Safety and Reliability of Embedded Systems. (Sicherheit und Zuverlässigkeit eingebetteter Systeme) Stochastic Reliability Analysis
|
|
- Barnaby Morrison
- 5 years ago
- Views:
Transcription
1 (Schrh und Zuvrlässgk ngbr Sysm) Sochasc Rlably Analyss
2 Conn Dfnon of Rlably Hardwar- vs. Sofwar Rlably Tool Asssd Rlably Modlng Dscrpons of Falurs ovr Tm Rlably Modlng Exampls of Dsrbuon Funcons Th xponnal dsrbuon Th Wbull dsrbuon Th Posson dsrbuon Musa's Excuon Tm Modl Drmnaon of Modl Paramrs Slcon of Modls Basd on Falur Obsrvaon 2
3 Dfnon Rlably Par of h qualy wh rgard o h bhavor of an ny durng or afr gvn m nrvals undr gvn applcaon condons (ranslad from DIN 44) Th propry of an ny o fulfll s rlably rqurmns durng or afr a gvn m span undr gvn applcaon condons (ranslad from DIN ISO 9 Tl 4) A masur for h capably of an m undr consdraon o rman funconal, xprssd by h probably ha h dmandd funcon s xcud whou falur undr gvn condons durng a gvn m span (Broln) 3
4 Hardwar- vs. Sofwar Rlably Hardwar Rlably (ypcal assumpons) Falurs ar a rsul of physcal dgradaon Whn h fauly componn s subsud, h rlably bcoms h nal valu of hs componn Th rlably of h sysm dos no xcd h nal valu of h sysm rlably hrough h subsuon of componns wh nw componns Hardwar rlably s drmnd by farly consan paramrs T 2 T 3 4
5 Hardwar- vs. Sofwar Rlably Sofwar Rlably (ypcal assumpons) Falurs ar a rsul of dsgn rrors ha ar conand n h produc from h sar and appar accdnally Afr faul corrcon h sysm rlably xcds s nal valu (undr h assumpon ha no addonal fauls ar nroducd) Fauls ha ar nroducd durng dbuggng dcras rlably Rlably paramrs ar assumd o vary T T 2 T 3 5
6 Tool Asssd Rlably Modlng How rlabl s my sysm now? How rlabl wll b a h plannd rlas da? How many falurs wll hav occurrd by hn?... 6
7 Tool Asssd Rlably Modlng Us of modls Whch modls do xs? How can I fnd ou, whch modl fs my purposs bs? How can I dfn h modl paramrs n ordr o g dpndabl rlably prdcons? 7
8 Dscrpon of falur ovr m Falur ms Tm nrvals bwn falurs Toal numbr of falurs a a pon n m Falurs whn a gvn m nrval Falur Tms Ausfallzpunk T T2 T3 T- T T' T2' T3' T' ' Znrvall zwschn Ausfälln Inrvals Bwn Falurs Numbr of Falurs Anzahl Ausfäll 8
9 Modlng of Rlably Lfm T Larg numbr of smlar sysms undr consdraon Smulanous sar of h sysms a m = Obsrvd m of h frs falur of ach sysm s h so-calld lfm T of hs sysm Plo of h fracon of fald sysms ovr s h so-calld mprcal dsrbuon funcon of h lfm (or mprcal lf dsrbuon) 9
10 Modlng of Rlably If h numbr of sysms bcoms largr (approxmas nfny), h mprcal lf dsrbuon approxmas h lf dsrbuon F() Hr, lfm T s a random varabl and F() s h probably ha an arbrary sysm s no opraonal a F() = P{T } F() s h probably ha lfm T s lss or qual o, manng ha a sysm has alrady fald by. W us h followng assumpons: F( = ) =,.. a nw sysm s nac, and lm F() =,.. vry sysm fals somms Falur Tms of Sysms T (h) n / N,,2,3,4,5,6,7,8,9, F(),94,74,264,37,457,585,668,765,879,94
11 Modlng of Rlably Lf dsrbuon F(),,8 n/n F(),632,6,4,2, = 2834 h
12 Modlng of Rlably Rlably funcon R() F() gvs h probably ha a m a las on falur has occurrd; hus R() = - F() s h probably ha a m no falur has occurrd y Probably dnsy f() Th probably dnsy f() dscrbs h modfcaon of h probably ha a sysm fals ovr m () = d F() d 2
13 Modlng of Rlably MTBF, MTTF A rlvan masur for rlably s h Man Tm To Falur (MTTF) or Man Tm Bwn Falur (MTBF) Th MTTF rsp. MTBF dfns h man valu of h lfm rsp. h man valu for h m nrval bwn wo succssv falurs I s drmnd by calculang h followng ngral: T = E(T) = Falur ra f() d Th falur ra s h rlav boundary valu of fald ns a m n a m nrval ha approxmas zro, rfrrng o h ns sll funconal a h bgnnng of h m nrval () df() / d () = = = R() R() - dr() / d R() 3
14 Modlng of Rlably Th condonal probably ha a sysm ha oprad falur fr unl also survvs h prod s R( + ) R() Thus, h probably ha h produc fals whn s R( + ) - F( + ) F () ( - F( + )) - = - = = R() - F() - F() F( + ) F() - F() 4
15 Modlng of Rlably As h gvn probably for shor m nrvals s proporonal o, w dvd h rm by and drmn h boundary valu whn approxmas lm F( + ) F() - F() = R() lm F( + ) F() = f() R() = () Thus h probably ha a sysm, ha s opraonal a m fals whn h (shor) m nrval, s approxmaly () 5
16 Modlng of Rlably R() and falur ra,,8 R(),6,4,2, = 2834 h h () -5 /h 4, 3,53 3, 2,,, h 6
17 Exampl for h Dsrbuon Funcon Assumpon: For h gvn daa (abl p. ) lfm s xponnally dsrbud: F() = - Th paramr (falur ra) has o b drmnd basd on falur obsrvaons n ordr o achv an opmal adusmn of h funcon, accordng o a prdrmnd crron. Th Maxmum-Lklhood-Mhod provds h followng paramr for h xponnal dsrbuon: = N N T = =,353 / h Rlably: R() = F() = - 7
18 Exampl for h Dsrbuon Funcon Th falur ra s consan ovr m () df() / d - dr() / d () = = = = - = R() R() R() A consan falur ra causs an xponnal dsrbuon of h lfm Drmnaon of h MTTF T = E(T) = () d = - d = - d = (- ) = If lfm s xponnally dsrbud, h MTTF s h rcprocal of h falur ra and hus consan - 8
19 Th Exponnal Dsrbuon Lf dsrbuon: F() = - - Dnsy funcon: () = - Rlably funcon: R() = - F() = - Falur ra: () = MTTF: T = 9
20 Th Wbull Dsrbuon Lf Dsrbuon : F() = -() ;, > or: - F() = ;, >, d. h. = Dnsy: df() () = d = ( ) - -() Rlably: R() = (-) Falur ra: () () = = ( ) R() - 2
21 Th Wbull Dsrbuon Falur ra of h Wbull dsrbuon dpndng on h form paramr 5 () =5 =3 4 =2 3 = 2 =,5 = =,5,5,,5 2, 2
22 Th Posson Dsrbuon Assumpons Th probably of mor han on falur whn h (shor) m nrval can b gnord. Thus, falurs occur rlavly nfrqunly Th probably of a falur whn, rspcvly whn [, + ], s (s dfnon of falur ra). Th probably s proporonal o h lngh of h m nrval P x () s h probably, ha whn m nrval [, ] x falurs occur 22
23 Th Posson Dsrbuon No falurs Th probably ha whn m nrval [, +] no falurs occur s drmnd by mulplyng h probably ha unl m no falurs hav occurrd (P ()) and h probably ha whn [, +] no falurs occur (- ): For owards on rcvs: P P P P P lm P P d P d P P () =, snc nw sysms (=) ar always opraonal by dfnon. For a consan valu of and P () = h dffrnal quaon has h soluon: P 23
24 Th Posson Dsrbuon Th probably ha a nw sysm shows no falurs unl s R() P R Usng h dfnons for F() and f(), w g: df F R and f d 24
25 Th Posson Dsrbuon Falurs Th probably ha whn m nrval [, +] x falurs occur can b drmnd as follows: Px P P x falurs bwn and... x 2 Px 2 P falurs bwn and P P falur bwn and Px P no falur bwn and 25
26 Th Posson Dsrbuon Du o h prcondon h probably o obsrv mor han on falur n s zro. Thrfor w g: x Px Px P falur bwn and P P x x x x P P no falur bwn and P P Px Px Px P x Px 26
27 Th Posson Dsrbuon Wh approxmang zro: lm P x P dp x x d P x P x Th followng rm for P x () s a soluon for hs dffrnal quaon P x x! (Posson Dsrbuon) x 27
28 28 Th Posson Dsrbuon Ths can b shown vry asly Th probably P X () provds h corrc valu P () also for h cas ha w rad sparaly bfor P P x x x x d x d d dp x x x x x x x X!!!! P d dp x X!
29 Th Posson Dsrbuon P X () fulflls h boundary condons for =,.. P () = and P X () =, for x. Furhrmor h sum of h probabls of all x for vry mus b,.. P x x x! x x x x! x x! x x! Th spcfd sum on h lf hand sd of h quaon s h powr srs of h xponnal funcon on h rgh hand sd. Th Posson Dsrbuon hus fulflls h prcondons. If s consan, h man valu s ()=. Ths s calld a homognous Posson Procss. If s a funcon of m, h man valu s d and P x x! Ths s calld a non-homognous Posson Procss (NHPP) x 29
30 Falur Tms and Tms bwn Falurs Th m of falur s T Th m nrval bwn falur ( - ) and falur s T T = T, T = = M() s h numbr of falurs a M T 3
31 Falur Tms and Tms bwn Falurs Th probably for falurs unl m s P P M Th probably for a las falurs a s P M!! P T 3
32 Musa's Excuon Tm Modl A sofwar sysm fals du o rrors n h sofwar randomly a, 2,... ( hr rfrs o xcuon m,.. CPU-sconds) I s assumd ha h numbr of falurs obsrvd n s lnarly proporonal o h numbr of fauls conand n h sofwar a hs m () s h oal numbr of falurs for ms () s a lmd funcon of Th numbr of falurs s a monoonc ncrasng funcon of A = no falurs hav bn obsrvd y: ()= Afr vry long xcuon m ( ) h valu () s qual o a. a s h oal numbr of falurs n nfn m. (Thr ar also modls whr nfn numbrs of falurs ar assumd o happn) 32
33 Musa's Excuon Tm Modl Modl dvlopmn Th numbr of falurs obsrvd n a m nrval s proporonal o and o h numbr of rrors no y dcd ba Wh w g: d d ba b ' Wh ()= and ()=a w g: ba b b a Th falur ra s: b ' ab 33
34 Musa's Elmnary Excuon Modl Th curv for h accumulad numbr of falurs () approxmas asympocally h xpcd oal numbr of falurs a 34
35 Musa's Elmnary Excuon Modl Th curv for h falur ra () for = sars a h nal falur ra = ab and approxmas asympocally h valu. Th nal falur ra s proporonal o h xpcd numbr of falurs a, wh h consan of proporonaly b b a a b a ab a b a b a b a a and ab ab 35
36 Musa's Excuon Tm Modl a ab a a ba ab 36
37 37 Musa's Excuon Tm Modl If s h prsn falur ra and a arg z s dfnd, addonal falurs wll occur unl hs arg s rachd Th addonal m unl hs arg s rachd s z z z a a a z z z z a a a ln ln ln ln ln
38 38 If s nsrd no h gnral quaon of h Posson dsrbuon, w g: Musa's Excuon Tm Modl a a a a a a a a a a P T!!!
39 Exampls of Modlng For a program wh an xpcd oal numbr of 3 falurs wh an nal falur ra of,/cpu-scond, modls ar o b gnrad Wha s h probably ha a a parcular xcuon m a las a cran numbr of falurs wll hav occurrd? Formula for P[T ] for, 2 and 3 falurs,9,8 Probably Wahrschnlchk,7 T,6,5 T2,4,3 T3,2, Tm Zpunk (xcuon (Ausführungsz: m: CPU-Sc.) CPU-Sk.) 39
40 Exampls of Modlng Wha wll b h numbr of falurs w.r.. xcuon m? Formula for () 25 2 Falurs Ausfäll Excuon Ausführungsz m (CPU-Sc.) (CPU-Sk.) 4
41 Exampls of Modlng How wll h falur ra dvlop dpndng on h xcuon m? Formula for (),,9,8,7 Ausfallra Falur ra ( (/CPU-Sc.) / CPU-Sk.),6,5,4,3,2, Ausführungsz Excuon m (CPU-Sc.) (CPU-Sk.) 4
42 Drmnaon of Modl Paramrs Las squars Targ: Dfn paramrs n such a way ha h sum of h squars of h dvaons bwn h calculad and h obsrvd valus bcoms mnmal. If F rfrs o h valu of h mprcal dsrbuon funcon a pon, h followng rm s o b mnmzd: n 2 Maxmum-Lklhood-Mhod n 2 F F Targ: Choos paramrs n such a way ha h probably s maxmzd o produc a "smlar" obsrvaon o h prsn obsrvaon. Th probably dnsy has o b known 42
43 Drmnaon of Modl Paramrs Las squars Targ: Dfn paramrs n such a way ha h sum of h squars of h dvaons bwn h calculad and h obsrvd valus bcoms mnmal. If F rfrs o h valu of h mprcal dsrbuon funcon a pon, h followng rm s o b mnmzd: n n 2 F F For h xponnal dsrbuon w g: n n 2 xp xp 2 n 2 F F F 2 43
44 44 Drmnaon of Modl Paramrs Las squars Th valu ha mnmzs hs rm s o b drmnd Th valu s calculad by drmnng h zro pon n n F d d d d 2 xp 2 xp 2! ˆ ˆ F ˆ
45 Drmnaon of Modl Paramrs Las squars Somms numrcal mhod mus b usd for hs ask. A Nwonan raon provds h followng rsuls for h Exponnal Dsrbuon wh: and: n f n f df n n d n xp n xp 2 2 d f 2 F F 2 For h falur ms of h abl on pag h sarch for zro pons accordng o h Nwonan raon provds a valu ˆ 3, * -5 /h for h xponnal dsrbuon 2 45
46 Drmnaon of Modl Paramrs Maxmum-Lklhood-Mhod Targ: Choos paramrs n such a way ha h probably s maxmzd o produc a "smlar" obsrvaon o h prsn obsrvaon Prcondon: Probably dnsy has o b known Lklhood funcon F Produc of h dnss a h obsrvd falur ms Th valu s proporonal o h probably o obsrv falur ms ha do no xcd h dvaon w.r.. h prsn obsrvaon I s a funcon of h dsrbuon funcon's paramrs ha ar o b drmnd Exampl: Th paramr of h xponnal dsrbuon s o b drmnd wh h Maxmum-Lklhood-Mhod, f 46
47 47 Drmnaon of Modl Paramrs Maxmum-Lklhood-Mhod Wh n obsrvd falur ms,..., n w g h Lklhood Funcon: Du o h monooncy of h logarhmc funcon, L und ln L hav dncal maxma In ordr o calcula h valu ha maxmzs h Lklhood Funcon, h drvaon accordng o mus b drmnd n n n n n n n f f f L ,...,,,...,, n n n L ln,...,, ln n n n d L d,,..., ln ˆ
48 Drmnaon of Modl Paramrs Maxmum-Lklhood-Mhod ˆ s h zro pon. For h xponnal dsrbuon w g: n n! ˆ n n 48
49 Modl Slcon basd on Falur Obsrvaons U-Plo-Mhod Prqunal-Lklhood-Mhod Holdou-Evaluaon 49
50 Modl Slcon basd on Falur Obsrvaons U-Plo U-Plo Graphc mhod ha ss whhr a dsrbuon funcon can b accpd wh rgard o h prsn obsrvaon Addonally, sascal ss (.g. Kolmogoroff-Smrnov) mgh b usd If a random varabl T s dscrbd by h dsrbuon F(), h F( ) of h random varabl ar qually dsrbud ovr h nrval [,] 5
51 Modl Slcon basd on Falur Obsrvaons U-Plo Th n valus U ar chard n a U-Plo as follows Th valus U ar usd as y-valus n such a way ha h valu U wh h poson s arbud o h x-valu / n If h valus U ar approxmaly qually dsrbud, h appld pons ar locad "nar by" h funcon y = x, for x 5
52 Modl Slcon basd on Falur Obsrvaons U-Plo Exampl T (h) n / N,,2,3,4,5,6,7,8,9, F(),94,74,264,37,457,585,668,765,879,94 Th valus prsnd n h abl for F() ar h U accordng o h dfnon sad abov 52
53 Modl Slcon basd on Falur Obsrvaons U-Plo U-Plo of h daa U,,9,8,7,6,5,4,3,2,,,,,2,3,4,5,6,7,8,9, 53
54 Modl Slcon basd on Falur Obsrvaons Prqunal-Lklhood-Mhod Th Prqunal-Lklhood-Mhod compars h suably of wo dsrbuon funcons undr consdraon wh rgard o a gvn falur obsrvaon I s basd on h followng approach Th falur nrval s a ralzaon of a random varabl wh h dsrbuon F () and h dnsy f () F () and f () ar unknown Th dnss of h dsrbuon funcons A and B ( rsp. ) can b drmnd basd on h falur nrvals,..., - A If h dsrbuon A s mor suabl han h dsrbuon B, can b xpcd ha h valu fˆ s grar han h valu B fˆ fˆ A fˆ Th quon wll b grar han B ˆ f A ˆ f B 54
55 Modl Slcon basd on Falur Obsrvaons Prqunal-Lklhood-Mhod f() ^ f B () f () ^f A () ^f A ( ) ^ f B ( ) 55
56 Modl Slcon basd on Falur Obsrvaons Prqunal-Lklhood-Mhod If hs analyss s don for vry obsrvd falur m nrval w g h socalld Prqunal-Lklhood-Rao concrnng h dsrbuons A and B PLR AB If A s mor appropra han B wh rgard o h prsn falur daa, h PLR shows a rsng ndncy Exampl s fˆ fˆ A B W compar h xponnal dsrbuon and h normal dsrbuon basd on h daa from h abl on pag usng h Prqunal-Lklhood-Mhod 56
57 57 Modl Slcon basd on Falur Obsrvaons Prqunal-Lklhood-Mhod Th paramrs of h dsrbuons ar drmnd usng a Maxmum-Lklhood-Approach. For h xponnal dsrbuon, w g: For h normal dsrbuon w g: Th paramrs accordng o h Maxmum-Lklhood-Mhod ar: ˆ k k / 2 2 2,, f 2 2 ˆ ; ˆ k k k k
58 Modl Slcon basd on Falur Obsrvaons Prqunal-Lklhood-Mhod Th followng abl shows h dnss of h xponnal dsrbuon and h normal dsrbuon for h arrval m nrvals basd on h falur ms T o T - from h abl on pag Th calculaon sars wh = 4. In addon h logarhm of h quon of h dnss and h logarhm of h PLR s conand n h abl Th rsng of h PLR undrlns ha h assumpon of xponnally dsrbud arrval ms for h prsn daa maks mor sns han h assumpon of normally dsrbud arrval ms 58
59 Modl Slcon basd on Falur Obsrvaons Prqunal-Lklhood-Mhod T (h) (h) f Exp / -6 74,9 84,8 32,5 52,4 3,3 3,8 7,3 f Norm / -9, , , log (f Exp / f Norm) log (PLR ) 4,83 -,46 5,63 -,29,49 8,67,49 4,83 4,37, 9,7,2 8,87 9,36 59
60 Modl Slcon basd on Falur Obsrvaons Prqunal-Lklhood-Mhod PLR of h daa 2 log(plr )
61 Modl Slcon basd on Falur Obsrvaons Holdou Evaluaon Approach Only pars of h falur daa ar usd for modl calbraon. Th rmanng daa ar usd o udg h prdcon qualy of h calbrad modl If an xponnal dsrbuon and a Wbull dsrbuon ar calbrad o h frs 6 falur ms (abl p. ) usng a Las-Squars-Algorhm, w g h followng rsuls: Exponnal dsrbuon: Wbull dsrbuon: F F xp xp 3,89292*,5525* 5 / h, / h 6
62 Modl Slcon basd on Falur Obsrvaons Holdou Evaluaon Th Wbull dsrbuon has as xpcd - a br adusmn o h falur ms T o T 6. Th sum of h dvaon squars for h frs 6 falur ms s,459 compard o,79 n h xponnal dsrbuon Th prdcon qualy of h Wbull dsrbuon s howvr wors han ha of h xponnal dsrbuon. Th sum of h dvaon squars for h falur ms T 7 o T s,446 for h Wbull dsrbuon; for h xponnal dsrbuon s only,2. W mgh prfr o us h xponnal dsrbuon n ordr o avod ovr-calbraon 62
63 Sochasc Rlably Analyss Summary Sofwar Rlably can b adqualy masurd and prdcd usng appropra modls Th us of sochasc rlably modls rqurs som knowldg w.r.. h undrlyng mahmacs Appropra ools ar a prcondon for h succssful us of rlably modls 63
Safety and Reliability of Embedded Systems. (Sicherheit und Zuverlässigkeit eingebetteter Systeme) Stochastic Reliability Analysis
Safy and Rlably of Embddd Sysms (Schrh und Zuvrlässgk ngbr Sysm) Sochasc Rlably Analyss Safy and Rlably of Embddd Sysms Conn Dfnon of Rlably Hardwar- vs. Sofwar Rlably Tool Asssd Rlably Modlng Dscrpons
More informationConsider a system of 2 simultaneous first order linear equations
Soluon of sysms of frs ordr lnar quaons onsdr a sysm of smulanous frs ordr lnar quaons a b c d I has h alrna mar-vcor rprsnaon a b c d Or, n shorhand A, f A s alrady known from con W know ha h abov sysm
More informationFAULT TOLERANT SYSTEMS
FAULT TOLERANT SYSTEMS hp://www.cs.umass.du/c/orn/faultolransysms ar 4 Analyss Mhods Chapr HW Faul Tolranc ar.4.1 Duplx Sysms Boh procssors xcu h sam as If oupus ar n agrmn - rsul s assumd o b corrc If
More informationt=0 t>0: + vr - i dvc Continuation
hapr Ga Dlay and rcus onnuaon s rcu Equaon >: S S Ths dffrnal quaon, oghr wh h nal condon, fully spcfs bhaor of crcu afr swch closs Our n challng: larn how o sol such quaons TUE/EE 57 nwrk analys 4/5 NdM
More informationAdvanced Queueing Theory. M/G/1 Queueing Systems
Advand Quung Thory Ths slds ar rad by Dr. Yh Huang of Gorg Mason Unvrsy. Sudns rgsrd n Dr. Huang's ourss a GMU an ma a sngl mahn-radabl opy and prn a sngl opy of ah sld for hr own rfrn, so long as ah sld
More informationSummary: Solving a Homogeneous System of Two Linear First Order Equations in Two Unknowns
Summary: Solvng a Homognous Sysm of Two Lnar Frs Ordr Equaons n Two Unknowns Gvn: A Frs fnd h wo gnvalus, r, and hr rspcv corrspondng gnvcors, k, of h coffcn mar A Dpndng on h gnvalus and gnvcors, h gnral
More informationChap 2: Reliability and Availability Models
Chap : lably ad valably Modls lably = prob{s s fully fucog [,]} Suppos from [,] m prod, w masur ou of N compos, of whch N : # of compos oprag corrcly a m N f : # of compos whch hav fald a m rlably of h
More informationThe Variance-Covariance Matrix
Th Varanc-Covaranc Marx Our bggs a so-ar has bn ng a lnar uncon o a s o daa by mnmzng h las squars drncs rom h o h daa wh mnsarch. Whn analyzng non-lnar daa you hav o us a program l Malab as many yps o
More informationApplying Software Reliability Techniques to Low Retail Demand Estimation
Applyng Sofwar Rlably Tchnqus o Low Ral Dmand Esmaon Ma Lndsy Unvrsy of Norh Txas ITDS Dp P.O. Box 30549 Dnon, TX 7603-549 940 565 3174 lndsym@un.du Robr Pavur Unvrsy of Norh Txas ITDS Dp P.O. Box 30549
More informationinnovations shocks white noise
Innovaons Tm-srs modls ar consrucd as lnar funcons of fundamnal forcasng rrors, also calld nnovaons or shocks Ths basc buldng blocks sasf var σ Srall uncorrlad Ths rrors ar calld wh nos In gnral, f ou
More informationState Observer Design
Sa Obsrvr Dsgn A. Khak Sdgh Conrol Sysms Group Faculy of Elcrcal and Compur Engnrng K. N. Toos Unvrsy of Tchnology Fbruary 2009 1 Problm Formulaon A ky assumpon n gnvalu assgnmn and sablzng sysms usng
More informationBoosting and Ensemble Methods
Boosng and Ensmbl Mhods PAC Larnng modl Som dsrbuon D ovr doman X Eampls: c* s h arg funcon Goal: Wh hgh probably -d fnd h n H such ha rrorh,c* < d and ar arbrarly small. Inro o ML 2 Wak Larnng
More informationSupplementary Figure 1. Experiment and simulation with finite qudit. anharmonicity. (a), Experimental data taken after a 60 ns three-tone pulse.
Supplmnar Fgur. Eprmn and smulaon wh fn qud anharmonc. a, Eprmnal daa akn afr a 6 ns hr-on puls. b, Smulaon usng h amlonan. Supplmnar Fgur. Phagoran dnamcs n h m doman. a, Eprmnal daa. Th hr-on puls s
More informationWave Superposition Principle
Physcs 36: Was Lcur 5 /7/8 Wa Suroson Prncl I s qu a common suaon for wo or mor was o arr a h sam on n sac or o xs oghr along h sam drcon. W wll consdr oday sral moran cass of h combnd ffcs of wo or mor
More informationFrequency Response. Response of an LTI System to Eigenfunction
Frquncy Rsons Las m w Rvsd formal dfnons of lnary and m-nvaranc Found an gnfuncon for lnar m-nvaran sysms Found h frquncy rsons of a lnar sysm o gnfuncon nu Found h frquncy rsons for cascad, fdbac, dffrnc
More informationProblem 1: Consider the following stationary data generation process for a random variable y t. e t ~ N(0,1) i.i.d.
A/CN C m Sr Anal Profor Òcar Jordà Wnr conomc.c. Dav POBLM S SOLIONS Par I Analcal Quon Problm : Condr h followng aonar daa gnraon proc for a random varabl - N..d. wh < and N -. a Oban h populaon man varanc
More informationReliability analysis of time - dependent stress - strength system when the number of cycles follows binomial distribution
raoal Joural of Sascs ad Ssms SSN 97-675 Volum, Numbr 7,. 575-58 sarch da Publcaos h://www.rublcao.com labl aalss of m - dd srss - srgh ssm wh h umbr of ccls follows bomal dsrbuo T.Sumah Umamahswar, N.Swah,
More informationCIVL 8/ D Boundary Value Problems - Triangular Elements (T6) 1/8
CIVL 8/7 -D Boundar Valu Problm - rangular Elmn () /8 SI-ODE RIAGULAR ELEMES () A quadracall nrpolad rangular lmn dfnd b nod, hr a h vrc and hr a h mddl a ach d. h mddl nod, dpndng on locaon, ma dfn a
More informationTheoretical Seismology
Thorcal Ssmology Lcur 9 Sgnal Procssng Fourr analyss Fourr sudd a h Écol Normal n Pars, augh by Lagrang, who Fourr dscrbd as h frs among Europan mn of scnc, Laplac, who Fourr rad lss hghly, and by Mong.
More information9. Simple Rules for Monetary Policy
9. Smpl Ruls for Monar Polc John B. Talor, Ma 0, 03 Woodford, AR 00 ovrvw papr Purpos s o consdr o wha xn hs prscrpon rsmbls h sor of polc ha conomc hor would rcommnd Bu frs, l s rvw how hs sor of polc
More informationMicroscopic Flow Characteristics Time Headway - Distribution
CE57: Traffic Flow Thory Spring 20 Wk 2 Modling Hadway Disribuion Microscopic Flow Characrisics Tim Hadway - Disribuion Tim Hadway Dfiniion Tim Hadway vrsus Gap Ahmd Abdl-Rahim Civil Enginring Dparmn,
More informationAR(1) Process. The first-order autoregressive process, AR(1) is. where e t is WN(0, σ 2 )
AR() Procss Th firs-ordr auorgrssiv procss, AR() is whr is WN(0, σ ) Condiional Man and Varianc of AR() Condiional man: Condiional varianc: ) ( ) ( Ω Ω E E ) var( ) ) ( var( ) var( σ Ω Ω Ω Ω E Auocovarianc
More informationCharging of capacitor through inductor and resistor
cur 4&: R circui harging of capacior hrough inducor and rsisor us considr a capacior of capacianc is conncd o a D sourc of.m.f. E hrough a rsisr of rsisanc R, an inducor of inducanc and a y K in sris.
More informationBethe-Salpeter Equation Green s Function and the Bethe-Salpeter Equation for Effective Interaction in the Ladder Approximation
Bh-Salp Equaon n s Funcon and h Bh-Salp Equaon fo Effcv Inacon n h Ladd Appoxmaon Csa A. Z. Vasconcllos Insuo d Físca-UFRS - upo: Físca d Hadons Sngl-Pacl Popagao. Dagam xpanson of popagao. W consd as
More information8. Queueing systems. Contents. Simple teletraffic model. Pure queueing system
8. Quug sysms Cos 8. Quug sysms Rfrshr: Sml lraffc modl Quug dscl M/M/ srvr wag lacs Alcao o ack lvl modllg of daa raffc M/M/ srvrs wag lacs lc8. S-38.45 Iroduco o Tlraffc Thory Srg 5 8. Quug sysms 8.
More informationHomework: Introduction to Motion
Homwork: Inroducon o Moon Dsanc vs. Tm Graphs Nam Prod Drcons: Answr h foowng qusons n h spacs provdd. 1. Wha do you do o cra a horzona n on a dsancm graph? 2. How do you wak o cra a sragh n ha sops up?
More informationSIMEON BALL AND AART BLOKHUIS
A BOUND FOR THE MAXIMUM WEIGHT OF A LINEAR CODE SIMEON BALL AND AART BLOKHUIS Absrac. I s shown ha h paramrs of a lnar cod ovr F q of lngh n, dmnson k, mnmum wgh d and maxmum wgh m sasfy a cran congrunc
More informationEngineering Circuit Analysis 8th Edition Chapter Nine Exercise Solutions
Engnrng rcu naly 8h Eon hapr Nn Exrc Soluon. = KΩ, = µf, an uch ha h crcu rpon oramp. a For Sourc-fr paralll crcu: For oramp or b H 9V, V / hoo = H.7.8 ra / 5..7..9 9V 9..9..9 5.75,.5 5.75.5..9 . = nh,
More informationLecture 4 : Backpropagation Algorithm. Prof. Seul Jung ( Intelligent Systems and Emotional Engineering Laboratory) Chungnam National University
Lcur 4 : Bacpropagaon Algorhm Pro. Sul Jung Inllgn Sm and moonal ngnrng Laboraor Chungnam Naonal Unvr Inroducon o Bacpropagaon algorhm 969 Mn and Papr aac. 980 Parr and Wrbo dcovrd bac propagaon algorhm.
More informationLecture 1: Numerical Integration The Trapezoidal and Simpson s Rule
Lcur : Numrical ngraion Th Trapzoidal and Simpson s Rul A problm Th probabiliy of a normally disribud (man µ and sandard dviaion σ ) vn occurring bwn h valus a and b is B A P( a x b) d () π whr a µ b -
More informationTransient Analysis of Two-dimensional State M/G/1 Queueing Model with Multiple Vacations and Bernoulli Schedule
Inrnaonal Journal of Compur Applcaons (975 8887) Volum 4 No.3, Fbruary 22 Transn Analyss of Two-dmnsonal Sa M/G/ Quung Modl wh Mulpl Vacaons and Brnoull Schdul Indra Assoca rofssor Dparmn of Sascs and
More informationUNIT #5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
Answr Ky Nam: Da: UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS Par I Qusions. Th prssion is quivaln o () () 6 6 6. Th ponnial funcion y 6 could rwrin as y () y y 6 () y y (). Th prssion a is quivaln o
More informationConventional Hot-Wire Anemometer
Convnonal Ho-Wr Anmomr cro Ho Wr Avanag much mallr prob z mm o µm br paal roluon array o h nor hghr rquncy rpon lowr co prormanc/co abrcaon roc I µm lghly op p layr 8µm havly boron op ch op layr abrcaon
More information4.1 The Uniform Distribution Def n: A c.r.v. X has a continuous uniform distribution on [a, b] when its pdf is = 1 a x b
4. Th Uniform Disribuion Df n: A c.r.v. has a coninuous uniform disribuion on [a, b] whn is pdf is f x a x b b a Also, b + a b a µ E and V Ex4. Suppos, h lvl of unblivabiliy a any poin in a Transformrs
More informationCHAPTER: 3 INVERSE EXPONENTIAL DISTRIBUTION: DIFFERENT METHOD OF ESTIMATIONS
CHAPTER: 3 INVERSE EXPONENTIAL DISTRIBUTION: DIFFERENT METHOD OF ESTIMATIONS 3. INTRODUCTION Th Ivrs Expoal dsrbuo was roducd by Kllr ad Kamah (98) ad has b sudd ad dscussd as a lfm modl. If a radom varabl
More informationThe Hyperelastic material is examined in this section.
4. Hyprlastcty h Hyprlastc matral s xad n ths scton. 4..1 Consttutv Equatons h rat of chang of ntrnal nrgy W pr unt rfrnc volum s gvn by th strss powr, whch can b xprssd n a numbr of dffrnt ways (s 3.7.6):
More informationInstitute of Actuaries of India
Insiu of Acuaris of India ubjc CT3 Probabiliy and Mahmaical aisics Novmbr Examinaions INDICATIVE OLUTION Pag of IAI CT3 Novmbr ol. a sampl man = 35 sampl sandard dviaion = 36.6 b for = uppr bound = 35+*36.6
More information2.1. Differential Equations and Solutions #3, 4, 17, 20, 24, 35
MATH 5 PS # Summr 00.. Diffrnial Equaions and Soluions PS.# Show ha ()C #, 4, 7, 0, 4, 5 ( / ) is a gnral soluion of h diffrnial quaion. Us a compur or calculaor o skch h soluions for h givn valus of h
More informationGrand Canonical Ensemble
Th nsmbl of systms mmrsd n a partcl-hat rsrvor at constant tmpratur T, prssur P, and chmcal potntal. Consdr an nsmbl of M dntcal systms (M =,, 3,...M).. Thy ar mutually sharng th total numbr of partcls
More informationELEN E4830 Digital Image Processing
ELEN E48 Dgal Imag Procssng Mrm Eamnaon Sprng Soluon Problm Quanzaon and Human Encodng r k u P u P u r r 6 6 6 6 5 6 4 8 8 4 P r 6 6 P r 4 8 8 6 8 4 r 8 4 8 4 7 8 r 6 6 6 6 P r 8 4 8 P r 6 6 8 5 P r /
More informationChapter 9 Transient Response
har 9 Transn sons har 9: Ouln N F n F Frs-Ordr Transns Frs-Ordr rcus Frs ordr crcus: rcus conan onl on nducor or on caacor gornd b frs-ordr dffrnal quaons. Zro-nu rsons: h crcu has no ald sourc afr a cran
More informationOn the Derivatives of Bessel and Modified Bessel Functions with Respect to the Order and the Argument
Inrnaional Rsarch Journal of Applid Basic Scincs 03 Aailabl onlin a wwwirjabscom ISSN 5-838X / Vol 4 (): 47-433 Scinc Eplorr Publicaions On h Driais of Bssl Modifid Bssl Funcions wih Rspc o h Ordr h Argumn
More informationGaussian Random Process and Its Application for Detecting the Ionospheric Disturbances Using GPS
Journal of Global Posonng Sysms (005) Vol. 4, No. 1-: 76-81 Gaussan Random Procss and Is Applcaon for Dcng h Ionosphrc Dsurbancs Usng GPS H.. Zhang 1,, J. Wang 3, W. Y. Zhu 1, C. Huang 1 (1) Shangha Asronomcal
More informationJOSE L. HURTADO, FRANCISCO JOGLAR 1, MOHAMMAD MODARRES 2
Inrnaonal Journal of Prformably Engnrng, Vol., No., July 25, pp. 37-5 RAMS Consulans Prnd n Inda. Inroducon JOSE L. HURTADO, FRANCISCO JOGLAR, MOHAMMAD MODARRES 2 Dparmn of Mchancal Engnrng, Rlably Engnrng
More informationA MATHEMATICAL MODEL FOR NATURAL COOLING OF A CUP OF TEA
MTHEMTICL MODEL FOR NTURL COOLING OF CUP OF TE 1 Mrs.D.Kalpana, 2 Mr.S.Dhvarajan 1 Snior Lcurr, Dparmn of Chmisry, PSB Polychnic Collg, Chnnai, India. 2 ssisan Profssor, Dparmn of Mahmaics, Dr.M.G.R Educaional
More informationThe transition:transversion rate ratio vs. the T-ratio.
PhyloMah Lcur 8 by Dan Vandrpool March, 00 opics of Discussion ransiion:ransvrsion ra raio Kappa vs. ransiion:ransvrsion raio raio alculaing h xpcd numbr of subsiuions using marix algbra Why h nral im
More informationReview - Probabilistic Classification
Mmoral Unvrsty of wfoundland Pattrn Rcognton Lctur 8 May 5, 6 http://www.ngr.mun.ca/~charlsr Offc Hours: Tusdays Thursdays 8:3-9:3 PM E- (untl furthr notc) Gvn lablld sampls { ɛc,,,..., } {. Estmat Rvw
More informationCONTINUOUS TIME DYNAMIC PROGRAMMING
Eon. 511b Sprng 1993 C. Sms I. Th Opmaon Problm CONTINUOUS TIME DYNAMIC PROGRAMMING W onsdr h problm of maxmng subj o and EU(C, ) d (1) j ^ d = (C, ) d + σ (C, ) dw () h(c, ), (3) whr () and (3) hold for
More informationFI 3103 Quantum Physics
/9/4 FI 33 Quanum Physcs Aleander A. Iskandar Physcs of Magnesm and Phooncs Research Grou Insu Teknolog Bandung Basc Conces n Quanum Physcs Probably and Eecaon Value Hesenberg Uncerany Prncle Wave Funcon
More information(heat loss divided by total enthalpy flux) is of the order of 8-16 times
16.51, Rok Prolson Prof. Manl Marnz-Sanhz r 8: Convv Ha ransfr: Ohr Effs Ovrall Ha oss and Prforman Effs of Ha oss (1) Ovrall Ha oss h loal ha loss r n ara s q = ρ ( ) ngrad ha loss s a S, and sng m =
More informationPartition Functions for independent and distinguishable particles
0.0J /.77J / 5.60J hrodynacs of oolcular Syss Insrucors: Lnda G. Grffh, Kbrly Haad-Schffrl, Moung G. awnd, Robr W. Fld Lcur 5 5.60/0.0/.77 vs. q for dsngushabl vs ndsngushabl syss Drvaon of hrodynac Proprs
More informationFinal Exam : Solutions
Comp : Algorihm and Daa Srucur Final Exam : Soluion. Rcuriv Algorihm. (a) To bgin ind h mdian o {x, x,... x n }. Sinc vry numbr xcp on in h inrval [0, n] appar xacly onc in h li, w hav ha h mdian mu b
More informationOne dimensional steady state heat transfer of composite slabs
BUILDING PHYSICS On dmnsonal sady sa a ransfr of compos slas Par 2 Ass. Prof. Dr. Norr Harmay Budaps Unvrsy of Tcnology and Economcs Dparmn of Buldng Enrgcs and Buldng Srvc Engnrng Inroducon - Buldng Pyscs
More informationDepartment of Economics University of Toronto
Deparmen of Economcs Unversy of Torono ECO408F M.A. Economercs Lecure Noes on Heeroskedascy Heeroskedascy o Ths lecure nvolves lookng a modfcaons we need o make o deal wh he regresson model when some of
More informationGuaranteed Cost Control for a Class of Uncertain Delay Systems with Actuator Failures Based on Switching Method
49 Inrnaonal Journal of Conrol, Ru Wang Auomaon, and Jun and Zhao Sysms, vol. 5, no. 5, pp. 49-5, Ocobr 7 Guarand Cos Conrol for a Class of Uncran Dlay Sysms wh Acuaor Falurs Basd on Swchng Mhod Ru Wang
More information10.5 Linear Viscoelasticity and the Laplace Transform
Scn.5.5 Lnar Vclacy and h Lalac ranfrm h Lalac ranfrm vry uful n cnrucng and analyng lnar vclac mdl..5. h Lalac ranfrm h frmula fr h Lalac ranfrm f h drvav f a funcn : L f f L f f f f f c..5. whr h ranfrm
More informationReduced The Complexity of Soft Input Soft Output Maximum A posteriori Decoder of Linear Block Code By Using Parallel Trellises Structure
Journal of Babylon nvrsy/engnrng Scncs/ No.4/ Vol.25: 27 Rducd Th Complxy of Sof Inpu Sof upu Maxmum A posror Dcodr of Lnar Block Cod By sng Paralll Trllss Srucur Samr Abdul Cahm Khohr Hadr Jabbar Abd
More informationReliability of time dependent stress-strength system for various distributions
IOS Joural of Mathmatcs (IOS-JM ISSN: 78-578. Volum 3, Issu 6 (Sp-Oct., PP -7 www.osrjourals.org lablty of tm dpdt strss-strgth systm for varous dstrbutos N.Swath, T.S.Uma Mahswar,, Dpartmt of Mathmatcs,
More informationCOHORT MBA. Exponential function. MATH review (part2) by Lucian Mitroiu. The LOG and EXP functions. Properties: e e. lim.
MTH rviw part b Lucian Mitroiu Th LOG and EXP functions Th ponntial function p : R, dfind as Proprtis: lim > lim p Eponntial function Y 8 6 - -8-6 - - X Th natural logarithm function ln in US- log: function
More informationLucas Test is based on Euler s theorem which states that if n is any integer and a is coprime to n, then a φ(n) 1modn.
Modul 10 Addtonal Topcs 10.1 Lctur 1 Prambl: Dtrmnng whthr a gvn ntgr s prm or compost s known as prmalty tstng. Thr ar prmalty tsts whch mrly tll us whthr a gvn ntgr s prm or not, wthout gvng us th factors
More informationEXST Regression Techniques Page 1
EXST704 - Rgrssion Tchniqus Pag 1 Masurmnt rrors in X W hav assumd that all variation is in Y. Masurmnt rror in this variabl will not ffct th rsults, as long as thy ar uncorrlatd and unbiasd, sinc thy
More informationA Note on Estimability in Linear Models
Intrnatonal Journal of Statstcs and Applcatons 2014, 4(4): 212-216 DOI: 10.5923/j.statstcs.20140404.06 A Not on Estmablty n Lnar Modls S. O. Adymo 1,*, F. N. Nwob 2 1 Dpartmnt of Mathmatcs and Statstcs,
More informationControl Systems (Lecture note #6)
6.5 Corol Sysms (Lcur o #6 Las Tm: Lar algbra rw Lar algbrac quaos soluos Paramrzao of all soluos Smlary rasformao: compao form Egalus ad gcors dagoal form bg pcur: o brach of h cours Vcor spacs marcs
More informationApplied Statistics and Probability for Engineers, 6 th edition October 17, 2016
Applid Saisics and robabiliy for Enginrs, 6 h diion Ocobr 7, 6 CHATER Scion - -. a d. 679.. b. d. 88 c d d d. 987 d. 98 f d.. Thn, = ln. =. g d.. Thn, = ln.9 =.. -7. a., by symmry. b.. d...6. 7.. c...
More informationSpring 2006 Process Dynamics, Operations, and Control Lesson 2: Mathematics Review
Spring 6 Procss Dynamics, Opraions, and Conrol.45 Lsson : Mahmaics Rviw. conx and dircion Imagin a sysm ha varis in im; w migh plo is oupu vs. im. A plo migh imply an quaion, and h quaion is usually an
More informationChapter 13 Laplace Transform Analysis
Chapr aplac Tranorm naly Chapr : Ouln aplac ranorm aplac Tranorm -doman phaor analy: x X σ m co ω φ x X X m φ x aplac ranorm: [ o ] d o d < aplac Tranorm Thr condon Unlaral on-dd aplac ranorm: aplac ranorm
More informationCPSC 211 Data Structures & Implementations (c) Texas A&M University [ 259] B-Trees
CPSC 211 Daa Srucurs & Implmnaions (c) Txas A&M Univrsiy [ 259] B-Trs Th AVL r and rd-black r allowd som variaion in h lnghs of h diffrn roo-o-laf pahs. An alrnaiv ida is o mak sur ha all roo-o-laf pahs
More informationHigher order derivatives
Robrto s Nots on Diffrntial Calculus Chaptr 4: Basic diffrntiation ruls Sction 7 Highr ordr drivativs What you nd to know alrady: Basic diffrntiation ruls. What you can larn hr: How to rpat th procss of
More informationEXERCISE - 01 CHECK YOUR GRASP
DIFFERENTIAL EQUATION EXERCISE - CHECK YOUR GRASP 7. m hn D() m m, D () m m. hn givn D () m m D D D + m m m m m m + m m m m + ( m ) (m ) (m ) (m + ) m,, Hnc numbr of valus of mn will b. n ( ) + c sinc
More informationCHAPTER 7d. DIFFERENTIATION AND INTEGRATION
CHAPTER 7d. DIFFERENTIATION AND INTEGRATION A. J. Clark School o Engnrng Dpartmnt o Cvl and Envronmntal Engnrng by Dr. Ibrahm A. Assakka Sprng ENCE - Computaton Mthods n Cvl Engnrng II Dpartmnt o Cvl and
More informationChapter 7 Stead St y- ate Errors
Char 7 Say-Sa rror Inroucon Conrol ym analy an gn cfcaon a. rann ron b. Sably c. Say-a rror fnon of ay-a rror : u c a whr u : nu, c: ouu Val only for abl ym chck ym ably fr! nu for ay-a a nu analy U o
More informationSoft k-means Clustering. Comp 135 Machine Learning Computer Science Tufts University. Mixture Models. Mixture of Normals in 1D
Comp 35 Machn Larnng Computr Scnc Tufts Unvrsty Fall 207 Ron Khardon Th EM Algorthm Mxtur Modls Sm-Suprvsd Larnng Soft k-mans Clustrng ck k clustr cntrs : Assocat xampls wth cntrs p,j ~~ smlarty b/w cntr
More information8-node quadrilateral element. Numerical integration
Fnt Elmnt Mthod lctur nots _nod quadrlatral lmnt Pag of 0 -nod quadrlatral lmnt. Numrcal ntgraton h tchnqu usd for th formulaton of th lnar trangl can b formall tndd to construct quadrlatral lmnts as wll
More information10/7/14. Mixture Models. Comp 135 Introduction to Machine Learning and Data Mining. Maximum likelihood estimation. Mixture of Normals in 1D
Comp 35 Introducton to Machn Larnng and Data Mnng Fall 204 rofssor: Ron Khardon Mxtur Modls Motvatd by soft k-mans w dvlopd a gnratv modl for clustrng. Assum thr ar k clustrs Clustrs ar not rqurd to hav
More informationContinous system: differential equations
/6/008 Coious sysm: diffrial quaios Drmiisic modls drivaivs isad of (+)-( r( compar ( + ) R( + r ( (0) ( R ( 0 ) ( Dcid wha hav a ffc o h sysm Drmi whhr h paramrs ar posiiv or gaiv, i.. giv growh or rducio
More informationMECE 3320 Measurements & Instrumentation. Static and Dynamic Characteristics of Signals
MECE 330 MECE 330 Masurms & Isrumao Sac ad Damc Characrscs of Sgals Dr. Isaac Chouapall Dparm of Mchacal Egrg Uvrs of Txas Pa Amrca MECE 330 Sgal Cocps A sgal s h phscal formao abou a masurd varabl bg
More informationRELATIONSHIPS BETWEEN SPECTRAL PEAK FREQUENCIES OF A CAUSAL AR(P) PROCESS AND ARGUMENTS OF ROOTS OF THE ASSOCIATED AR POLYNOMIAL.
RELATIONSHIPS BETWEEN SPECTRAL PEAK FREQUENCIES OF A CAUSAL AR(P) PROCESS AND ARGUMENTS OF ROOTS OF THE ASSOCIATED AR POLYNOMIAL A Wrng Proc Prsnd o T Faculy of Darmn of Mamacs San Jos Sa Unvrsy In Paral
More informationCh. 24 Molecular Reaction Dynamics 1. Collision Theory
Ch. 4 Molcular Raction Dynamics 1. Collision Thory Lctur 16. Diffusion-Controlld Raction 3. Th Matrial Balanc Equation 4. Transition Stat Thory: Th Eyring Equation 5. Transition Stat Thory: Thrmodynamic
More informationCSE 245: Computer Aided Circuit Simulation and Verification
CSE 45: Compur Aidd Circui Simulaion and Vrificaion Fall 4, Sp 8 Lcur : Dynamic Linar Sysm Oulin Tim Domain Analysis Sa Equaions RLC Nwork Analysis by Taylor Expansion Impuls Rspons in im domain Frquncy
More informationSolution in semi infinite diffusion couples (error function analysis)
Soluon n sem nfne dffuson couples (error funcon analyss) Le us consder now he sem nfne dffuson couple of wo blocks wh concenraon of and I means ha, n a A- bnary sysem, s bondng beween wo blocks made of
More informationGauge Theories. Elementary Particle Physics Strong Interaction Fenomenology. Diego Bettoni Academic year
Gau Thors Elmary Parcl Physcs Sro Iraco Fomoloy o Bo cadmc yar - Gau Ivarac Gau Ivarac Whr do Laraas or Hamloas com from? How do w kow ha a cra raco should dscrb a acual hyscal sysm? Why s h lcromac raco
More informationEconomics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 3/28/2012. UW Madison
Economics 302 (Sc. 001) Inrmdia Macroconomic Thory and Policy (Spring 2011) 3/28/2012 Insrucor: Prof. Mnzi Chinn Insrucor: Prof. Mnzi Chinn UW Madison 16 1 Consumpion Th Vry Forsighd dconsumr A vry forsighd
More informationControl System Engineering (EE301T) Assignment: 2
Conrol Sysm Enginring (EE0T) Assignmn: PART-A (Tim Domain Analysis: Transin Rspons Analysis). Oain h rspons of a uniy fdack sysm whos opn-loop ransfr funcion is (s) s ( s 4) for a uni sp inpu and also
More informationLecture 2: Current in RC circuit D.K.Pandey
Lcur 2: urrn in circui harging of apacior hrough Rsisr L us considr a capacior of capacianc is conncd o a D sourc of.m.f. E hrough a rsisr of rsisanc R and a ky K in sris. Whn h ky K is swichd on, h charging
More information3(8 ) (8 x x ) 3x x (8 )
Scion - CHATER -. a d.. b. d.86 c d 8 d d.9997 f g 6. d. d. Thn, = ln. =. =.. d Thn, = ln.9 =.7 8 -. a d.6 6 6 6 6 8 8 8 b 9 d 6 6 6 8 c d.8 6 6 6 6 8 8 7 7 d 6 d.6 6 6 6 6 6 6 8 u u u u du.9 6 6 6 6 6
More informationNAME: ANSWER KEY DATE: PERIOD. DIRECTIONS: MULTIPLE CHOICE. Choose the letter of the correct answer.
R A T T L E R S S L U G S NAME: ANSWER KEY DATE: PERIOD PREAP PHYSICS REIEW TWO KINEMATICS / GRAPHING FORM A DIRECTIONS: MULTIPLE CHOICE. Chs h r f h rr answr. Us h fgur bw answr qusns 1 and 2. 0 10 20
More informationOn the Speed of Heat Wave. Mihály Makai
On h Spd of Ha Wa Mihály Maai maai@ra.bm.hu Conns Formulaion of h problm: infini spd? Local hrmal qulibrium (LTE hypohsis Balanc quaion Phnomnological balanc Spd of ha wa Applicaion in plasma ranspor 1.
More informationV.Abramov - FURTHER ANALYSIS OF CONFIDENCE INTERVALS FOR LARGE CLIENT/SERVER COMPUTER NETWORKS
R&RATA # Vol.) 8, March FURTHER AALYSIS OF COFIDECE ITERVALS FOR LARGE CLIET/SERVER COMPUTER ETWORKS Vyacheslav Abramov School of Mahemacal Scences, Monash Unversy, Buldng 8, Level 4, Clayon Campus, Wellngon
More informationSearch sequence databases 3 10/25/2016
Sarch squnc databass 3 10/25/2016 Etrm valu distribution Ø Suppos X is a random variabl with probability dnsity function p(, w sampl a larg numbr S of indpndnt valus of X from this distribution for an
More informationResponse of MDOF systems
Response of MDOF syses Degree of freedo DOF: he nu nuber of ndependen coordnaes requred o deerne copleely he posons of all pars of a syse a any nsan of e. wo DOF syses hree DOF syses he noral ode analyss
More informationNEW APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA
NE APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA Mirca I CÎRNU Ph Dp o Mathmatics III Faculty o Applid Scincs Univrsity Polithnica o Bucharst Cirnumirca @yahoocom Abstract In a rcnt papr [] 5 th indinit intgrals
More informationChapter 10. The singular integral Introducing S(n) and J(n)
Chaptr Th singular intgral Our aim in this chaptr is to rplac th functions S (n) and J (n) by mor convnint xprssions; ths will b calld th singular sris S(n) and th singular intgral J(n). This will b don
More informationDEPARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING SIGNALS AND SYSTEMS. Assoc. Prof. Dr. Burak Kelleci. Spring 2018
DEPARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING SIGNALS AND SYSTEMS Aoc. Prof. Dr. Burak Kllci Spring 08 OUTLINE Th Laplac Tranform Rgion of convrgnc for Laplac ranform Invr Laplac ranform Gomric valuaion
More informationCHAPTER CHAPTER14. Expectations: The Basic Tools. Prepared by: Fernando Quijano and Yvonn Quijano
Expcaions: Th Basic Prpard by: Frnando Quijano and Yvonn Quijano CHAPTER CHAPTER14 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 14-1 Today s Lcur Chapr 14:Expcaions: Th Basic Th
More informationChapter 6 Student Lecture Notes 6-1
Chaptr 6 Studnt Lctur Nots 6-1 Chaptr Goals QM353: Busnss Statstcs Chaptr 6 Goodnss-of-Ft Tsts and Contngncy Analyss Aftr compltng ths chaptr, you should b abl to: Us th ch-squar goodnss-of-ft tst to dtrmn
More informationUNIVERSITAT AUTÒNOMA DE BARCELONA MARCH 2017 EXAMINATION
INTERNATIONAL TRADE T. J. KEHOE UNIVERSITAT AUTÒNOMA DE BARCELONA MARCH 27 EXAMINATION Please answer wo of he hree quesons. You can consul class noes, workng papers, and arcles whle you are workng on he
More informationCS434a/541a: Pattern Recognition Prof. Olga Veksler. Lecture 4
CS434a/54a: Paern Recognon Prof. Olga Veksler Lecure 4 Oulne Normal Random Varable Properes Dscrmnan funcons Why Normal Random Varables? Analycally racable Works well when observaon comes form a corruped
More informationAperiodic and Sporadic Jobs. Scheduling Aperiodic and Sporadic Jobs
CPSC-663: Ral-Tm Sym Arodc and Soradc Job Schdulng Arodc and Soradc Job Dfnon Comaron o radonal chdulng of aynchronou vn Pollng Srvr Dfrrabl Srvr Soradc Srvr Gnralzd Procor Sharng Conan Ulzaon Srvr Toal
More informationSolutions of the linearized Richards equation with arbitrary boundary and initial conditions: flux and soil moisture respectively
Hydrology ays Soluons of h lnard Rchards uaon wh arbrary boundary and nal condons: flux and sol mosur rspcvly M. Mnan S. Pugnagh Unvrsà dgl Sud d Modna Rggo Emla p. Inggnra d Maral dllambn Va Vgnols 95
More information4. Which of the following organs develops first?
Biology 4. Which of h following organs dvlops firs? (A) Livr (C) Kidny (B) Har (D) Noochord 12. During mbryonic priod, animals rpa mbryonic sags of hir ancsors. This law is calld (A) Flokin s law (B) Biognic
More information