RATIONAL APPROXIMATION AND IDENTIFICATION OF DISTRIBUTED PARAMETER SYSTEMS

Size: px
Start display at page:

Download "RATIONAL APPROXIMATION AND IDENTIFICATION OF DISTRIBUTED PARAMETER SYSTEMS"

Transcription

1 oeed of he 7h Wold Coe he Ieaoal edeao of Auoa Cool RAIOAL AROXIAIO AD IDEIICAIO O DISRIBUED ARAEER SYSES V Gubaev O Zhukov Sae Reeah Iue of ASU SAU 4 Aad Gluhkov Kev 368 S Ukae e-al: vf@aekevua Aba: he ufed fe deoal odel uue whh aue o bae o develo he ehod aloh of e aoal aoxao defao ooed fo dbued aaee e wh dee u ouu he odeed uaed ealzao ovee o fe-deoal o-aoal odel of e fo ulea e oeao Aoxao eeeed b ee exao o deede ba fuo whh ae fudaeal oluo of oda dffeeal equao he u of oda ealzao have ueeded eao of eave defao aloh ad equeal odel eouo b eaae a o of oe o eveal ode Kewod: dbued aaee e odel aoxao eave defao oda ealzao uea Gee fuo IRODUCIO hee ae a aoahe ehod deal wh aaee defao oble fo dbued aaee e I oe of hee aoahe he odel uue eleed a a bouda value oble fo aal dffeeal equao (DE A he ae e hee ae a ublao whee odel baed o fe-deoal aoxao o fe elee dezao of DE ae odeed A ahe oeheve eae of he defao oble fo dbued aaee e ha bee evewed fo exale (Bak Kuh 989 he aoal aoxao defao of he fe deoal e ae odeed h ae I ooed o al he uveal aoah fo odel uue eleo whh eealze he u of u ouu elao fo wde la of fe fe-deoal e lud vaou DE e b ea of Gee fuo ufed adzed fuo Suh odel uue ake oble uaed aoal aoxao oveee o he oal e wh ulea e oeao (Glove 988 akla 99 all ohooal ba fuo ae eloed fo oal aoxao of able e hee ae a ublao devoed o h oble (ee e Wahlbe 994; akla 99 Heubee 995 Va De Hof eal 995 Whe aoxae odel eoued u defao o he bae of u- ouu daa oued b exeeal eo o oe hee ae addoal obale oe odel olex well-oede (akla 99 I ode o oe wh h oble he ef eave defao aloh whh e o fd aoal aoxao aee wh uea avalable daa develoed he dea of he offeed aoah o aoxae e b ea of ee exao wh ee o deede ba fuo whh ae fudaeal oluo of fe-deoal oda dffeeal equao he defao edued o aoxao of exeeall obaed ouu b ea of uh fe ee wh ukow o ol exao oeffe bu alo eevalue whh ae aaee of ba fuo he oble uh eae a be ouvel olved f aoal aoxao wll be ake he fo of ouda ealzao Al of uh ealzao allow u eleed daa al odal aal o eoe odel b eaae a fo whh we ue he e ubodel beaue he oa oe o eveal e ode ouda fo ovde alo ohe efeee whh wee ulzed ooed aloh HE ROBLE SAEE o odel defao ool of he olex eal e equed a f o hooe he aoae odel uue I ve had o do h whou a o foao eeal kowlede abou he la If he obe dbued ae aaee o /8/$ 8 IAC /876-5-KR-956

2 haae ae e-deede he we deal wh he ae-e e whh a be haaezed b ala fuo he le ae b veo fuo ha deed o boh he aal vaable z defed oe aea lud he bouda e o eax ( eeal ae A a ule he oee uh e ae alo deeed b he bouda al odo uhe lea e wll be odeed ol ha alo a o foao I h ae he ufed ad fo of odel uue uveal eouh well ahed wh ex ehod of odel defao he dea of uh adzao wa offeed b Bukovk he wde la of e wh dbued lued aaee wa olleed uued ad fo (Bukovk 979 he a haae of e ad fo he Gee fuo o he ule eoe fuo he Gee fuo alled alo a he fluee fuo o he oue fuo Alo wh he ala o veo vaable w ha haaeze he ae-e e ae le odue he adzed fuo f ha eeed a eealzed fuo b ea of whh a exeal volue bouda o al fluee (u o he e a be we dow he ufed fo If he Gee fuo H ζ τ he adzed fuo f ae kow he e ae deeed b equao w H ζ τ f ( ζ τ dζ dτ ( whee he loue of he e he uue ( lude he a quaza odel A la ae he e l a aaee he ( eeeed a w ( z H ζ f ( ζ dζ ( Se wh lued aaee ae he eal ae of ( w ( H ( τ f ( τ d τ (3 he equao (3 well-kow Cauh foula w ( Ф( w Ф( τ u( τ dτ (4 whee Ф ( τ he ao ax of lea dffeeal equao e whh eeae he Gee fuo he eealzed adzed fuo f ( τ exeed a ( τ u( τ w δ ( τ f whee δ eealzed Da fuo I veo ae w ol( w w K w k f z ol( f f K f So w L L H ζ τ f ( ζ dζ dτ k K k l k l l (5 I wde-ead ae whe e hf-vaa he Gee fuo ha exeo H ζ τ H ζ τ o aal u ofe eouh o kow o he feld w bu loal o eal haae whh a be eaued o eaed Reee he a he ouu vaable ol(( K o loal w z wheea eal eauee we have ( ae ( z w( z dz ψ whee ( z fuo defed o he e z / he e ode wh Se ( z ψ weh ψ ( z whe a be oe ube of o f eealzed fuo he bouda o ohe ula ao defed b uue Howeve he e deedee f oeed a a ule wh exeal lued aaee he fo f R u f ( z whee u defe he vaable of he exeal ao o he e f ( z debe dbued fluee o exale e wh eleoae oee he ue wd ae exeal lued u aal haae ae defed b ofuao of ol wd A a eul fo uh e wh he fe ube of u ouu (wdeead ae ae he odel uue a be we a ( H u τ τ dτ ; ; R (6 whee H ( τ ψ ( z dz H ζ τ f ( ζ dζ Hee ψ ( z ae odeed a eealzed fuo ha ovde all eauee lud owe adz fo I hould be oed ha H ( τ ae eeaed b he ae Gee fuo Coequel he e haae of elee H ( τ hould be he ae o olee eah ohe hu he weh fuo ψ (z f ( ζ wll deee he obevabl o oollabl oee of eleva eealzed deee of feedo 3 RAIOAL AROXIAIO Lea e-vaa e ude defe auo uh ha odel (6 a be we he ovoluo fo wh o-aoal (fe-deo ae o aoal (fe-deoal e afe ax fuo G ( wll be odeed Suh e fo wde eouh la of ax-valued afe fuo ae quae of lea oeao (ae A B C D a bewee dffee 6453

3 fe-deoal (o fe-deoal lea veo ae o ha G( D C( I A B A f h la lude he e wh oeao of ulea e ha due bouded Hakel oeao (Glove e al 988 whh ula value σ ( σ af σ < I kow ha he Hakel oeao Г ulea f G( oeod ax-valued afe fuo C( I A B a be eeeed he fo G ( Re( ξ ( ξ G( [ G ( ] (7 ude auo ha olex ube ae loaed he lef half-lae (able e ula value ae dffee ( C Г whee C o Г σ a ulea o of Г I le h eul alo ead o he ae of ulle ula value b u he ha of Shd a (Adaa e al 97 Howeve ol le ula value ae wll be odeed hee he ee (7 ufol ovee Re > he ulea o of aoaed Hakel oeao he ule eoe ax H ( of e-vaa e he ae of ulea oeao Г o of he elee H ( ha a be exeed b deooo H ( ξ ( Re( ξ e (8 he fuo H ( ae ouou alo evewhee o he eax af H u l η { R H l η l C η C } Γ / fo all Мo Aodl wh (Glove e al 988 ee (7 ovee H H H ; oveee of ule eoe ax H ( fo exao (8 o L H Hakel L ovded b he laal loue heoe (ee e akla 99 heefoe he afe ax wh elee ( G ( Re( ξ ( ξ ( o oeod ule eoe ax ha o of elee ( ξ H Re( ξ e ( a be eleed a uaed odel of e Hee oveee G ( G ( H H fo uaaed whee oe of afoeeoed o I fa foula ( debe he aoa fedeoal daal e wh afe ax-valued elee we he fo of aal fao deooo Eah e ( aalooul ( oeod o he eeal deee of feedo o ode of he (9 e Exeo ( ( ae equvale o A H C e B G ( C ( I A B ( whee ae A B C defe he fedeoal ae-ae e e dx A x B u d (3 C x he deo of veo u ae equal o R eevel he oal ouu ealzao (Glove e al 988 balaed ealzao ae uuall ulzed aoxao heo he uaed e ( C A B ude uh ealzao ode wh ( bu fd he equao whh lk elee of ae C A B wh ( he eevalue ξ oeffe oval ak Coeo bewee odel (3 ( beoe le eouh f we ake he oda fo of ealzao ead of balaed o oal ouu ealzao I h ae he ax A a be we a A da{ S S S } whee daoal blok α β S ξ α ± β β α he ae C B ae alo exeed he blok fo C [ C C C ] B [ B B B ] whee L b b L b R C B L b b L b R he aoe oeao So ( a be we a ( α H ( o β β e (4 whee ( b b b b oeove uable o ele he obevable oal oda ealzao f oe of olu of eah ax C aued ; o oollable oal oda ealzao el b b ; R eah blok B I he f ae equao oe he oeffe of deooo (4 wh elee of ae C B ae b R R ( b ( ( R ( ( ( ; R ; ( ( R ( (5 eod ae exeed a ( ; ; ( ( ; ; ; ( 6454

4 b b ( ( ( ( ( ( ( ( ( ( ( ( (6 If he e ha oe u a ouu he eaoable o ue he obevable oal oda ealzao whe he e ha oe ouu a u eaoable o ue oollable oal oda ealzao I hee ae exao oeffe elee of ae of he ae ae odel have he uque oul I eeal ae fo e wh a u ouu we have he ovedeeed e of oul equao o oluo (5 (6 wee alulaed b LS ha led o he avea oedue fo defe e of oeffe Bede he eal eevalue deooo (4 ae he eal ae ha eeved a β b e ( o β Coequel he odel deo o ube of deee of feedo equal o whee oeod o he olex eevalue o he eal oe eevel heefoe (4 aoxae uue fo elee of ule eoe ax ha we a deooo H ( wh ee of deede ba fuo whh ae fudaeal oluo of he equvale lea e of dffeeal equao he Lalae afoao of (4 [ ]( LH lead o aoal afe fuo ha eeeed a aal fao ula deooo wh ole α ± β he lef half-lae ; 4 IERAIVE IDEIICAIO Ohooal ba fuo have eloed he effeve ool fo he uoe of e aoxao defao I eablhed fa ha eve able e ha a uque ee exao e of uh ba a fe-leh ee of uh exao a eve a a aoxae odel Howeve eal udeable ha he aua of he aoxao wll be eeall deede o he hoe of ba fuo If he da of he ba eea e he da e o be odeled ae loed we wll have he fa oveee So ooed fo aoxao eave defao o al deede bu o eeal ohooal ba whh loe o eefuo of he ode e he ule eoe fuo (4 ae exeed a deooo of deede fuo ha ae fudaeal oluo of (3 Hee ae kow o ol ( exao oeffe bu eevalue ( aaee α β alo If eevalue ae kow he oal aoal aoxao would be aaloou o he ohooal ba ae So offeed o eae a f α β ( afe ha fd he oal value of ( he develoed ehod e defao a be aled fo ealz of h aoah he eauee obaed fo exee ae avalable daa If equed o eablh he aoal aoxao of kow bouda-valued oble fo DE wh fe ube of exeal u ouu he eleva daa a be obaed fo ouaoal ulao o eal vual la defao oble ea he ae he u a lude dffee al bu hould be foave exe all fa e ode o eablh he foaabl odo le ode a f he ex fluee ( ( u ( u u o ω ω (7 aled o eve eaae u Iu (7 allow o fo vae dffee fluee Releva eoe a he -h ouu ( ( ( ( d d β ( d ω d ( 3 ( 4 oω o β e α (8 whee ( ( ( d [ u ( u ( ] 3 4 ( ( ( [ u ( u ( ] 3 4 ( ( ( ( d [ u ( u ( ] 3 4 ( ( ( [ u ( u ( ] 3 4 ( ( ( 3 ( d u ( ( 3 4 ( ( u ( ( 3 4 ( ( ( 4 ( d u ( ( 3 4 (9 ( ( ( u ( ( 3 4 α α α ( β ω α ( β ω β ω 3 β ω 4 α ( β ω α ( β ω he ouu (8 o of boh eefuo whh defe ae fuo ha laf he ead-ae oe whh ae aued b (7 Bu efeed o ele fo (8 ehe foed oo o ae oe ue he eaael o ele he foed vbao fo able e eouh o ake he daa fo >> whee ae e he oal 6455

5 aoxao of (>> b uaed u a be aed ou b fe-feque defao ehod Howeve defao o he bae of foed oo hee ex he oble of odel deo eleo Aael he eave defao o he bae of ae daa oe efeable fo eouo of aoxae odel I ode o ele he ae behavo le efo he uleea eao of alo ov eval π A a eul we eeve a ew al ω ha equal o ( α d β d o β e ( π ω dθ π θ ω dθ θ ( θ θ ω π ( ( θ dθ ( Coeffe d d ( ae exeed leal va d d bu ubeoe wa Afe e he al fo exee alula he oval ak of aaee α β d d evalua fo ( hould be olved Code ow he ouao of fo (9 h ak a be oel olved f deea ( ( [ ] u u 3 4 [ ] ( ( u u 3 4 equal o zeo Whe aaee α β ae ukow he eeal ae dfful o eae he alude ( d d whh exe all ode ude odeao I que oble ha he ae u a ve exao axu fo oe ode whle ohe ode wll be o he level of dubae So ueed o ue al ha ae le fo aal whh ae able o exe he ode wde eevalue ae he eaula ule wh alude u ha aahed o he -h u o he eval [ ] afe hee odo o eave defao hee a be ued he fee oo a ha a be we a ( u e α ( e α α ( β ( ( α ( { [ β ( θ ] o[ β ( ] θ} e o β ( ( o he ae behavo a equal o ( ( α ( u { ( e [ β ( θ ] α β ( ( α ( θ ( e o β ( θ oθ [ ] } Aod o ( ( he alude of ex ode deeae veel oooall o α β eae del oooall o u Bede eaoable o eae he wdh of ule fo all value of α he fa eevalue ha a be defed ou he lae ( α β eal doa ha lude he ode wh foave al o he bakoud of daa eo he o boadb he u ake a deal ule u u δ ( ha ve he ouu ( ( u ( [ o ( ( β ( α ( ] e β (3 Code ow ea oble eave hee of aoxae odel eouo I ueed u aalal ouu ( ( o (3 oeod exeeal daa o he ae [ ] o [ ] o eou odel eavel b dee a eah eao aaee of oe o eveal ode Oe hould a wh ode ha ve he al o oe ao eouh lae a he ed of eval ha eal Obvoul ode wh he alle value of α wll ve a obuo hee Whe we oe ea o o he ube of eeall foave ode wll ow o aou of laeα h wll be ued eave defao he dea o eee he odel a aeao of ubodel Eah ubodel wll be eoued eaael Daa o he ubeval eal allow o deee all ukow aaee of he f ubodel Afe ha we evaluae he ouu of h ubodel u ( ( o (3 uba fo ha wa obaed exee hu we ( ( fd a ew al whh adble fo eao of eod ubodel aaee h al wll eal have he ow foave eval [ ] o [ ] we ele ubeval fo eod ubodel efo he ae ao a fo f ubodel Suba al ( ( fo we defe ew oeod ubeval ollow hd ubodel a be defed Suh eao ae eeaed ul he al ( ( ( K beoe duhable o q he oe bakoud Aeao of all ubodel whh wee defed wll ve he ouda ealzao of fedeoal aoxao ha oe wh he ex uea Le u o aloh of ubodel aaee eao I offeed he hee o of wo ae A he f ae all ubodel α β hould be deeed he eod ae ha addeed o exao oeffe evaluao a be ealzed b ad LS ehod Se he eod ae he well-kow ak we debe ol aloh of ubodel eevalue eao Dffee aoahe wee odeed oe of whh o he follow q q ( ( ( ( o K whee q 6456

6 ( ( we fo ew al d ( ( ( ( q ( γ γ d (4 q q ( d ( d ( ( q q ( α α β q q α β d α β d ( ( ( ( γ γ ( τ d (5 whee τ q 3 q q ( q 4 ( α β ( α β ( q ( τ ( ( τ dτ q α ( q ( τ dτ α β γ ae vaed Le ake he equee of ( ( γ fo 3 aled daa { } q { ( ( β } α fo 4 wh he ubeal ae q of def ubodel Cooe he Hakel ae ( ( ( K q ξ q q ( ( Y 3 L ( ξ q q q q ( ( ( ( η η L ξ η q q q (6 ξ η 4 ( Le he SVD of Y be ve b q ( ( ( ( Y U V (7 q q q q ( ( whee U q V ae ohooal ae q Σ ( q a daoal ax wh he ula value o-ea ode o he daoal Le aalze behavo of ula value whe α β γ ae vaed Reul ehe oe ula value (fo ae wh γ o wo (fo α β ed o zeo Coeod lluao ae eeeed o f f whee ula value behavo fo ae of eal eevalue how oeod o dffeeal f - o eal afoao Suh aloh beoe oe effeve f a o oble o fd he ouh eao fo eevalue o o o ou afflao eval fo he Soee h a be doe del fo ae behavo o ubeval 3 4 Reak If we va aaeeα β γ hee ae eaaed o ol ula value of ubodel o be defed bu alo he ula value of he ode wh weak eoe o dubae I a ae oble o eae he eevalue oe eel b aalz of o ula value afoao Reak Soe ouu fo dffee a oa o-foave al of defe ode due o he bad oollabl o bad obevabl So he olee odel oled fo all def ode wh ee o R u-ouu 5 COCLUSIO Seleve daa hoe fo ubodel defao ea ea la o ohooalzao oedue So e of oohooal ee exao due o ef al beoe oble o ealze eave odel eouo b eaae a he a d of he develoed eave defao ehod ha eao ed o aoal aoxae odel wh aaee ba fuo whh ve al devao bewee da of eah eal e eealzed deee of feedo he odel oeove e eao ae eaed whe all foave ouu al of ode beoe exhaued we oba he odel deo ha full oe wh he eo avalable daa REERACES Adaa V DZ Aov G Ke (97 Aal oee of Shd a fo a Hakel Oeao he eealzed Shu-aka oble ah USSR-Sb Bak H K Kuh (989 Eao ehque fo Dbued aaee Se Bkäue Boo Bukovk AG (979 Dbued aaee Se Chaae 4 ( ua See oow Glove K R Cua R ao (988 Realzao Aoxao of Lea Ife- Deoal Se wh Eo Boud SIA Co OzVol akla (99 O Idefao of Sable Se Oal Aoxao Auoaa akla (99 Aoxao of Sable Se b Laee le Auoaa Vol Heubee S Va de Hof OH Boa (995 A eealzed Ohooal Ba fo Lea Da Se IEEE a Auo Cool AC Wahlbe Bo (994 Laee Kauz odel e h IAC S o Se Idefao SYSID 94 Vol3 - Deak Coehae 6457

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

APPLICATION OF A Z-TRANSFORMS METHOD FOR INVESTIGATION OF MARKOV G-NETWORKS

APPLICATION OF A Z-TRANSFORMS METHOD FOR INVESTIGATION OF MARKOV G-NETWORKS Joa of Aed Mahema ad Comaoa Meha 4 3( 6-73 APPLCATON OF A Z-TRANSFORMS METHOD FOR NVESTGATON OF MARKOV G-NETWORKS Mha Maay Vo Nameo e of Mahema Ceohowa Uey of Tehoogy Cęohowa Poad Fay of Mahema ad Come

More information

Support Appendix The Logistics Impact of a Mixture of Order-Streams in a Manufacturer-Retailer System Ananth V Iyer and Apurva Jain

Support Appendix The Logistics Impact of a Mixture of Order-Streams in a Manufacturer-Retailer System Ananth V Iyer and Apurva Jain So Aedx Te og Ia o a Mxe o Ode-Sea a Maae-Reale Sye Aa V Iye ad Ava Ja Teoe 4: e ad q be e obably geeag o o e eady-ae be o ode ee e ye by a avg H ode ad a M ode eevely Te ad q Wee ad be e ee oo o e ollowg

More information

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

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

More information

ON 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

Application of second derivative Runge-Kutta collocation methods to stiff systems of initial value problems

Application of second derivative Runge-Kutta collocation methods to stiff systems of initial value problems eoado Joal o See ISSN 8- Ie 8 Jaa-Je. - Alao o eod deae Re-Ka olloao meod o em o al ale oblem Samala ARKUS ad Dada Glb AKUBU * Deame o aema ad Sa Ue o ad PB 9 ad Boo Sae Nea Deame o aemaal See Abbaka Taawa

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

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

EMA5001 Lecture 3 Steady State & Nonsteady State Diffusion - Fick s 2 nd Law & Solutions

EMA5001 Lecture 3 Steady State & Nonsteady State Diffusion - Fick s 2 nd Law & Solutions EMA5 Lecue 3 Seady Sae & Noseady Sae ffuso - Fck s d Law & Soluos EMA 5 Physcal Popees of Maeals Zhe heg (6) 3 Noseady Sae ff Fck s d Law Seady-Sae ffuso Seady Sae Seady Sae = Equlbum? No! Smlay: Sae fuco

More information

ELECTROMAGNETISM, NUCLEAR STRUCTURES & GRAVITATION

ELECTROMAGNETISM, NUCLEAR STRUCTURES & GRAVITATION . l & a s s Vo Flds o as l axwll a l sla () l Fld () l olasao () a Flx s () a Fld () a do () ad è s ( ). F wo Sala Flds s b dd l a s ( ) ad oool a s ( ) a oal o 4 qaos 3 aabls - w o Lal osas - oz abo Lal-Sd

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

Modified Inverse Weibull Distribution

Modified Inverse Weibull Distribution J. Sa. Appl. Po. No. 5-5 NSP Moded Ivee Webull Dbuo Muhaad Shuab Kha ad Robe K School o Maheacal ad Phcal Scece he Uve o Newcale Callaha NSW 8 Auala Eal Adde huab.a@al.co obe.k@ewcale.edu.au Receved Apl

More information

A PATRA CONFERINŢĂ A HIDROENERGETICIENILOR DIN ROMÂNIA,

A PATRA CONFERINŢĂ A HIDROENERGETICIENILOR DIN ROMÂNIA, A PATRA ONFERINŢĂ A HIDROENERGETIIENILOR DIN ROMÂNIA, Do Pael MODELLING OF SEDIMENTATION PROESS IN LONGITUDINAL HORIZONTAL TANK MODELAREA PROESELOR DE SEPARARE A FAZELOR ÎN DEANTOARE LONGITUDINALE Da ROBESU,

More information

Maximum Likelihood Estimation

Maximum Likelihood Estimation Mau Lkelhood aon Beln Chen Depaen of Copue Scence & Infoaon ngneeng aonal Tawan oal Unvey Refeence:. he Alpaydn, Inoducon o Machne Leanng, Chape 4, MIT Pe, 4 Saple Sac and Populaon Paaee A Scheac Depcon

More information

Advanced Particle Physics & Introduction to Standard Model: II. Prerequisites

Advanced Particle Physics & Introduction to Standard Model: II. Prerequisites vace Pacle Phyc & Iouco o Saa oel: II. Peeque J. Pawlowk / U. Uwe II. Peeque. Relavc keac. Wave eco o ee acle. o elavc eubao heoy. Scaeg a a ao alue 5. o eco a hae ace 6. ecay wh lee a alz lo Leaue: F.

More information

Chapter 5 Transmission Lines

Chapter 5 Transmission Lines ap 5 ao 5- aacc of ao ao l: a o cou ca cu o uppo a M av c M o qua-m o. Fo M o a H M H a M a µ M. cu a M av av ff caacc. A M av popaa o ff lcc a paal flco a paal ao ll occu. A ob follo ul. ll la: p a β

More information

dm dt = 1 V The number of moles in any volume is M = CV, where C = concentration in M/L V = liters. dcv v

dm dt = 1 V The number of moles in any volume is M = CV, where C = concentration in M/L V = liters. dcv v Mg: Pcess Aalyss: Reac ae s defed as whee eac ae elcy lue M les ( ccea) e. dm he ube f les ay lue s M, whee ccea M/L les. he he eac ae beces f a hgeeus eac, ( ) d Usually s csa aqueus eeal pcesses eac,

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

-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

On Probability Density Function of the Quotient of Generalized Order Statistics from the Weibull Distribution

On Probability Density Function of the Quotient of Generalized Order Statistics from the Weibull Distribution ISSN 684-843 Joua of Sac Voue 5 8 pp. 7-5 O Pobaby Dey Fuco of he Quoe of Geeaed Ode Sac fo he Webu Dbuo Abac The pobaby dey fuco of Muhaad Aee X k Y k Z whee k X ad Y k ae h ad h geeaed ode ac fo Webu

More information

The Non-Truncated Bulk Arrival Queue M x /M/1 with Reneging, Balking, State-Dependent and an Additional Server for Longer Queues

The Non-Truncated Bulk Arrival Queue M x /M/1 with Reneging, Balking, State-Dependent and an Additional Server for Longer Queues Alied Maheaical Sciece Vol. 8 o. 5 747-75 The No-Tucaed Bul Aival Queue M x /M/ wih Reei Bali Sae-Deede ad a Addiioal Seve fo Loe Queue A. A. EL Shebiy aculy of Sciece Meofia Uiveiy Ey elhebiy@yahoo.co

More information

IMACS CONTROL ELECTRONICS

IMACS CONTROL ELECTRONICS e Io ell el e d peop (I) I OO OI ee Iuo of o e Oevoe ee de, lfo 0 O () () I ex ee I le of oe.do ex ee I lo. le: I ove ee ze: le: l e:. I evo: Il e: e: ep00 :0:. ee 0 of 0 le: :\OI\I u 0\oo ool ye\i oo

More information

Optimization of Passive Constrained Layer Damping Treatments for Vibration Control of Cylindrical Shells

Optimization of Passive Constrained Layer Damping Treatments for Vibration Control of Cylindrical Shells Oao of Pae Coae aye Dag eae fo bao Cool of Cylal Sell H. Zeg. S. H. Pa a. R. Aba ae ee e layo oao of ae oae laye ag PCD eae fo bao ool of ylal ell e a boaba foe eao. e eao goeg e bao eoe ae ee g e eegy

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

Physics 232 Exam II Mar. 28, 2005

Physics 232 Exam II Mar. 28, 2005 Phi 3 M. 8, 5 So. Se # Ne. A piee o gl, ide o eio.5, h hi oig o oil o i. The oil h ide o eio.4.d hike o. Fo wh welegh, i he iile egio, do ou ge o eleio? The ol phe dieee i gie δ Tol δ PhDieee δ i,il δ

More information

T T V e g em D e j ) a S D } a o "m ek j g ed b m "d mq m [ d, )

T T V e g em D e j ) a S D } a o m ek j g ed b m d mq m [ d, ) . ) 6 3 ; 6 ;, G E E W T S W X D ^ L J R Y [ _ ` E ) '" " " -, 7 4-4 4-4 ; ; 7 4 4 4 4 4 ;= : " B C CA BA " ) 3D H E V U T T V e g em D e j ) a S D } a o "m ek j g ed b m "d mq m [ d, ) W X 6 G.. 6 [ X

More information

Some Integrals Pertaining Biorthogonal Polynomials and Certain Product of Special Functions

Some Integrals Pertaining Biorthogonal Polynomials and Certain Product of Special Functions Global Joual o Scece Fote Reeach atheatc ad Deco Scece Volue Iue Veo Te : Double Bld ee Reewed Iteatoal Reeach Joual ublhe: Global Joual Ic SA Ole ISSN: 49-466 & t ISSN: 975-5896 Soe Itegal etag Bothogoal

More information

Fractional Integrals Involving Generalized Polynomials And Multivariable Function

Fractional Integrals Involving Generalized Polynomials And Multivariable Function IOSR Joual of ateatcs (IOSRJ) ISSN: 78-578 Volue, Issue 5 (Jul-Aug 0), PP 05- wwwosoualsog Factoal Itegals Ivolvg Geealzed Poloals Ad ultvaable Fucto D Neela Pade ad Resa Ka Deatet of ateatcs APS uvest

More information

Chapter 5. Long Waves

Chapter 5. Long Waves ape 5. Lo Waes Wae e s o compaed ae dep: < < L π Fom ea ae eo o s s ; amos ozoa moo z p s ; dosac pesse Dep-aeaed coseao o mass

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

THE LOWELL LEDGER, INDEPENDENT NOT NEUTRAL.

THE LOWELL LEDGER, INDEPENDENT NOT NEUTRAL. E OE EDGER DEEDE O EUR FO X O 2 E RUO OE G DY OVEER 0 90 O E E GE ER E ( - & q \ G 6 Y R OY F EEER F YOU q --- Y D OVER D Y? V F F E F O V F D EYR DE OED UDER EDOOR OUE RER (E EYEV G G R R R :; - 90 R

More information

Chapter 2: Descriptive Statistics

Chapter 2: Descriptive Statistics Chapte : Decptve Stattc Peequte: Chapte. Revew of Uvaate Stattc The cetal teecy of a oe o le yetc tbuto of a et of teval, o hghe, cale coe, ofte uaze by the athetc ea, whch efe a We ca ue the ea to ceate

More information

LIPSCHITZ ESTIMATES FOR MULTILINEAR COMMUTATOR OF MARCINKIEWICZ OPERATOR

LIPSCHITZ ESTIMATES FOR MULTILINEAR COMMUTATOR OF MARCINKIEWICZ OPERATOR Reseh d ouiios i heis d hei Siees Vo. Issue Pges -46 ISSN 9-699 Puished Oie o Deee 7 Joi Adei Pess h://oideiess.e IPSHITZ ESTIATES FOR UTIINEAR OUTATOR OF ARINKIEWIZ OPERATOR DAZHAO HEN Dee o Siee d Ioio

More information

district department or positionnumber e fa Vr Ar 4 tj qj home phone tut t ounty Elections Official of Filing of Candidacy by Decleration ORS

district department or positionnumber e fa Vr Ar 4 tj qj home phone tut t ounty Elections Official of Filing of Candidacy by Decleration ORS F f ddy f p SEL ev 6 RS 49 h f e f pub ed d y be pubhed epdued p e ype peby bk k ub f ffe fude dde e 4v4L 6 hw e hud ppe b e e u fx b 7 f AUS p d dep pube e fa f Pde V A 4 q k 6 S4 8 W9 f ede 4 9f e L

More information

Handout on. Crystal Symmetries and Energy Bands

Handout on. Crystal Symmetries and Energy Bands dou o Csl s d g Bds I hs lu ou wll l: Th loshp bw ss d g bds h bs of sp-ob ouplg Th loshp bw ss d g bds h ps of sp-ob ouplg C 7 pg 9 Fh Coll Uvs d g Bds gll hs oh Th sl pol ss ddo o h l slo s: Fo pl h

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

14.3 Frequency-nonselective, slowly fading channel Frequency-nonselective, slowly fading channel. Ideal performance under AWGN

14.3 Frequency-nonselective, slowly fading channel Frequency-nonselective, slowly fading channel. Ideal performance under AWGN CUCM --- Po-g Che --- 43 Fequey-oeeve owy adg hae Oevao o Fo he gue o aheve a PO eve o 4 he ye u povde a SR hghe ha 35dB whh o o paa So aeave ouo houd e ae o opeae he adg ee uh a he ue o eduday e dvey

More information

NONDIFFERENTIABLE MATHEMATICAL PROGRAMS. OPTIMALITY AND HIGHER-ORDER DUALITY RESULTS

NONDIFFERENTIABLE MATHEMATICAL PROGRAMS. OPTIMALITY AND HIGHER-ORDER DUALITY RESULTS HE PUBLISHING HOUSE PROCEEDINGS OF HE ROMANIAN ACADEMY, See A, OF HE ROMANIAN ACADEMY Volue 9, Nube 3/8,. NONDIFFERENIABLE MAHEMAICAL PROGRAMS. OPIMALIY AND HIGHER-ORDER DUALIY RESULS Vale PREDA Uvety

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

Example: Two Stochastic Process u~u[0,1]

Example: Two Stochastic Process u~u[0,1] Co o Slo o Coco S Sh EE I Gholo h@h. ll Sochc Slo Dc Slo l h PLL c Mo o coco w h o c o Ic o Co B P o Go E A o o Po o Th h h o q o ol o oc o lco q ccc lco l Bc El: Uo Dbo Ucol Sl Ab bo col l G col G col

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

FROM THE BCS EQUATIONS TO THE ANISOTROPIC SUPERCONDUCTIVITY EQUATIONS. Luis A. PérezP. Chumin Wang

FROM THE BCS EQUATIONS TO THE ANISOTROPIC SUPERCONDUCTIVITY EQUATIONS. Luis A. PérezP. Chumin Wang FROM THE BCS EQUATIONS TO THE ANISOTROPIC SUPERCONDUCTIVITY EQUATIONS J. Samuel Mllá Faulad de Igeería Uversdad Auóoma del Carme Méxo. M Lus A. PérezP Isuo de Físa F UNAM MéxoM xo. Chum Wag Isuo de Ivesgaoes

More information

are positive, and the pair A, B is controllable. The uncertainty in is introduced to model control failures.

are positive, and the pair A, B is controllable. The uncertainty in is introduced to model control failures. Lectue 4 8. MRAC Desg fo Affe--Cotol MIMO Systes I ths secto, we cosde MRAC desg fo a class of ult-ut-ult-outut (MIMO) olea systes, whose lat dyacs ae lealy aaetezed, the ucetates satsfy the so-called

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

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

ELEC 6041 LECTURE NOTES WEEK 3 Dr. Amir G. Aghdam Concordia University

ELEC 6041 LECTURE NOTES WEEK 3 Dr. Amir G. Aghdam Concordia University ecre Noe Prepared b r G. ghda EE 64 ETUE NTE WEE r. r G. ghda ocorda Uer eceraled orol e - Whe corol heor appled o a e ha co of geographcall eparaed copoe or a e cog of a large ber of p-op ao ofe dered

More information

PDF hosted at the Radboud Repository of the Radboud University Nijmegen

PDF hosted at the Radboud Repository of the Radboud University Nijmegen DF hoed he Rdbod Reoo o he Rdbod e Nege The oog ex bhe eo Fo ddo oo bo h bo k h k hhdhdee266238 ee be ded h h oo geeed o 226 d be be o hge Oxd hohk ee ee d e) e He h e He odge Reheek" Kh ee e Roe Cho Rohe

More information

Consider a Binary antipodal system which produces data of δ (t)

Consider a Binary antipodal system which produces data of δ (t) Modulaion Polem PSK: (inay Phae-hi keying) Conide a inay anipodal yem whih podue daa o δ ( o + δ ( o inay and epeively. Thi daa i paed o pule haping ile and he oupu o he pule haping ile i muliplied y o(

More information

Suppose we have observed values t 1, t 2, t n of a random variable T.

Suppose we have observed values t 1, t 2, t n of a random variable T. Sppose we have obseved vales, 2, of a adom vaable T. The dsbo of T s ow o belog o a cea ype (e.g., expoeal, omal, ec.) b he veco θ ( θ, θ2, θp ) of ow paamees assocaed wh s ow (whee p s he mbe of ow paamees).

More information

Refinement of Parameters and Motion Forecast for High-Orbit Objects with a Big Area to Mass Ratio

Refinement of Parameters and Motion Forecast for High-Orbit Objects with a Big Area to Mass Ratio Refeet of Paaete ad Moto Foeat fo Hgh-Obt Objet wth a Bg Aea to Ma Rato Steayat V.A., Agaov V.M., Khutoovky Z.N. Itoduto The uoe of th eot to develo the ethod ad algoth fo deteato of obt of objet wth a

More information

Reliability Analysis. Basic Reliability Measures

Reliability Analysis. Basic Reliability Measures elably /6/ elably Aaly Perae faul Πelably decay Teporary faul ΠOfe Seady ae characerzao Deg faul Πelably growh durg eg & debuggg A pace hule Challeger Lauch, 986 Ocober 6, Bac elably Meaure elably:

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

Channel Capacity of Distributed Antenna Network Using Transmit/Receive Diversity in a Multi-cell Environment

Channel Capacity of Distributed Antenna Network Using Transmit/Receive Diversity in a Multi-cell Environment Cae Capa of Dbued Aea ewo Ug a/reeve Dve a u-e voe Sa KUAGAI Ruue ASUKAA auo BARA ad uu ADACI Dep of ea ad Couao geeg Gaduae Soo of geeg oou Uve 6-6-5 Aza-Aoba Aaa Aoba-u Seda 98-8579 JAA -a: {uaga auawa

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

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

c- : r - C ' ',. A a \ V

c- : r - C ' ',. A a \ V HS PAGE DECLASSFED AW EO 2958 c C \ V A A a HS PAGE DECLASSFED AW EO 2958 HS PAGE DECLASSFED AW EO 2958 = N! [! D!! * J!! [ c 9 c 6 j C v C! ( «! Y y Y ^ L! J ( ) J! J ~ n + ~ L a Y C + J " J 7 = [ " S!

More information

A Fusion Method of Fault Diagnosis Based on Nonlinear Spectral Analysis

A Fusion Method of Fault Diagnosis Based on Nonlinear Spectral Analysis Fo eod o Fal ago Baed o olear Seral al Ra We ogzao a Sool o Elero ad Iorao Egeerg X'a Jaoog Uver X'a 749.R. a rwe@are.o za@.ed. oggag Zo a Zag ad Xeg Wag Sool o Elero ad Iorao Egeerg X'a Jaoog Uver X'a

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

( ) ( ) 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

EQUATION SHEETS FOR ELEC

EQUATION SHEETS FOR ELEC QUTON SHTS FO C 47 Fbuay 7 QUTON SHTS FO C 47 Fbuay 7 hs hυ h ω ( J ) h.4 ω υ ( µ ) ( ) h h k π υ ε ( / s ) G Os (Us > x < a ) Sll s aw s s s Shal z z Shal buay (, aus ) z y y z z z Shal ls ( s sua, s

More information

Physics 15 Second Hour Exam

Physics 15 Second Hour Exam hc 5 Second Hou e nwe e Mulle hoce / ole / ole /6 ole / ------------------------------- ol / I ee eone ole lee how ll wo n ode o ecee l ced. I ou oluon e llegle no ced wll e gen.. onde he collon o wo 7.

More information

Java Applets / Flash Java Applet vs. Flash

Java Applets / Flash Java Applet vs. Flash ava Alet / Flah ava Alet v. Flah oltal oblem wth Mooft hhl otable moe dfflt develomet ot a oblem le o exellet val develomet tool Alet / Flah ood fo tato volv omlex e t whee XTML t elemet ae ot adeqate

More information

φ (x,y,z) in the direction of a is given by

φ (x,y,z) in the direction of a is given by UNIT-II VECTOR CALCULUS Dectoal devatve The devatve o a pot ucto (scala o vecto) a patcula decto s called ts dectoal devatve alo the decto. The dectoal devatve o a scala pot ucto a ve decto s the ate o

More information

M-ary Detection Problem. Lecture Notes 2: Detection Theory. Example 1: Additve White Gaussian Noise

M-ary Detection Problem. Lecture Notes 2: Detection Theory. Example 1: Additve White Gaussian Noise Hi ue Hi ue -ay Deecio Pole Coide he ole of decidig which of hyohei i ue aed o oevig a ado vaiale (veco). he efoace cieia we coide i he aveage eo oailiy. ha i he oailiy of decidig ayhig ece hyohei H whe

More information

-Z ONGRE::IONAL ACTION ON FY 1987 SUPPLEMENTAL 1/1

-Z ONGRE::IONAL ACTION ON FY 1987 SUPPLEMENTAL 1/1 -Z-433 6 --OGRE::OA ATO O FY 987 SUPPEMETA / APPR)PRATO RfQUEST PAY AD PROGRAM(U) DE ARTMET OF DEES AS O' D 9J8,:A:SF ED DEFS! WA-H ODM U 7 / A 25 MRGOPf RESOUTO TEST HART / / AD-A 83 96 (~Go w - %A uj

More information

Lecture 3 Topic 2: Distributions, hypothesis testing, and sample size determination

Lecture 3 Topic 2: Distributions, hypothesis testing, and sample size determination Lecure 3 Topc : Drbuo, hypohe eg, ad ample ze deermao The Sude - drbuo Coder a repeaed drawg of ample of ze from a ormal drbuo of mea. For each ample, compue,,, ad aoher ac,, where: The ac he devao of

More information

MIL-DTL SERIES 2

MIL-DTL SERIES 2 o ll oo I--26482 I 2 I--26482 I 2 OI O 34 70 14 4 09 70 14 4 71 l, l o 74 l, u 75 lu, I ou 76 lu, luu, l oz luu, lol l luu, olv u ov lol l l l, v ll z 8, 10, 12, 14,, 18,, 22, o 24 I o lyou I--69 o y o

More information

Analysis of a Stochastic Lotka-Volterra Competitive System with Distributed Delays

Analysis of a Stochastic Lotka-Volterra Competitive System with Distributed Delays Ieraoal Coferece o Appled Maheac Sulao ad Modellg (AMSM 6) Aaly of a Sochac Loa-Volerra Copeve Sye wh Drbued Delay Xagu Da ad Xaou L School of Maheacal Scece of Togre Uvery Togre 5543 PR Cha Correpodg

More information

Calibration Approach Based Estimators of Finite Population Mean in Two - Stage Stratified Random Sampling

Calibration Approach Based Estimators of Finite Population Mean in Two - Stage Stratified Random Sampling I.J.Curr.crobol.App.Sc (08) 7(): 808-85 Ieraoal Joural of Curre crobolog ad Appled Scece ISS: 39-7706 olue 7 uber 0 (08) Joural hoepage: hp://www.jca.co Orgal Reearch Arcle hp://do.org/0.0546/jca.08.70.9

More information

(1) Cov(, ) E[( E( ))( E( ))]

(1) Cov(, ) E[( E( ))( E( ))] Impac of Auocorrelao o OLS Esmaes ECON 3033/Evas Cosder a smple bvarae me-seres model of he form: y 0 x The four key assumpos abou ε hs model are ) E(ε ) = E[ε x ]=0 ) Var(ε ) =Var(ε x ) = ) Cov(ε, ε )

More information

The Solutions of Initial Value Problems for Nonlinear Fourth-Order Impulsive Integro-Differential Equations in Banach Spaces

The Solutions of Initial Value Problems for Nonlinear Fourth-Order Impulsive Integro-Differential Equations in Banach Spaces WSEAS TRANSACTIONS o MATHEMATICS Zhag Lglg Y Jgy Lu Juguo The Soluos of Ial Value Pobles fo Nolea Fouh-Ode Ipulsve Iego-Dffeeal Equaos Baach Spaces Zhag Lglg Y Jgy Lu Juguo Depae of aheacs of Ta Yua Uvesy

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

Neutrosophic Hyperideals of Semihyperrings

Neutrosophic Hyperideals of Semihyperrings Nuooph m Vol. 06 05 Uv o Nw Mo Nuooph Hpl o mhpg D Ml Dpm o Mhm j P Moh Collg Up Hooghl-758 mljumh@gml.om A. h pp w hv ou uooph hpl o mhpg o om opo o hm o u oo pop. Kwo: C Pou Compoo l o Nuooph mhpmg.

More information

Overview. Solving PDEs. Solving PDEs II. Midterm Exam. Review Spherical Laplace. The wave equation February 23, ME 501B Engineering Analysis 1

Overview. Solving PDEs. Solving PDEs II. Midterm Exam. Review Spherical Laplace. The wave equation February 23, ME 501B Engineering Analysis 1 The wave eqao ebay 3 9 aplae Eqao Colso ad The Wave Eqao ay Caeo Mehaal Egeeg 5 Sea Egeeg alyss ebay 3 9 Ovevew evew aeal o dae eeal appoah fo solvg PDEs Ohe deas abo aplae s Eqao Devao ad physal eag of

More information

SOME NEW SEQUENCE SPACES AND ALMOST CONVERGENCE

SOME NEW SEQUENCE SPACES AND ALMOST CONVERGENCE Faulty of Siees ad Matheatis, Uivesity of Niš, Sebia Available at: http://www.pf.i.a.yu/filoat Filoat 22:2 (28), 59 64 SOME NEW SEQUENCE SPACES AND ALMOST CONVERGENCE Saee Ahad Gupai Abstat. The sequee

More information

Some applications of DS spread spectrum signals

Some applications of DS spread spectrum signals --- Po-g Che --- 3.. Some applao of DS pead peum gal Theefoe, he b-po p fo lea ode oaeaed wh a bay epeo ode obaed hough e ode of-deo deodg whee p ymbol- POoue Φ J / P 496 [4 p p] m w m / 4 6 759[4 p p]

More information

Integrated Optical Waveguides

Integrated Optical Waveguides Su Opls Faha Raa Cll Uvs Chap 8 Ia Opal Wavus 7 Dl Slab Wavus 7 Iu: A va f ff a pal wavus a us f a u lh a hp Th s bas pal wavu s a slab wavus shw blw Th suu s uf h - Lh s u s h b al al fl a h -la fas Cla

More information

= y and Normed Linear Spaces

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

More information

Overview. Review Superposition Solution. Review Superposition. Review x and y Swap. Review General Superposition

Overview. Review Superposition Solution. Review Superposition. Review x and y Swap. Review General Superposition ylcal aplace Soltos ebay 6 9 aplace Eqato Soltos ylcal Geoety ay aetto Mechacal Egeeg 5B Sea Egeeg Aalyss ebay 6 9 Ovevew evew last class Speposto soltos tocto to aal cooates Atoal soltos of aplace s eqato

More information

Solution. The straightforward approach is surprisingly difficult because one has to be careful about the limits.

Solution. The straightforward approach is surprisingly difficult because one has to be careful about the limits. ose ad Varably Homewor # (8), aswers Q: Power spera of some smple oses A Posso ose A Posso ose () s a sequee of dela-fuo pulses, eah ourrg depedely, a some rae r (More formally, s a sum of pulses of wdh

More information

CAT. NO /irtl,417~ S- ~ I ';, A RIDER PUBLICATION BY H. A. MIDDLETON

CAT. NO /irtl,417~ S- ~ I ';, A RIDER PUBLICATION BY H. A. MIDDLETON CAT. NO. 139-3 THIRD SUPPLEMENT I /irtl,417~ S- ~ I ';,... 0 f? BY H. A. MIDDLETON.. A RIDER PUBLICATION B36 B65 B152 B309 B319 B329 B719 D63 D77 D152 DA90 DAC32 DAF96 DC70 DC80 DCC90 DD6 DD7 DF62 DF91

More information

Learning of Graphical Models Parameter Estimation and Structure Learning

Learning of Graphical Models Parameter Estimation and Structure Learning Learg of Grahal Models Parameer Esmao ad Sruure Learg e Fukumzu he Isue of Sasal Mahemas Comuaoal Mehodology Sasal Iferee II Work wh Grahal Models Deermg sruure Sruure gve by modelg d e.g. Mxure model

More information

8. Queueing systems lect08.ppt S Introduction to Teletraffic Theory - Fall

8. Queueing systems lect08.ppt S Introduction to Teletraffic Theory - Fall 8. Queueg sysems lec8. S-38.45 - Iroduco o Teleraffc Theory - Fall 8. Queueg sysems Coes Refresher: Smle eleraffc model M/M/ server wag laces M/M/ servers wag laces 8. Queueg sysems Smle eleraffc model

More information

SYSTEMS OF NON-LINEAR EQUATIONS. Introduction Graphical Methods Close Methods Open Methods Polynomial Roots System of Multivariable Equations

SYSTEMS OF NON-LINEAR EQUATIONS. Introduction Graphical Methods Close Methods Open Methods Polynomial Roots System of Multivariable Equations SYSTEMS OF NON-LINEAR EQUATIONS Itoduto Gaphal Method Cloe Method Ope Method Polomal Root Stem o Multvaale Equato Chapte Stem o No-Lea Equato /. Itoduto Polem volvg o-lea equato egeeg lude optmato olvg

More information

Summary of Grade 1 and 2 Braille

Summary of Grade 1 and 2 Braille Sa of Gade 1 ad 2 Baie Wiia Pa Seebe 1998, Ai 1999 1 Baie Aabe Te fooig i i of TEX aco ad Baie bo coaied i baie Te e coad \baie{} cove eece of ag o Baie bo A ag ca be oe caace ic aea a i, o i caace ic

More information

New approach for numerical solution of Fredholm integral equations system of the second kind by using an expansion method

New approach for numerical solution of Fredholm integral equations system of the second kind by using an expansion method Ieraoal Reearch Joural o Appled ad Bac Scece Avalable ole a wwwrabcom ISSN 5-88X / Vol : 8- Scece xplorer Publcao New approach or umercal oluo o Fredholm eral equao yem o he ecod d by u a expao mehod Nare

More information

Polarization Basics E. Polarization Basics The equations

Polarization Basics E. Polarization Basics The equations Plazan Ba he equan [ ω δ ] [ ω δ ] eeen a a f lane wave: he w mnen f he eleal feld f an wave agang n he z den, n neeal mnhma. he amlude, and hae δ, fluuae lwl wh ee he ad llan f he ae ω. z Plazan Ba [

More information

Cyclically Interval Total Colorings of Cycles and Middle Graphs of Cycles

Cyclically Interval Total Colorings of Cycles and Middle Graphs of Cycles Ope Joural of Dsree Mahemas 2017 7 200-217 hp://wwwsrporg/joural/ojdm ISSN Ole: 2161-7643 ISSN Pr: 2161-7635 Cylally Ierval Toal Colorgs of Cyles Mddle Graphs of Cyles Yogqag Zhao 1 Shju Su 2 1 Shool of

More information

AN ALGEBRAIC APPROACH TO M-BAND WAVELETS CONSTRUCTION

AN ALGEBRAIC APPROACH TO M-BAND WAVELETS CONSTRUCTION AN ALGEBRAIC APPROACH TO -BAN WAELETS CONSTRUCTION Toy L Qy S Pewe Ho Ntol Lotoy o e Peeto Pe Uety Be 8 P. R. C Att T e eet le o to ott - otool welet e. A yte of ott eto ote fo - otool flte te olto e o

More information

ABSOLUTE INDEXED SUMMABILITY FACTOR OF AN INFINITE SERIES USING QUASI-F-POWER INCREASING SEQUENCES

ABSOLUTE INDEXED SUMMABILITY FACTOR OF AN INFINITE SERIES USING QUASI-F-POWER INCREASING SEQUENCES Available olie a h://sciog Egieeig Maheaics Lees 2 (23) No 56-66 ISSN 249-9337 ABSLUE INDEED SUMMABILIY FACR F AN INFINIE SERIES USING QUASI-F-WER INCREASING SEQUENCES SKAIKRAY * RKJAI 2 UKMISRA 3 NCSAH

More information

Fault Tolerant Computing. Fault Tolerant Computing CS 530 Reliability Analysis

Fault Tolerant Computing. Fault Tolerant Computing CS 530 Reliability Analysis Probably /4/6 CS 5 elably Aaly Yahwa K. Malaya Colorado Sae very Ocober 4, 6 elably Aaly: Oule elably eaure: elably, avalably, Tra. elably, T M MTTF ad (, MTBF Bac Cae Sgle u wh perae falure, falure rae

More information

LLOQ=UWQOW=^j @ LOW O LOO O U L U LO U O OOLL L L LOW U O O LO OUU O OOLL U O UO UO UX UXLY UL UOO Y Y U O OOLL O Y OUU O OOLL U L U U L U OU OO O W U O W ULY U U W LL W U W LL W ULY ULO K U L L L OOL

More information

_ =- 314 TH / 3 RD 60M AR M NT GROUP C L) _. 5 TH AIR F0 RCE ` Pl R?N ]9. ia UNIT, - _ : --.

_ =- 314 TH / 3 RD 60M AR M NT GROUP C L) _. 5 TH AIR F0 RCE ` Pl R?N ]9. ia UNIT, - _ : --. H OR UN UN4 Q NOV 99 O ^ 0 342g = o 3 RD 60M AR M N GROUP ) = 34 H q 5 H AR F0 RE P R?N ]9 9 B UA DA Q N0U 99 n > o > 4 = H PAGE DEAFED AW E0 2958 R2 R g 8 B B F 0 328 p NOV 99 DA 3 9 9 3 ne o B o O o

More information

Fall 2004/05 Solutions to Assignment 5: The Stationary Phase Method Provided by Mustafa Sabri Kilic. I(x) = e ixt e it5 /5 dt (1) Z J(λ) =

Fall 2004/05 Solutions to Assignment 5: The Stationary Phase Method Provided by Mustafa Sabri Kilic. I(x) = e ixt e it5 /5 dt (1) Z J(λ) = 8.35 Fall 24/5 Solution to Aignment 5: The Stationay Phae Method Povided by Mutafa Sabi Kilic. Find the leading tem fo each of the integal below fo λ >>. (a) R eiλt3 dt (b) R e iλt2 dt (c) R eiλ co t dt

More information

Circular Motion Problem Solving

Circular Motion Problem Solving iula Motion Poblem Soling Aeleation o a hange in eloity i aued by a net foe: Newton nd Law An objet aeleate when eithe the magnitude o the dietion of the eloity hange We aw in the lat unit that an objet

More information

Moments of Generalized Order Statistics from a General Class of Distributions

Moments of Generalized Order Statistics from a General Class of Distributions ISSN 684-843 Jol of Sttt Vole 5 28. 36-43 Moet of Geelzed Ode Sttt fo Geel l of Dtto Att Mhd Fz d Hee Ath Ode ttt eod le d eel othe odel of odeed do le e ewed el e of geelzed ode ttt go K 995. I th e exlt

More information

CE 561 Lecture Notes. Optimal Timing of Investment. Set 3. Case A- C is const. cost in 1 st yr, benefits start at the end of 1 st yr

CE 561 Lecture Notes. Optimal Timing of Investment. Set 3. Case A- C is const. cost in 1 st yr, benefits start at the end of 1 st yr CE 56 Letue otes Set 3 Optmal Tmg of Ivestmet Case A- C s ost. ost st y, beefts stat at the ed of st y C b b b3 0 3 Case B- Cost. s postpoed by oe yea C b b3 0 3 (B-A C s saved st yea C C, b b 0 3 Savg

More information

Chapter 3: Vectors and Two-Dimensional Motion

Chapter 3: Vectors and Two-Dimensional Motion Chape 3: Vecos and Two-Dmensonal Moon Vecos: magnude and decon Negae o a eco: eese s decon Mulplng o ddng a eco b a scala Vecos n he same decon (eaed lke numbes) Geneal Veco Addon: Tangle mehod o addon

More information

Efficient Estimators for Population Variance using Auxiliary Information

Efficient Estimators for Population Variance using Auxiliary Information Global Joural of Mahemacal cece: Theor ad Praccal. IN 97-3 Volume 3, Number (), pp. 39-37 Ieraoal Reearch Publcao Houe hp://www.rphoue.com Effce Emaor for Populao Varace ug Aular Iformao ubhah Kumar Yadav

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