On One Property of the Wiener Integral and its Statistical Application
|
|
- Loren Cobb
- 5 years ago
- Views:
Transcription
1 saqatvelos eceebata eovl aaes oabe # 9 BUETIN OF THE GEORGIAN NATIONA AADEM OF SIENES vol o 9 Maheacs O Oe Pope o he Wee Ieal a s Sascal Applcao Pee Babla* Elzba Naaaa** Mzeva Pasasa & Gol Sohaze # * I Javahshvl Tbls Sae Uves ** Acae Mebe I Javahshvl Tbls Sae Uves & Soh Uves # A Tseeel Sae Uves as ABSTRAT Fo he Wee eal oe pope o veso s esablshe Ths pope s se o cosco o opaaec sascal esao o he o loahc evave o sbo ao pocesses hch s obseve Wee ose 9 Bll Geo Nal Aca Sc e os: Wee eal loahc evave opaaec esao e he s o epee ao pocesses ξ η hee s a saa Wee pocess be e obsevao Us he obseve vales (aecoes ξ ξ ξ e ae o cosc a esae o he o loahc evave o he sbo o he pocess η Fo ao vales (he η a o o epe o hs poble s cosee [] he oe-esoal case To solve he poble e appl he echqe o opaaec esao o Wee eals I he s pa o hs o e ve oe veso heoe o he Wee eal Ths heoe eealzes he ell-o esl o Rooe [] o he oe-esoal case I he Wee eal heo hs esl s o epee ees a eables s o cosc he seco pa o he o e-esoal appoaos o esao o he o loahc evave e-esoal space We ll cose he space o coos cos o [ ] he -aleba o Boel sbses a he Wee ease μ o e he ( a be pos o [ ] We ll eoe b ( he F be soe coal o I s asse ha boe le h veces a he pos ( ( ( F ( F ( ( e I s esoo ha o e have F ( F he sese o so coveece I s ell o ([] ha o a coos boe coal F ebese eal h espec o a Wee ease ( s hs eal ha s calle he Wee eal ca be ee b he eqal F μ ( l π 9 Bll Geo Nal Aca Sc
2 O Oe Pope o he Wee Ieal a s Sascal Applcao hee F ep E ( E s a -esoal Eclea space A aaloos ola also hols o lple Wee eals le s cose he aso hch e call he Wee Fo a coos boe coal aso o ( μ ( (ea he e he coseao o he s o epee ao elees e ae a oce he ollo B E e he he ea e E be a sepaable lea opolocal space h a Boel -aleba o s sbses epee ao elees ξ a η h vales E a h pobabl sbos ( A P{ ω ξ A} ν ( A P{ ω : η A} especvel o B ( E be ee o he pobabl space { I P} ζ ξ ca a sbo ( A P{ ω : ζ A} he covolo o ( A μ( A ν ( A B( E E μ : a Ω Fo he s η e (* hee μ ( A eoes he sh o μ oo he veco E Iee b he eealze ola o oal pobabl e oba { η A} P{ ξ A η } P{ η } P{ ξ A } ν ( P ξ E Whch s eqvale o (* I π ( A s a ease sch ha slaeosl boh a μ ae absolel coos h espec o π (o π 5 μ he (* ca be ee he o eaple μ ρ ρ μ ( ν ( hee ρ a ρ μ π π E hch s sall apple he e-esoal case o sbo eses h espec o a ebese ease The ole hch hs epesso plas vaos pobles o aalss a pacla he heo o paabolc eeal eqaos s ell-o (see o eaple [] We ae eese he qeso o veso o aso ( Fo he sae o splc e ve he esl o [] hch has bee eoe above e ξ be a saa oall sbe ao vale h paaees ( e he R be a co sch ha he covolo ϕ hee ϕ ep π s ee Theoe (Rooe [] Ue he above asspos ( τ l τ We ea eael ha he co a all s evaves ae as a hole he pass hs s o he l e ca e ( Sch sple vaa o Rooe s heoe as eealzao E ae boe he Bll Geo Nal Aca Sc vol o 9
3 Pee Babla Elzba Naaaa Mzeva Pasasa Gol Sohaze Bll Geo Nal Aca Sc vol o 9 Theoe e he co have evaves o all oes a he ae oehe h s evaves as a hole be boe The he eal eqao ep π ( has a solo he class o boe cos A solo o ( ca be epesee as hee a s s s s ϕ ϕ s a oal evave o s-h oe o he co ϕ ϕ hee s s a o-eave ee be Poo The o co ll be soh oall o e he eal as a Macla sees a he po : Sbs hs epesso ( a a o acco ha o > o o ep π e oba ( ( Ae eleea asoaos e ca e ( We eeae hs eqal o es a lpl boh pas o he esl eqal b he cosa Ae ha e eeae ( o es a lpl boh pas o he esl eqal b he cosa a so o I he eeal case e eeae eqal ( es a lpl boh pas o he esl eqal b a so o I ao o ( e oba a be o eqales: 6 6 ( (6
4 O Oe Pope o he Wee Ieal a s Sascal Applcao Bll Geo Nal Aca Sc vol o 9 No o ( e sbac (5 a (6 sbac he e eqal a he e eqal a so o We o so a o acco he cobaoal e The e all oba (7 hch coces h he eqal e ae o pove All hese oal asoaos ae se becase as ca be easl vee b he coo o he heoe he absole vale o he eeal e o he oal sees (7 vashes a a scel qc ae a hee (7 covees absolel a ol The heoe s pove oolla I he coos o Theoe e cose he eqal ep π (8 The (9 Iee e oce he oao ϕ ψ he (8 aes he o ep ψ π ϕ o hch Theoe s applcable Ae sbso a asoao e oba (9 e s o o ( Isea o ( e cose he eqal ep ψ π E ep ( Ioc he oao e e ( he o
5 Pee Babla Elzba Naaaa Mzeva Pasasa Gol Sohaze Bll Geo Nal Aca Sc vol o 9 π ep ( e s appl Theoe o eqal ( o Fo hs e ee hs eqal as ep e π Us oolla e oba ep ( Fo he se o oolla e ee ( he o π ep e B ola (9 e oba ep Pocee so sep b sep -es aloehe e all oba
6 O Oe Pope o he Wee Ieal a s Sascal Applcao 5 Bll Geo Nal Aca Sc vol o 9 ( Ths e have sho ha ( ca be vee a he vese s e o ( Noe ha ola ( e asse a sep-b-sep applcao o eeal eqaos o he cos The poe o he ae a he paal ae s calclae as sal b he Neo ola o hhe evaves e s asse ha s ae o he class o boe coals oehe h he evaves The e ca asse ha he sees ( covee ol a absolel Iee as see o eqal ( hee es all evaves a he ae boe The o he eeal e ( e oba a esae M (I he epesso o he le s asse o be he ce cosa hle ae he vaables o he eeal e o he sees Ths esae ( ves he ese poo Sce he sees ( covee absolel a ol e ca pass o he l e he sao s The e oba he l he vese o he Wee aso (: l ( Theeoe he ollo saee s e Theoe The vese aso o he Wee aso ( ess he class o coals oehe h he evaves o all oes hch ae boe ae as a hole a he vese aso ca be calclae b ola ( hee s he ohooal poeco o he coal Rea Feqel sea o ( he ollo eo o a clcal Wee ease s se: ep l E F F π μ I ha case ola ( has he o
7 6 Pee Babla Elzba Naaaa Mzeva Pasasa Gol Sohaze Bll Geo Nal Aca Sc vol o 9 (5 hle ( s e as l (6 Rea I s ees o oe ha (6 (le ( ca be se o calclae soe Wee eals We llsae hs b seveal eaples: e The o (6 e oba Theeoe μ Hece e have E μ e The o (6 e oba Theeoe ( μ Hece a o acco he pece eaple e have E μ B aaloos calclaos o < e sho ha { } E μ I e ae e he ep a ae ca o soe calclaos e oba e Ee e μ 5 e s calclae ( ep μ Fo hs e ae ep hee Fo e have ep I s eas o calclae ha
8 O Oe Pope o he Wee Ieal a s Sascal Applcao 7 Bll Geo Nal Aca Sc vol o 9 ep ep Theeoe ep ep ep l ep ep l ( ep l ep μ Ths ( ( ( μ ep ep Ths ples ha ( ep ep μ e s pocee o he applcao o he esls obae Asse ha e have he s o ao elees W hee W s a saa Wee pocess a oes o epe o W e be epee obsevaos (aecoes o a elee We ae o esae he loahc evave h l o he sbo μ o he ao pocess alo h We cose he pos < < < e a as We oce he oao W W W W a cose he eqal W Ths s he eqal he e-esoal space R a e asse he esece o sbo eses e ca e ep E p p π B ola (5 e have p p (7 Fo bev e oce he oao
9 8 Pee Babla Elzba Naaaa Mzeva Pasasa Gol Sohaze The (7 aes he o Bll Geo Nal Aca Sc vol o 9 ( ( ϕ D p ~ D p ( ~ ( ϕ (8 I he e-esoal case he loahc evave o a sbo h es p calclae b he ola R s ( ap h l h (9 p hee ( eoes he scala poc o he vecos R a h s he ohooal poeco o he veco h R O he vales o he obseve cos a he selece pos e copose he a o obsevaos ( Ma ( cosss o epee a eqall sbe ao vales Us hs a e cosc he esae o he es (acall o p a he esae p b ola (8 a he soh loahc evave b ola (9 e se he sasc Fo esa he o es hee ( p pˆ ( a Fo a he scsso e ae eqal The Fo (8 e oba pˆ apˆ ap No o he loahc evave l ( l ( h ( ( R ae eve posve boe cos h I o case ( ( a ( ( h D ap h ϕ( h ( ap h p e ca e a esae he o D a D ( ( h ϕ( ( ( ϕ(
10 O Oe Pope o he Wee Ieal a s Sascal Applcao 9 So he ollo saee s e Theoe I he space [ ] e have he obsevao o he ealzao o he s o epee ao pocesses W hee W s a saa Wee pocess he he esae o he loahc evave o he sbo o he ao pocess s ve b he ola l D a ( ( hϕ( l ( h l l D ϕ hee ( ( s a eve posve sooh es co < < [ ] a as ae chose so ha < as he pos ateaa ves eals et Tvsebsa a s sas aoeebs Sesaeb pee babla* elzba aaaa** zeva acaca & ol soaze # * avasvls sa Tblss saelo vese ** aaes ev avasvls sa Tblss saelo vese & sos vese # a eetls saelo vese qtas asos aela ves eals Sebebs et Tvseba oelc aoeeba cob loatl aoebls aapaael sas Seasebs asaeba set SeTvevT pocess aalebsatvs oelzec avveba eba ves SeSoTebs pobebs REFERENES E Naaaa (989 Nopaaec esao o pobabl eses a eesso cves le Acaec Pblshes Gop Doech P Rooe (957 aa J Mah 9: 5- I M ovalch (96 UMN (Avaces o Maheacal Sceces VIII (9: 97- ( Rssa Dales (967 UMN (Avaces o Maheacal Sceces : -5 ( Rssa Receve Decebe 8 Bll Geo Nal Aca Sc vol o 9
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-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 informationChapter 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( ) ( ) 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 informationIncreasing the Image Quality of Atomic Force Microscope by Using Improved Double Tapered Micro Cantilever
Rece Reseaces Teecocaos foacs Eecocs a Sga Pocessg ceasg e age Qa of oc Foce Mcope Usg pove oe Tapee Mco aeve Saeg epae of Mecaca Egeeg aava Bac sac za Uves aava Tea a a_saeg@aavaa.ac. sac: Te esoa feqec
More informationON 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 informationHyperbolic Heat Equation as Mathematical Model for Steel Quenching of L-shape and T-shape Samples, Direct and Inverse Problems
SEAS RANSACIONS o HEA MASS RANSER Bos M Be As Bs Hpeo He Eo s Me Moe o See Qe o L-spe -spe Spes De Iese Poes ABIA BOBINSKA o Pss Mes es o L Ze See 8 L R LAIA e@o MARARIA BIKE ANDRIS BIKIS Ise o Mes Cope
More informationNUMERICAL EVALUATION of DYNAMIC RESPONSE
NUMERICAL EVALUATION of YNAMIC RESPONSE Aalycal solo of he eqao of oo for a sgle degree of freedo syse s sally o ossble f he excao aled force or grod accelerao ü g -vares arbrarly h e or f he syse s olear.
More informationSolution to Some Open Problems on E-super Vertex Magic Total Labeling of Graphs
Aalable a hp://paed/aa Appl Appl Mah ISS: 9-9466 Vol 0 Isse (Deceber 0) pp 04- Applcaos ad Appled Maheacs: A Ieraoal Joral (AAM) Solo o Soe Ope Probles o E-sper Verex Magc Toal Labelg o Graphs G Marh MS
More informationNonlocal 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 informationExample: 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 informationLecture 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 informationANGULAR COMPLEX MELLIN TRANSFORM
Sc. Revs. Che. Co.: 3 0 99-304 ISSN 77-669 ANGULAR COMPLEX MELLIN TRANSFORM V. N. MAHALLE * A. S. GUDADHE a a R. D. TAYWADE b Ba. R. D. I.. N.. D. College Baea Ralway BADNERA M.S. INDIA a Deptt. o Matheatcs
More informationIntegral Form of Popoviciu Inequality for Convex Function
Procees of e Paksa Acaey of Sceces: A. Pyscal a ozaoal Sceces 53 3: 339 348 206 oyr Paksa Acaey of Sceces ISSN: 258-4245 r 258-4253 ole Paksa Acaey of Sceces Researc Arcle Ieral For of Pooc Ieqaly for
More informationOverview. 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 informationNonlinear Control of a Single-Link Flexible Joint Manipulator via Predictive Control
WEA AACO o YEM ad COO.. lle-alcalá. U. ceaa-cao. Alcáaa-amíez. ame-poce olea Cool o a le-k Fleble o Maplao va Pedcve Cool.. E-ACAÁ. U. CEAGA-CAO. ACÁAA-AMÍEZ AD. AME-POCE Depaameo de Elecóca Gpo Cool de
More informationAxiomatic Definition of Probability. Problems: Relative Frequency. Event. Sample Space Examples
Rado Sgals robabl & Rado Varables: Revew M. Sa Fadal roessor o lecrcal geerg Uvers o evada Reo Soe phscal sgals ose cao be epressed as a eplc aheacal orla. These sgals s be descrbed probablsc ers. ose
More informationX-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 informationOn 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 informationELECTROMAGNETISM, 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 informationTHIS 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 informationSupport 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 informationTechnical 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 informationON 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 informationβ A Constant-G m Biasing
p 2002 EE 532 Anal IC Des II Pae 73 Cnsan-G Bas ecall ha us a PTAT cuen efeence (see p f p. 66 he nes) bas a bpla anss pes cnsan anscnucance e epeaue (an als epenen f supply lae an pcess). Hw h we achee
More informationThe Properties of Probability of Normal Chain
I. J. Coep. Mah. Sceces Vol. 8 23 o. 9 433-439 HIKARI Ld www.-hkar.co The Properes of Proaly of Noral Cha L Che School of Maheacs ad Sascs Zheghou Noral Uversy Zheghou Cy Hea Provce 4544 Cha cluu6697@sa.co
More informationThe far field calculation: Approximate and exact solutions. Persa Kyritsi November 10th, 2005 B2-109
Th fa fl calculao: Appoa a ac oluo Pa K Novb 0h 005 B-09 Oul Novb 0h 005 Pa K Iouco Appoa oluo flco fo h gou ac oluo Cocluo Pla wav fo Ic fl: pla wav k ( ) jk H ( ) λ λ ( ) Polaao fo η 0 0 Hooal polaao
More informationCptS 570 Machine Learning School of EECS Washington State University. CptS Machine Learning 1
ps 57 Machne Leann School of EES Washnon Sae Unves ps 57 - Machne Leann Assume nsances of classes ae lneal sepaable Esmae paamees of lnea dscmnan If ( - -) > hen + Else - ps 57 - Machne Leann lassfcaon
More informationLagrangian & 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 informationANSWERS 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 informationI-POLYA PROCESS AND APPLICATIONS Leda D. Minkova
The XIII Inenaonal Confeence Appled Sochasc Models and Daa Analyss (ASMDA-009) Jne 30-Jly 3, 009, Vlns, LITHUANIA ISBN 978-9955-8-463-5 L Sakalaskas, C Skadas and E K Zavadskas (Eds): ASMDA-009 Seleced
More informationParameter Estimation and Hypothesis Testing of Two Negative Binomial Distribution Population with Missing Data
Avlble ole wwwsceceeccom Physcs Poce 0 475 480 0 Ieol Cofeece o Mecl Physcs Bomecl ee Pmee smo Hyohess es of wo Neve Boml Dsbuo Poulo wh Mss D Zhwe Zho Collee of MhemcsJl Noml UvesyS Ch zhozhwe@6com Absc
More informationStrong Result for Level Crossings of Random Polynomials. Dipty Rani Dhal, Dr. P. K. Mishra. Department of Mathematics, CET, BPUT, BBSR, ODISHA, INDIA
Iteatioal Joual of Reseach i Egieeig ad aageet Techology (IJRET) olue Issue July 5 Available at http://wwwijetco/ Stog Result fo Level Cossigs of Rado olyoials Dipty Rai Dhal D K isha Depatet of atheatics
More informationAnalysis 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 informationELEC 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 informationPOSITIVITY AND REACHABILITY OF FRACTIONAL ELECTRICAL CIRCUITS
asz Kaczo Posy a achably o Facoal Elccal cs POSIIVIY ND EHIIY OF FION EEI IUIS asz KZOEK* *Facly o Elccal Egg ałyso Usy o chology l Wsa D - ałyso aczo@sppwpl bsac: oos o h posy o acoal la lccal ccs copos
More informationChapter 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 informationEMA5001 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 informationOverview. 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 informationModified 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 informationInternational 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 informationPhysics 201 Lecture 15
Phscs 0 Lecue 5 l Goals Lecue 5 v Elo consevaon of oenu n D & D v Inouce oenu an Iulse Coens on oenu Consevaon l oe geneal han consevaon of echancal eneg l oenu Consevaon occus n sses wh no ne eenal foces
More informationChapter 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 informationAfrican 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 informationCHATTERJEA 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 informationThe 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 information4.1 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 informationUpper Bound For Matrix Operators On Some Sequence Spaces
Suama Uer Bou formar Oeraors Uer Bou For Mar Oeraors O Some Sequece Saces Suama Dearme of Mahemacs Gaah Maa Uersy Yogyaara 558 INDONESIA Emal: suama@ugmac masomo@yahoocom Isar D alam aer aa susa masalah
More informationChapter 1 - Free Vibration of Multi-Degree-of-Freedom Systems - I
CEE49b Chaper - Free Vbrao of M-Degree-of-Freedo Syses - I Free Udaped Vbrao The basc ype of respose of -degree-of-freedo syses s free daped vbrao Aaogos o sge degree of freedo syses he aayss of free vbrao
More informationSECURITY EVALUATION FOR SNOW 2.0-LIKE STREAM CIPHERS AGAINST CORRELATION ATTACKS OVER EXTENSION FIELDS
SECURIY EVALUAION FOR SNOW.-LIKE SREAM CIPHERS AGAINS CORRELAION AACKS OVER EXENSION FIELDS A. N. Alekseychk * S. M. Koshok ** M. V. Poemsky *** Ise of Secal Commcao ad Ifomao Secy Naoal echcal Uvesy of
More informationA 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 informationÖRNEK 1: THE LINEAR IMPULSE-MOMENTUM RELATION Calculate the linear momentum of a particle of mass m=10 kg which has a. kg m s
MÜHENDİSLİK MEKANİĞİ. HAFTA İMPULS- MMENTUM-ÇARPIŞMA Linea oenu of a paicle: The sybol L denoes he linea oenu and is defined as he ass ies he elociy of a paicle. L ÖRNEK : THE LINEAR IMPULSE-MMENTUM RELATIN
More informationContinuous Time Markov Chains
Couous me Markov chas have seay sae probably soluos f a oly f hey are ergoc, us lke scree me Markov chas. Fg he seay sae probably vecor for a couous me Markov cha s o more ffcul ha s he scree me case,
More informationOrder Statistics. 1 n. Example Four measurements are taken on a random variable, x, which take on values.
Oe Sascs e be couous epee.v. wh sbuo a es (. We eoe K be he oee aom vaable whee < < K < a because he ae couous we ca goe equal sg. m ma ( K ( K The pobabl es uco o a ae easl ou: e be a couous.v. ha has
More informationFractional 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 informationMaximum 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_...,1 4._.,1 v,_ 4r 1.. _.= _',-.3, _~ .';~f_-w-:2 -»5r- ;.::..'_.;,; ff. -*;, ;1_:\'."\.=.,;. '. -: _'1.,,..'. Q.
= + < < < = < c + = < = $! == = = = # c = = +! j z = = $=! = # % == =! < == = + = = = @ j +% j= = =s = } o } = == = } < =e = < = = z } s = < = s = @ } = =
More informationNumerical Study of Large-area Anti-Resonant Reflecting Optical Waveguide (ARROW) Vertical-Cavity Semiconductor Optical Amplifiers (VCSOAs)
USOD 005 uecal Sudy of Lage-aea An-Reonan Reflecng Opcal Wavegude (ARROW Vecal-Cavy Seconduco Opcal Aplfe (VCSOA anhu Chen Su Fung Yu School of Eleccal and Eleconc Engneeng Conen Inoducon Vecal Cavy Seconduco
More informationSome 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 information4/3/2017. PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103
PHY 7 Eleodnais 9-9:50 AM MWF Olin 0 Plan fo Leue 0: Coninue eading Chap Snhoon adiaion adiaion fo eleon snhoon deies adiaion fo asonoial objes in iula obis 0/05/07 PHY 7 Sping 07 -- Leue 0 0/05/07 PHY
More informationNUMERICAL SOLUTIONS TO ORDINARY DIFFERENTIAL EQUATIONS
NUMERICAL SOLUTIONS TO ORDINARY DIFFERENTIAL EQUATIONS If e eqao coas dervaves of a - order s sad o be a - order dffereal eqao. For eample a secod-order eqao descrbg e oscllao of a weg aced po b a sprg
More information_ 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 informationAttention of the Authorised Dealers is invited to Regulation 6 of the Notification No.FEMA
. c Pv ff s s s K g e C Seebe 13, 2013 Ue e evse cee, e ees w ve ece e e Reseve Bk f I w be eeg e fces ees f e gee f FEMA Fs Pg, eefe, e ee EDF/SOFTEX F N. w be Fs M. Rv J +91-9953006168, M. Mj Tew +91-9810636688,
More informationConvection in a Differentially Heated Narrow Slot By Teja Muppirala Advisor: Dr. Cho Lik Chan. University of Arizona, Spring/Summer 2002
Coco a Dffall Ha Naow Slo ja ala so: D. Co k Ca Us of zoa S/S Coco a ffall a aow slo of fl ca sla a ff s of bao o os of fl a os of slo. basc cl s a fl a o wall wll s o s cas a a fl a cool wall wll fall.
More informationOn 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 informationSolution of Impulsive Differential Equations with Boundary Conditions in Terms of Integral Equations
Joural of aheacs ad copuer Scece (4 39-38 Soluo of Ipulsve Dffereal Equaos wh Boudary Codos Ters of Iegral Equaos Arcle hsory: Receved Ocober 3 Acceped February 4 Avalable ole July 4 ohse Rabba Depare
More informationSome Probability Inequalities for Quadratic Forms of Negatively Dependent Subgaussian Random Variables
Joural of Sceces Islamc epublc of Ira 6(: 63-67 (005 Uvers of ehra ISSN 06-04 hp://scecesuacr Some Probabl Iequales for Quadrac Forms of Negavel Depede Subgaussa adom Varables M Am A ozorga ad H Zare 3
More informationGeneralized Duality for a Nondifferentiable Control Problem
Aeca Joal of Appled Matheatcs ad Statstcs, 4, Vol., No. 4, 93- Avalable ole at http://pbs.scepb.co/aas//4/3 Scece ad Edcato Pblsh DO:.69/aas--4-3 Geealzed Dalty fo a Nodffeetable Cotol Poble. Hsa,*, Vkas
More informationAPPLICATION 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 informationABSOLUTE 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 information8.5 Circles and Lengths of Segments
LenghofSegmen20052006.nb 1 8.5 Cicle and Lengh of Segmen In hi ecion we will how (and in ome cae pove) ha lengh of chod, ecan, and angen ae elaed in ome nal way. We will look a hee heoem ha ae hee elaionhip
More informationStrong Result for Level Crossings of Random Polynomials
IOSR Joual of haacy ad Biological Scieces (IOSR-JBS) e-issn:78-8, p-issn:19-7676 Volue 11, Issue Ve III (ay - Ju16), 1-18 wwwiosjoualsog Stog Result fo Level Cossigs of Rado olyoials 1 DKisha, AK asigh
More informationFRACTIONAL 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 information11/8/2002 CS 258 HW 2
/8/ CS 58 HW. G o a a qc of aa h < fo a I o goa o co a C cc c F ch ha F fo a I A If cc - c a co h aoa coo o ho o choo h o qc? I o g o -coa o o-coa? W ca choo h o qc o h a a h aa a. Tha f o o a h o h a:.
More informationχ be any function of X and Y then
We have show that whe we ae gve Y g(), the [ ] [ g() ] g() f () Y o all g ()() f d fo dscete case Ths ca be eteded to clude fuctos of ay ube of ado vaables. Fo eaple, suppose ad Y ae.v. wth jot desty fucto,
More informationThe 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 informationOutline. Review Homework Problem. Review Homework Problem II. Review Dimensionless Problem. Review Convection Problem
adial diffsio eqaio Febay 4 9 Diffsio Eqaios i ylidical oodiaes ay aeo Mechaical Egieeig 5B Seia i Egieeig Aalysis Febay 4, 9 Olie eview las class Gadie ad covecio boday codiio Diffsio eqaio i adial coodiaes
More informationF l a s h-b a s e d S S D s i n E n t e r p r i s e F l a s h-b a s e d S S D s ( S o-s ltiad t e D r i v e s ) a r e b e c o m i n g a n a t t r a c
L i f e t i m e M a n a g e m e n t o f F l a-b s ah s e d S S D s U s i n g R e c o v e r-a y w a r e D y n a m i c T h r o t t l i n g S u n g j i n L e, e T a e j i n K i m, K y u n g h o, Kainmd J
More informationflbc in Russia. PIWiREE COHORTS ARE NOT PULL- ING TOGETHER. SIGHTS AND SCENES IN ST. PETERSBURG.
# O E O KOE O F Y F O VO V NO 5 OE KEN ONY Y 2 9 OE NO 265 E K N F z 5 7 X ) $2 Q - EO NE? O - 5 OO Y F F 2 - P - F O - FEE > < 5 < P O - 9 #»»» F & & F $ P 57 5 9 E 64 } 5 { O $665 $5 $ 25 E F O 9 5 [
More information( ) ( ) ( ( )) ( ) ( ) ( ) ( ) ( ) = ( ) ( ) + ( ) ( ) = ( ( )) ( ) + ( ( )) ( ) Review. Second Derivatives for f : y R. Let A be an m n matrix.
Revew + v, + y = v, + v, + y, + y, Cato! v, + y, + v, + y geeral Let A be a atr Let f,g : Ω R ( ) ( ) R y R Ω R h( ) f ( ) g ( ) ( ) ( ) ( ( )) ( ) dh = f dg + g df A, y y A Ay = = r= c= =, : Ω R he Proof
More informationFinal Exam Applied Econometrics
Fal Eam Appled Ecoomercs. 0 Sppose we have he followg regresso resl: Depede Varable: SAT Sample: 437 Iclded observaos: 437 Whe heeroskedasc-cosse sadard errors & covarace Varable Coeffce Sd. Error -Sasc
More informationMathematical Statistics. Chapter VIII Sampling Distributions and the Central Limit Theorem
Mahmacal ascs 8 Chapr VIII amplg Dsrbos ad h Cral Lm Thorm Fcos of radom arabls ar sall of rs sascal applcao Cosdr a s of obsrabl radom arabls L For ampl sppos h arabls ar a radom sampl of s from a poplao
More information( m is the length of columns of A ) spanned by the columns of A : . Select those columns of B that contain a pivot; say those are Bi
Assgmet /MATH 47/Wte Due: Thusday Jauay The poblems to solve ae umbeed [] to [] below Fst some explaatoy otes Fdg a bass of the colum-space of a max ad povg that the colum ak (dmeso of the colum space)
More informationFault-tolerant Output Feedback Control for a Class of Multiple Input Fuzzy Bilinear Systems
Sesos & asduces Vol 7 Issue 6 Jue 04 pp 47-5 Sesos & asduces 04 by IFSA Publshg S L hp://wwwsesospoalco Faul-olea Oupu Feedbac Cool fo a Class of Mulple Ipu Fuzzy Blea Syses * YU Yag WAG We School of Eleccal
More informationLIPSCHITZ 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 informationSUBSEQUENCE CHARACTERIZAT ION OF UNIFORM STATISTICAL CONVERGENCE OF DOUBLE SEQUENCE
Reseach ad Coucatos atheatcs ad atheatcal ceces Vol 9 Issue 7 Pages 37-5 IN 39-6939 Publshed Ole o Novebe 9 7 7 Jyot cadec Pess htt//yotacadecessog UBEQUENCE CHRCTERIZT ION OF UNIFOR TTITIC CONVERGENCE
More informationMass-Spring Systems Surface Reconstruction
Mass-Spng Syses Physally-Based Modelng: Mass-Spng Syses M. Ale O. Vasles Mass-Spng Syses Mass-Spng Syses Snake pleenaon: Snake pleenaon: Iage Poessng / Sae Reonson: Iage poessng/ Sae Reonson: Mass-Spng
More informationAdvanced 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 informationOptical flow equation
Opical Flow Sall oio: ( ad ae le ha piel) H() I(++) Be foce o poible ppoe we ake he Talo eie epaio of I: (Sei) Opical flow eqaio Cobiig hee wo eqaio I he lii a ad go o eo hi becoe eac (Sei) Opical flow
More informationCHAPTER 10: LINEAR DISCRIMINATION
HAPER : LINEAR DISRIMINAION Dscmnan-based lassfcaon 3 In classfcaon h K classes ( k ) We defned dsmnan funcon g () = K hen gven an es eample e chose (pedced) s class label as f g () as he mamum among g
More informationSupplementary Information for On characterizing protein spatial clusters with correlation approaches
Supplementay Infomation fo On chaacteizing potein spatial clustes with coelation appoaches A. Shivananan, J. Unnikishnan, A. Raenovic Supplementay Notes Contents Deivation of expessions fo p = a t................................
More informationSpectrum of The Direct Sum of Operators. 1. Introduction
Specu of The Diec Su of Opeaos by E.OTKUN ÇEVİK ad Z.I.ISMILOV Kaadeiz Techical Uivesiy, Faculy of Scieces, Depae of Maheaics 6080 Tabzo, TURKEY e-ail adess : zaeddi@yahoo.co bsac: I his wok, a coecio
More informationVARIED SIZED FLOOR PLATE S O N - S I T E B U I L D I N G A M E N I T I E S
VAIED SIZED FLOO PLAE S O - S I E B U I L D I G A E I I E S AVAILABILIIES HIGH-ISE EIE 29H FLOO 16,584 SF LEASE OU ID-ISE PAIAL 18H FLOO 12,459 SF 08/2019 ID-ISE PAIAL 14H FLOO 7,232 SF 08/2019 LOW-ISE
More informationSome Different Perspectives on Linear Least Squares
Soe Dfferet Perspectves o Lear Least Squares A stadard proble statstcs s to easure a respose or depedet varable, y, at fed values of oe or ore depedet varables. Soetes there ests a deterstc odel y f (,,
More informationIV. STATICS AND DYNAMICS OF DEFORMABLE MEDIA.
V. TT ND DYNM OF DEFOMLE MED. 48. Defoabe eu. Naua sae a efoe sae. The heoes of he efoabe e a he efoabe suface ha we scusse ea a ve aua ae o evsog a oe geea efoabe eu ha he oe ha s habua cosee he heo of
More informationA 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 informationCentral limit theorem for functions of weakly dependent variables
Int. Statistical Inst.: Poc. 58th Wold Statistical Congess, 2011, Dublin (Session CPS058 p.5362 Cental liit theoe fo functions of weakly dependent vaiables Jensen, Jens Ledet Aahus Univesity, Depatent
More informationdm 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 informationChapter 2. Review of Hydrodynamics and Vector Analysis
her. Ree o Hdrodmcs d Vecor Alss. Tlor seres L L L L ' ' L L " " " M L L! " ' L " ' I s o he c e romed he Tlor seres. O he oher hd ' " L . osero o mss -dreco: L L IN ] OUT [mss l [mss l] mss ccmled h me
More informationI 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