c h a s a q u a r r y. J

More information

ON THE EXTENSION OF WEAK ARMENDARIZ RINGS RELATIVE TO A MONOID

ON THE EXTENSION OF WEAK ARMENDARIZ RINGS RELATIVE TO A MONOID wwweo/voue/vo9iue/ijas_9 9f ON THE EXTENSION OF WEAK AENDAIZ INGS ELATIVE TO A ONOID Eye A & Ayou Eoy Dee of e Nowe No Uvey Lzou 77 C Dee of e Uvey of Kou Ou Su E-: eye76@o; you975@yooo ABSTACT Fo oo we

More information

4. Runge-Kutta Formula For Differential Equations

4. Runge-Kutta Formula For Differential Equations NCTU Deprme o Elecrcl d Compuer Egeerg 5 Sprg Course by Pro. Yo-Pg Ce. Ruge-Ku Formul For Derel Equos To solve e derel equos umerclly e mos useul ormul s clled Ruge-Ku ormul

More information

_ J.. C C A 551NED. - n R ' ' t i :. t ; . b c c : : I I .., I AS IEC. r '2 5? 9

_ J.. C C A 551NED. - n R ' ' t i :. t ; . b c c : : I I .., I AS IEC. r '2 5? 9 C C A 55NED n R 5 0 9 b c c \ { s AS EC 2 5? 9 Con 0 \ 0265 o + s ^! 4 y!! {! w Y n < R > s s = ~ C c [ + * c n j R c C / e A / = + j ) d /! Y 6 ] s v * ^ / ) v } > { ± n S = S w c s y c C { ~! > R = n

More information

Caputo Equations in the frame of fractional operators with Mittag-Leffler kernels

Caputo Equations in the frame of fractional operators with Mittag-Leffler kernels nvenon Jounl o Reseh Tehnoloy n nneen & Mnemen JRTM SSN: 455-689 wwwjemom Volume ssue 0 ǁ Ooe 08 ǁ PP 9-45 Cuo uons n he me o onl oeos wh M-ele enels on Qn Chenmn Hou* Ynn Unvesy Jln Ynj 00 ASTRACT: n

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

Rotations.

Rotations. oons j.lbb@phscs.o.c.uk To s summ Fmes of efeence Invnce une nsfomons oon of wve funcon: -funcons Eule s ngles Emple: e e - - Angul momenum s oon geneo Genec nslons n Noehe s heoem Fmes of efeence Conse

More information

4. Runge-Kutta Formula For Differential Equations. A. Euler Formula B. Runge-Kutta Formula C. An Example for Fourth-Order Runge-Kutta Formula

4. Runge-Kutta Formula For Differential Equations. A. Euler Formula B. Runge-Kutta Formula C. An Example for Fourth-Order Runge-Kutta Formula NCTU Deprme o Elecrcl d Compuer Egeerg Seor Course By Pro. Yo-Pg Ce. Ruge-Ku Formul For Derel Equos A. Euler Formul B. Ruge-Ku Formul C. A Emple or Four-Order Ruge-Ku Formul

More information

Generalized Fibonacci-Type Sequence and its Properties

Generalized Fibonacci-Type Sequence and its Properties Geelized Fibocci-Type Sequece d is Popeies Ompsh Sihwl shw Vys Devshi Tuoil Keshv Kuj Mdsu (MP Idi Resech Schol Fculy of Sciece Pcific Acdemy of Highe Educio d Resech Uivesiy Udipu (Rj Absc: The Fibocci

More information

I I M O I S K J H G. b gb g. Chapter 8. Problem Solutions. Semiconductor Physics and Devices: Basic Principles, 3 rd edition Chapter 8

I I M O I S K J H G. b gb g. Chapter 8. Problem Solutions. Semiconductor Physics and Devices: Basic Principles, 3 rd edition Chapter 8 emcouc hyscs evces: Bsc rcles, r eo Cher 8 oluos ul rolem oluos Cher 8 rolem oluos 8. he fwr s e ex f The e ex f e e f ex () () f f f f l G e f f ex f 59.9 m 60 m 0 9. m m 8. e ex we c wre hs s e ex h

More information

TWO INTERFACIAL COLLINEAR GRIFFITH CRACKS IN THERMO- ELASTIC COMPOSITE MEDIA

TWO INTERFACIAL COLLINEAR GRIFFITH CRACKS IN THERMO- ELASTIC COMPOSITE MEDIA WO INERFIL OLLINER GRIFFIH RS IN HERMO- ELSI OMOSIE MEDI h m MISHR S DS * Deme o Mheml See I Ie o eholog BHU V-5 I he oee o he le o he e e o eeg o o olle Gh e he ee o he wo ohoo mel e e e emee el. he olem

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

A DUAL-RECIPROCITY BOUNDARY ELEMENT METHOD FOR ANISOTROPIC HEAT CONDUCTION IN INHOMOGENEOUS SOLIDS

A DUAL-RECIPROCITY BOUNDARY ELEMENT METHOD FOR ANISOTROPIC HEAT CONDUCTION IN INHOMOGENEOUS SOLIDS s Ieo ofeece Fo Scefc ou o ouo Eee s I-SE Ahes 8- Seebe 4 I-SE A DUA-REIPROIY BOUDARY EEE EHOD FOR AISOROPI HEA ODUIO I IHOOGEEOUS SOIDS W.. A K. K. hoo Dvso of Eee echcs Schoo of echc Pouco Eee y echooc

More information

THIS PAGE DECLASSIFIED IAW EO 12958

THIS PAGE DECLASSIFIED IAW EO 12958 THIS PAGE DECLASSIFIED IAW EO 2958 THIS PAGE DECLASSIFIED IAW EO 2958 THIS PAGE DECLASSIFIED IAW E0 2958 S T T T I R F R S T Exhb e 3 9 ( 66 h Bm dn ) c f o 6 8 b o d o L) B C = 6 h oup C L) TO d 8 f f

More information

ON TOTAL TIME ON TEST TRANSFORM ORDER ABSTRACT

ON TOTAL TIME ON TEST TRANSFORM ORDER ABSTRACT V M Chacko E CONVE AND INCREASIN CONVE OAL IME ON ES RANSORM ORDER R&A # 4 9 Vol. Decembe ON OAL IME ON ES RANSORM ORDER V. M. Chacko Depame of Sascs S. homas Collee hss eala-68 Emal: chackovm@mal.com

More information

Bethe-Salpeter Equation

Bethe-Salpeter Equation Behe-Slpee Equo No-elvs Fomlsm Behe-Slpee Equo: ouo o he op. Dgesso Seo Quzo. Dgesso: fs quzo s movo fo seo quzo. Quum Fel Theoel Hmlo Seo Quzo. Shöge Equo. Equo of Moo. Shöge Fomulo. Behe-Slpee Equo fo

More information

Interval Estimation. Consider a random variable X with a mean of X. Let X be distributed as X X

Interval Estimation. Consider a random variable X with a mean of X. Let X be distributed as X X ECON 37: Ecoomercs Hypohess Tesg Iervl Esmo Wh we hve doe so fr s o udersd how we c ob esmors of ecoomcs reloshp we wsh o sudy. The queso s how comforble re we wh our esmors? We frs exme how o produce

More information

Jacobi Similarity Transformation for SVD and Tikhonov Regularization for Least Squares Problem: The Theoretical foundation

Jacobi Similarity Transformation for SVD and Tikhonov Regularization for Least Squares Problem: The Theoretical foundation IOSR Joul of Mhemcs IOSR-JM e-issn: 78-578 -ISSN: 39-765X Volume Issue 5 Ve VII Se - Oc6 PP 76-85 wwwosoulsog Jcob Smly sfomo fo SVD d hoov Regulzo fo Les Sues Poblem: he heoecl foudo Sehe Ehdmhe Uwmus

More information

On the hydrogen wave function in Momentum-space, Clifford algebra and the Generating function of Gegenbauer polynomial

On the hydrogen wave function in Momentum-space, Clifford algebra and the Generating function of Gegenbauer polynomial O he hoge we fco Moe-sce ffo geb he eeg fco of egebe oo Meh Hge Hss To ce hs eso: Meh Hge Hss O he hoge we fco Moe-sce ffo geb he eeg fco of egebe oo 8 HL I: h- hs://hches-oeesf/h- Sbe o J 8 HL s

More information

Lagrangian & Hamiltonian Mechanics:

Lagrangian & Hamiltonian Mechanics: XII AGRANGIAN & HAMITONIAN DYNAMICS Iouco Hamlo aaoal Pcple Geealze Cooaes Geealze Foces agaga s Euao Geealze Momea Foces of Cosa, agage Mulples Hamloa Fucos, Cosevao aws Hamloa Dyamcs: Hamlo s Euaos agaga

More information

Eurasian International Center of Theoretical Physics, Eurasian National University, Astana , Kazakhstan

Eurasian International Center of Theoretical Physics, Eurasian National University, Astana , Kazakhstan Joul o Mhems d sem ee 8 8 87-95 do: 765/59-59/8 D DAVID PUBLIHIG E Loled oluos o he Geeled +-Dmesol Ldu-Lsh Equo Gulgssl ugmov Ao Mul d Zh gdullev Eus Ieol Cee o Theoel Phss Eus ol Uves As 8 Khs As: I

More information

Conquering kings their titles take ANTHEM FOR CONGREGATION AND CHOIR

Conquering kings their titles take ANTHEM FOR CONGREGATION AND CHOIR Coquerg gs her es e NTHEM FOR CONGREGTION ND CHOIR I oucg hs hm-hem, whch m be cuded Servce eher s Hm or s hem, he Cogrego m be referred o he No. of he Hm whch he words pper, d ved o o sgg he 1 s, 4 h,

More information

Calculus 241, section 12.2 Limits/Continuity & 12.3 Derivatives/Integrals notes by Tim Pilachowski r r r =, with a domain of real ( )

Calculus 241, section 12.2 Limits/Continuity & 12.3 Derivatives/Integrals notes by Tim Pilachowski r r r =, with a domain of real ( ) Clculu 4, econ Lm/Connuy & Devve/Inel noe y Tm Plchow, wh domn o el Wh we hve o : veco-vlued uncon, ( ) ( ) ( ) j ( ) nume nd ne o veco The uncon, nd A w done wh eul uncon ( x) nd connuy e he componen

More information

f(x) dx with An integral having either an infinite limit of integration or an unbounded integrand is called improper. Here are two examples dx x x 2

f(x) dx with An integral having either an infinite limit of integration or an unbounded integrand is called improper. Here are two examples dx x x 2 Impope Inegls To his poin we hve only consideed inegls f() wih he is of inegion nd b finie nd he inegnd f() bounded (nd in fc coninuous ecep possibly fo finiely mny jump disconinuiies) An inegl hving eihe

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

EGN 3321 Final Exam Review Spring 2017

EGN 3321 Final Exam Review Spring 2017 EN 33 l Em Reew Spg 7 *T fshg ech poblem 5 mues o less o pcce es-lke me coss. The opcs o he pcce em e wh feel he bee sessed clss, bu hee m be poblems o he es o lke oes hs pcce es. Use ohe esouces lke he

More information

International Mathematical Forum, Vol. 9, 2014, no. 13, HIKARI Ltd,

International Mathematical Forum, Vol. 9, 2014, no. 13, HIKARI Ltd, Ieol Mhemcl oum Vol. 9 4 o. 3 65-6 HIKARI Ld www.m-h.com hp//d.do.o/.988/m.4.43 Some Recuece Relo ewee he Sle Doule d Tple Mome o Ode Sc om Iveed mm Duo d hceo S. M. Ame * ollee o Scece d Hume Quwh Shq

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

The sphere of radius a has the geographical form. r (,)=(acoscos,acossin,asin) T =(p(u)cos v, p(u)sin v,q(u) ) T.

The sphere of radius a has the geographical form. r (,)=(acoscos,acossin,asin) T =(p(u)cos v, p(u)sin v,q(u) ) T. Che 5. Dieeil Geome o Sces 5. Sce i meic om I 3D sce c be eeseed b. Elici om z =. Imlici om z = 3. Veco om = o moe geel =z deedig o wo mees. Emle. he shee o dis hs he geoghicl om =coscoscossisi Emle. he

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

In order to ensure that an overall development in service by those. of total. rel:rtins lo the wapris are

In order to ensure that an overall development in service by those. of total. rel:rtins lo the wapris are AhAY ggkhu e evue he eve us wch my be eese s esu eucs ese mbes buges hve bee ke cvu vs. Css e vse e' he w m ceges cec ec css. Dec Dgqs_1q W qge5ee.pe_s_ v V cuss ke ecy 1 hc huse ees. bse cu wc esb shmes.

More information

Multiquadrics method for Couette flow of a yield-stress fluid under imposed torques

Multiquadrics method for Couette flow of a yield-stress fluid under imposed torques Ieol Wokshop o MeshFee Mehods 003 Mulqudcs mehod fo Couee flo of yeld-sess flud ude mposed oques M. E-R, A., C. ou, O. Seo-Gullume Absc: A L descpo of he Couee flo beee o col cyldes, of vscoplsc flud (.e.

More information

Homework 5 for BST 631: Statistical Theory I Solutions, 09/21/2006

Homework 5 for BST 631: Statistical Theory I Solutions, 09/21/2006 Homewok 5 fo BST 63: Sisicl Theoy I Soluions, 9//6 Due Time: 5:PM Thusy, on 9/8/6. Polem ( oins). Book olem.8. Soluion: E = x f ( x) = ( x) f ( x) + ( x ) f ( x) = xf ( x) + xf ( x) + f ( x) f ( x) Accoing

More information

Faraday s Law. To be able to find. motional emf transformer and motional emf. Motional emf

Faraday s Law. To be able to find. motional emf transformer and motional emf. Motional emf Objecie F s w Tnsfome Moionl To be ble o fin nsfome. moionl nsfome n moionl. 331 1 331 Mwell s quion: ic Fiel D: Guss lw :KV : Guss lw H: Ampee s w Poin Fom Inegl Fom D D Q sufce loop H sufce H I enclose

More information

Decompression diagram sampler_src (source files and makefiles) bin (binary files) --- sh (sample shells) --- input (sample input files)

Decompression diagram sampler_src (source files and makefiles) bin (binary files) --- sh (sample shells) --- input (sample input files) . Iroduco Probblsc oe-moh forecs gudce s mde b 50 esemble members mproved b Model Oupu scs (MO). scl equo s mde b usg hdcs d d observo d. We selec some prmeers for modfg forecs o use mulple regresso formul.

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

() t. () t r () t or v. ( t) () () ( ) = ( ) or ( ) () () () t or dv () () Section 10.4 Motion in Space: Velocity and Acceleration

() t. () t r () t or v. ( t) () () ( ) = ( ) or ( ) () () () t or dv () () Section 10.4 Motion in Space: Velocity and Acceleration Secion 1.4 Moion in Spce: Velociy nd Acceleion We e going o dive lile deepe ino somehing we ve ledy inoduced, nmely () nd (). Discuss wih you neighbo he elionships beween posiion, velociy nd cceleion you

More information

The Nehari Manifold for a Class of Elliptic Equations of P-laplacian Type. S. Khademloo and H. Mohammadnia. afrouzi

The Nehari Manifold for a Class of Elliptic Equations of P-laplacian Type. S. Khademloo and H. Mohammadnia. afrouzi Wold Alied cieces Joal (8): 898-95 IN 88-495 IDOI Pblicaios = h x g x x = x N i W whee is a eal aamee is a boded domai wih smooh boday i R N 3 ad< < INTRODUCTION Whee s ha is s = I his ae we ove he exisece

More information

Beechwood Music Department Staff

Beechwood Music Department Staff Beechwood Music Department Staff MRS SARAH KERSHAW - HEAD OF MUSIC S a ra h K e rs h a w t r a i n e d a t t h e R oy a l We ls h C o l le g e of M u s i c a n d D ra m a w h e re s h e ob t a i n e d

More information

( ) ( ) Weibull Distribution: k ti. u u. Suppose t 1, t 2, t n are times to failure of a group of n mechanisms. The likelihood function is

( ) ( ) Weibull Distribution: k ti. u u. Suppose t 1, t 2, t n are times to failure of a group of n mechanisms. The likelihood function is Webll Dsbo: Des Bce Dep of Mechacal & Idsal Egeeg The Uvesy of Iowa pdf: f () exp Sppose, 2, ae mes o fale of a gop of mechasms. The lelhood fco s L ( ;, ) exp exp MLE: Webll 3//2002 page MLE: Webll 3//2002

More information

4.1 Schrödinger Equation in Spherical Coordinates

4.1 Schrödinger Equation in Spherical Coordinates Phs 34 Quu Mehs D 9 9 Mo./ Wed./ Thus /3 F./4 Mo., /7 Tues. / Wed., /9 F., /3 4.. -. Shodge Sphe: Sepo & gu (Q9.) 4..-.3 Shodge Sphe: gu & d(q9.) Copuo: Sphe Shodge s 4. Hdoge o (Q9.) 4.3 gu Moeu 4.4.-.

More information

Calculation of Effective Resonance Integrals

Calculation of Effective Resonance Integrals Clculo of ffecve Resoce egrls S.B. Borzkov FLNP JNR Du Russ Clculo of e effecve oce egrl wc cludes e rel eerg deedece of euro flux des d correco o e euro cure e smle s eeded for ccure flux deermo d euro

More information

AC 2-3 AC 1-1 AC 1-2 CO2 AC 1-3 T CO2 CO2 F ES S I O N RY WO M No.

AC 2-3 AC 1-1 AC 1-2 CO2 AC 1-3 T CO2 CO2 F ES S I O N RY WO M No. SHEE OES. OVE PCE HOSS SSOCE PPUCES. VE EW CORO WR. S SE EEVO S EXS. 2. EW SSORS CCOS. S SE EEVO S HOSS. C 2-3 C - C -2 C 2- C -3 C 4- C 2-2 P SUB pproved Filename: :\\2669 RP Performing rts Center HVC\6-C\s\2669-3.dwg

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

On the Quasi-Hyperbolic Kac-Moody Algebra QHA7 (2)

On the Quasi-Hyperbolic Kac-Moody Algebra QHA7 (2) Ieaoal Reeach Joual of Egeeg ad Techology (IRJET) e-issn: 9 - Volume: Iue: May- www.e.e -ISSN: 9-7 O he Qua-Hyebolc Kac-Moody lgeba QH7 () Uma Mahewa., Khave. S Deame of Mahemac Quad-E-Mllah Goveme College

More information

A L A BA M A L A W R E V IE W

A L A BA M A L A W R E V IE W A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N

More information

Go over vector and vector algebra Displacement and position in 2-D Average and instantaneous velocity in 2-D Average and instantaneous acceleration

Go over vector and vector algebra Displacement and position in 2-D Average and instantaneous velocity in 2-D Average and instantaneous acceleration Mh Csquee Go oe eco nd eco lgeb Dsplcemen nd poson n -D Aege nd nsnneous eloc n -D Aege nd nsnneous cceleon n -D Poecle moon Unfom ccle moon Rele eloc* The componens e he legs of he gh ngle whose hpoenuse

More information

Addition & Subtraction of Polynomials

Addition & Subtraction of Polynomials Addiion & Sucion of Polynomil Addiion of Polynomil: Adding wo o moe olynomil i imly me of dding like em. The following ocedue hould e ued o dd olynomil 1. Remove enhee if hee e enhee. Add imil em. Wie

More information

«A first lesson on Mathematical Induction»

«A first lesson on Mathematical Induction» Bcgou ifotio: «A fist lesso o Mtheticl Iuctio» Mtheticl iuctio is topic i H level Mthetics It is useful i Mtheticl copetitios t ll levels It hs bee coo sight tht stuets c out the poof b theticl iuctio,

More information

1. Consider an economy of identical individuals with preferences given by the utility function

1. Consider an economy of identical individuals with preferences given by the utility function CO 755 Problem Se e Cbrer. Cosder ecoomy o decl dduls wh reereces e by he uly uco U l l Pre- rces o ll hree oods re ormled o oe. Idduls suly ood lbor < d cosume oods d. The oerme c mose d lorem es o oods

More information

THIS PAGE DECLASSIFIED IAW EO IRIS u blic Record. Key I fo mation. Ma n: AIR MATERIEL COMM ND. Adm ni trative Mar ings.

THIS PAGE DECLASSIFIED IAW EO IRIS u blic Record. Key I fo mation. Ma n: AIR MATERIEL COMM ND. Adm ni trative Mar ings. T H S PA G E D E CLA SSFED AW E O 2958 RS u blc Recod Key fo maon Ma n AR MATEREL COMM ND D cumen Type Call N u b e 03 V 7 Rcvd Rel 98 / 0 ndexe D 38 Eneed Dae RS l umbe 0 0 4 2 3 5 6 C D QC d Dac A cesson

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

What do you think I fought for at Omaha Beach? 1_1. My name is Phil - lip Spoon- er, and I ... "-- -. "a...,

What do you think I fought for at Omaha Beach? 1_1. My name is Phil - lip Spoon- er, and I ... -- -. a..., 2 Wht do you thnk ought o t Omh Bech? Fo STB Chous Text tken om testmony beoe Mne Stte Congess by hlp Spoone dgo J=60 Melss Dunphy Sopno MN m= " Good mon ng com mttee Good lto Teno 0 4 " L o" : 4 My nme

More information

Exact Moments of Record Values from Burr Distribution. with Applications

Exact Moments of Record Values from Burr Distribution. with Applications Ieo Jou of Comuo d Theoec Sc ISSN -59 I. J. Com. Theo. S. No. Nov-5 Ec Mome of Recod Vue fom Bu Dbuo wh Aco M. J. S. Kh A. Shm M. I. Kh d S. Kum 3 Deme of Sc d Oeo Reech Agh Mum Uve Agh Id Deme of Mhemc

More information

ANSWERS TO ODD NUMBERED EXERCISES IN CHAPTER 2

ANSWERS TO ODD NUMBERED EXERCISES IN CHAPTER 2 Joh Rley Novembe ANSWERS O ODD NUMBERED EXERCISES IN CHAPER Seo Eese -: asvy (a) Se y ad y z follows fom asvy ha z Ehe z o z We suppose he lae ad seek a oado he z Se y follows by asvy ha z y Bu hs oads

More information

CHATTERJEA CONTRACTION MAPPING THEOREM IN CONE HEPTAGONAL METRIC SPACE

CHATTERJEA CONTRACTION MAPPING THEOREM IN CONE HEPTAGONAL METRIC SPACE Fameal Joal of Mahemaic a Mahemaical Sciece Vol. 7 Ie 07 Page 5- Thi pape i aailable olie a hp://.fi.com/ Pblihe olie Jaa 0 07 CHATTERJEA CONTRACTION MAPPING THEOREM IN CONE HEPTAGONAL METRIC SPACE Caolo

More information

Exponential Synchronization of the Hopfield Neural Networks with New Chaotic Strange Attractor

Exponential Synchronization of the Hopfield Neural Networks with New Chaotic Strange Attractor ITM Web of Cofeeces, 0509 (07) DOI: 0.05/ mcof/070509 ITA 07 Expoeal Sychozao of he Hopfeld Neual Newos wh New Chaoc Sage Aaco Zha-J GUI, Ka-Hua WANG* Depame of Sofwae Egeeg, Haa College of Sofwae Techology,qogha,

More information

Circuits 24/08/2010. Question. Question. Practice Questions QV CV. Review Formula s RC R R R V IR ... Charging P IV I R ... E Pt.

Circuits 24/08/2010. Question. Question. Practice Questions QV CV. Review Formula s RC R R R V IR ... Charging P IV I R ... E Pt. 4/08/00 eview Fomul s icuis cice s BL B A B I I I I E...... s n n hging Q Q 0 e... n... Q Q n 0 e Q I I0e Dischging Q U Q A wie mde of bss nd nohe wie mde of silve hve he sme lengh, bu he dimee of he bss

More information

Professor Wei Zhu. 1. Sampling from the Normal Population

Professor Wei Zhu. 1. Sampling from the Normal Population AMS570 Pofesso We Zhu. Samplg fom the Nomal Populato *Example: We wsh to estmate the dstbuto of heghts of adult US male. It s beleved that the heght of adult US male follows a omal dstbuto N(, ) Def. Smple

More information

Graphing Review Part 3: Polynomials

Graphing Review Part 3: Polynomials Grphig Review Prt : Polomils Prbols Recll, tht the grph of f ( ) is prbol. It is eve fuctio, hece it is smmetric bout the bout the -is. This mes tht f ( ) f ( ). Its grph is show below. The poit ( 0,0)

More information

Physics 201, Lecture 5

Physics 201, Lecture 5 Phsics 1 Lecue 5 Tod s Topics n Moion in D (Chp 4.1-4.3): n D Kinemicl Quniies (sec. 4.1) n D Kinemics wih Consn Acceleion (sec. 4.) n D Pojecile (Sec 4.3) n Epeced fom Peiew: n Displcemen eloci cceleion

More information

Quality control. Final exam: 2012/1/12 (Thur), 9:00-12:00 Q1 Q2 Q3 Q4 Q5 YOUR NAME

Quality control. Final exam: 2012/1/12 (Thur), 9:00-12:00 Q1 Q2 Q3 Q4 Q5 YOUR NAME Qulity contol Finl exm: // (Thu), 9:-: Q Q Q3 Q4 Q5 YOUR NAME NOTE: Plese wite down the deivtion of you nswe vey clely fo ll questions. The scoe will be educed when you only wite nswe. Also, the scoe will

More information

P a g e 5 1 of R e p o r t P B 4 / 0 9

P a g e 5 1 of R e p o r t P B 4 / 0 9 P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e

More information

An Improvement on Disc Separation of the Schur Complement and Bounds for Determinants of Diagonally Dominant Matrices

An Improvement on Disc Separation of the Schur Complement and Bounds for Determinants of Diagonally Dominant Matrices ISSN 746-7659, Egd, UK Jor of Iformo d Compg See Vo. 5, No. 3, 2, pp. 224-232 A Improveme o Ds Sepro of he Shr Compeme d Bods for Deerms of Dgoy Dom Mres Zhohog Hg, Tgzh Hg Shoo of Mhem Sees, Uversy of

More information

Reinforcement learning

Reinforcement learning CS 75 Mchine Lening Lecue b einfocemen lening Milos Huskech milos@cs.pi.edu 539 Senno Sque einfocemen lening We wn o len conol policy: : X A We see emples of bu oupus e no given Insed of we ge feedbck

More information

On Almost Increasing Sequences For Generalized Absolute Summability

On Almost Increasing Sequences For Generalized Absolute Summability Joul of Applied Mthetic & Bioifotic, ol., o., 0, 43-50 ISSN: 79-660 (pit), 79-6939 (olie) Itetiol Scietific Pe, 0 O Alot Iceig Sequece Fo Geelized Abolute Subility W.. Suli Abtct A geel eult coceig bolute

More information

Integral Equations and their Relationship to Differential Equations with Initial Conditions

Integral Equations and their Relationship to Differential Equations with Initial Conditions Scece Refleco SR Vol 6 wwwscecereflecocom Geerl Leers Mhemcs GLM 6 3-3 Geerl Leers Mhemcs GLM Wese: hp://wwwscecereflecocom/geerl-leers--mhemcs/ Geerl Leers Mhemcs Scece Refleco Iegrl Equos d her Reloshp

More information

Nonlocal Boundary Value Problem for Nonlinear Impulsive q k Symmetric Integrodifference Equation

Nonlocal Boundary Value Problem for Nonlinear Impulsive q k Symmetric Integrodifference Equation OSR ol o Mec OSR-M e-ssn: 78-578 -SSN: 9-765X Vole e Ve M - A 7 PP 95- wwwojolog Nolocl Bo Vle Poble o Nole lve - Sec egoeece Eo Log Ceg Ceg Ho * Yeg He ee o Mec Yb Uve Yj PR C Abc: A oe ole lve egoeece

More information

The shortest path between two truths in the real domain passes through the complex domain. J. Hadamard

The shortest path between two truths in the real domain passes through the complex domain. J. Hadamard Complex Analysis R.G. Halbud R.Halbud@ucl.ac.uk Depamen of Mahemaics Univesiy College London 202 The shoes pah beween wo uhs in he eal domain passes hough he complex domain. J. Hadamad Chape The fis fundamenal

More information

I K J K J. Chapter 1. Problem Solutions. Semiconductor Physics and Devices: Basic Principles, 3 rd edition Chapter 1

I K J K J. Chapter 1. Problem Solutions. Semiconductor Physics and Devices: Basic Principles, 3 rd edition Chapter 1 Semcouc hyscs evces: sc rcles, r eo her. () cc: 8 cer oms /8 om 6 ce oms ½ oms ol o 4 oms er u cell () cc: 8 cer oms /8 om eclose om om ol o oms er u cell mo: 8 cer oms /8 om 6 ce oms ½ oms 4 eclose oms

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

Bayesian Estimation of the parameters of the Weibull-Weibull Length-Biased mixture distributions using time censored data

Bayesian Estimation of the parameters of the Weibull-Weibull Length-Biased mixture distributions using time censored data Bys Eso of h s of h Wull-Wull gh-bs xu suos usg so S. A. Sh N Bouss I.S.S. Co Uvsy I.N.P.S. Algs Uvsy shsh@yhoo.o ou005@yhoo.o As I hs h s of h Wull-Wull lgh s xu suos s usg h Gs slg hqu u y I sog sh.

More information

HERMITE SERIES SOLUTIONS OF LINEAR FREDHOLM INTEGRAL EQUATIONS

HERMITE SERIES SOLUTIONS OF LINEAR FREDHOLM INTEGRAL EQUATIONS Mhemcl nd Compuonl Applcons, Vol 6, o, pp 97-56, Assocon fo Scenfc Resech ERMITE SERIES SOLUTIOS OF LIEAR FREDOLM ITEGRAL EQUATIOS Slh Ylçınbş nd Müge Angül Depmen of Mhemcs, Fcul of Scence nd As, Cell

More information

On the Oscillation of Solutions of Fractional Vector Partial Differential Equations with Deviating Arguments

On the Oscillation of Solutions of Fractional Vector Partial Differential Equations with Deviating Arguments Aec evew o Mhec d Sc Je 7 ol 5 No 5-57 ISSN: 7-8 7-56 Ole Cogh The AhoAll gh eeved blhed b Aec eech Ie o olc eveloe OI: 56/v55 : h://doog/56/v55 O he Ocllo o Solo o Fcol eco l eel Eqo wh evg Age Sdhv d

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

THIS PAGE DECLASSIFIED IAW E

THIS PAGE DECLASSIFIED IAW E THS PAGE DECLASSFED AW E0 2958 BL K THS PAGE DECLASSFED AW E0 2958 THS PAGE DECLASSFED AW E0 2958 B L K THS PAGE DECLASSFED AW E0 2958 THS PAGE DECLASSFED AW EO 2958 THS PAGE DECLASSFED AW EO 2958 THS

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

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

Hoeffding, Azuma, McDiarmid

Hoeffding, Azuma, McDiarmid Hoeffding, Azum, McDirmid Krl Strtos 1 Hoeffding (sum of independent RVs) Hoeffding s lemm. If X [, ] nd E[X] 0, then for ll t > 0: E[e tx ] e t2 ( ) 2 / Proof. Since e t is conve, for ll [, ]: This mens:

More information

The Complete Graph: Eigenvalues, Trigonometrical Unit-Equations with associated t-complete-eigen Sequences, Ratios, Sums and Diagrams

The Complete Graph: Eigenvalues, Trigonometrical Unit-Equations with associated t-complete-eigen Sequences, Ratios, Sums and Diagrams The Complee Gph: Eigevlues Tigoomeicl Ui-Equios wih ssocied -Complee-Eige Sequeces Rios Sums d Digms Pul ugus Wie* Col Lye Jessop dfdeemi Je dewusi bsc The complee gph is ofe used o veify cei gph heoeicl

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

Dividing Algebraic Fractions

Dividing Algebraic Fractions Leig Eheme Tem Model Awe: Mlilig d Diidig Algei Fio Mlilig d Diidig Algei Fio d gide ) Yo e he me mehod o mlil lgei io o wold o mlil meil io. To id he meo o he we o mlil he meo o he io i he eio. Simill

More information

The Linear Probability Density Function of Continuous Random Variables in the Real Number Field and Its Existence Proof

The Linear Probability Density Function of Continuous Random Variables in the Real Number Field and Its Existence Proof MATEC Web of Cofeeces ICIEA 06 600 (06) DOI: 0.05/mateccof/0668600 The ea Pobablty Desty Fucto of Cotuous Radom Vaables the Real Numbe Feld ad Its Estece Poof Yya Che ad Ye Collee of Softwae, Taj Uvesty,

More information

The Solution of Heat Conduction Equation with Mixed Boundary Conditions

The Solution of Heat Conduction Equation with Mixed Boundary Conditions Joul of Mhec d Sc (: 346-35, 6 ISSN 549-3644 6 Scece Publco The Soluo of He Coduco Equo wh Mxed Bou Codo Ne Abdelzq Dee of Bc d Aled Scece, Tfl Techcl Uvey PO Box 79, Tfl, Jod Abc: The u devoed o deee

More information

B.S. DHILLON and ZHIJIAN LI

B.S. DHILLON and ZHIJIAN LI Ieol Joul of efobly Egeeg, Vol., No., Ocobe 5, pp. 79-89. RAMS Coul ed Id B.S. DHILLON d ZHIJIAN LI Depe of Mechcl Egeeg Uvey of Ow Ow, Oo, N 6N5 Cd Receved o Ocobe 3, 4 Abc: Th ppe pee hecl odel o pefo

More information

Introduction. Voice Coil Motors. Introduction - Voice Coil Velocimeter Electromechanical Systems. F = Bli

Introduction. Voice Coil Motors. Introduction - Voice Coil Velocimeter Electromechanical Systems. F = Bli UNIVERSITY O TECHNOLOGY, SYDNEY ACULTY O ENGINEERING 4853 Elecroechncl Syses Voce Col Moors Topcs o cover:.. Mnec Crcus 3. EM n Voce Col 4. orce n Torque 5. Mhecl Moel 6. Perornce Voce cols re wely use

More information

DEFINITION OF ASSOCIATIVE OR DIRECT PRODUCT AND ROTATION OF VECTORS

DEFINITION OF ASSOCIATIVE OR DIRECT PRODUCT AND ROTATION OF VECTORS 3 DEFINITION OF ASSOCIATIVE OR DIRECT PRODUCT AND ROTATION OF VECTORS This chpter summrizes few properties of Cli ord Algebr nd describe its usefulness in e ecting vector rottions. 3.1 De nition of Associtive

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

Shrinkage Estimators for Reliability Function. Mohammad Qabaha

Shrinkage Estimators for Reliability Function. Mohammad Qabaha A - Najah Uv. J. es. (N. Sc.) Vol. 7 3 Shkage Esmaos fo elably Fuco مقدرات التقلص لدالة الفاعلية ohammad Qabaha محمد قبها Depame of ahemacs Faculy of Scece A-Najah Naoal Uvesy alese E-mal: mohqabha@mal.ajah.edu

More information

Duration Notes 1. To motivate this measure, observe that the duration may also be expressed as. a a T a

Duration Notes 1. To motivate this measure, observe that the duration may also be expressed as. a a T a Duio Noes Mculy defied he duio of sse i 938. 2 Le he sem of pymes cosiuig he sse be,,..., d le /( + ) deoe he discou fco. he Mculy's defiiio of he duio of he sse is 3 2 D + 2 2 +... + 2 + + + + 2... o

More information

DUALITY IN MULTIPLE CRITERIA AND MULTIPLE CONSTRAINT LEVELS LINEAR PROGRAMMING WITH FUZZY PARAMETERS

DUALITY IN MULTIPLE CRITERIA AND MULTIPLE CONSTRAINT LEVELS LINEAR PROGRAMMING WITH FUZZY PARAMETERS Ida Joual of Fudameal ad ppled Lfe Sceces ISSN: 223 6345 (Ole) Ope ccess, Ole Ieaoal Joual valable a www.cbech.o/sp.ed/ls/205/0/ls.hm 205 Vol.5 (S), pp. 447-454/Noua e al. Reseach cle DULITY IN MULTIPLE

More information