ON H-TRICHOTOMY IN BANACH SPACES
|
|
- Sabrina Flynn
- 5 years ago
- Views:
Transcription
1 CODRUTA STOICA IHAIL EGA O H-TRICHOTOY I BAACH SPACES Absrac: I his papr w mphasiz h oio of skw-oluio smiflows cosidrd a gralizaio of smigroups oluio opraors ad skw-produc smiflows which aris i h sabiliy hory. W dfi ad characriz a paricular cas of richoomy calld h H-richoomy which is usful i dscribig h bhaiors of h soluio of oluio quaios. W mphasiz h fac ha h richomy iroducd i fii dimsios i [] ad [5] is a aural gralizaio of dichoomy. A similar cocp for sabiliy was sudid for oluio opraors i []. This papr cosidrs also ohr asympoic propris as xpoial growh ad dcay sabiliy ad isabiliy. ahmaics Subjc Classificaio: 4D9 Kywords: oluio quaio skw-oluio smiflow H-richoomy ITRODUCTIO Th cocp of skw-oluio smiflows ariss i h hory of oluio quaios which as wll as h hory of opimal corol is a impora ool i dscribig procsss drid from girig or coomics. Th dyamical sysms ha sudy h ral lif phoma ar complx ad h idificaio of appropriad mahmaical modls is difficul bcaus i h cas of sysms dscribd by parial diffrial quaios h sa spac is of of ifii dimsio. I is irsig o rcosidr h dfiiios of asympoic propris for diffrial quaios by mas of skwoluio smiflows. I wha follows w will cosidr a mor gral cas for asympoic bhaiors ha o iols cssarily xpoials bu isad proprly dfid fucios. L us dfi h s Γ of all coiuous fucios H : R. W will do by Θ h s of all fucios f : R wih h propry ha hr xiss a cosa μ R such ha f = μ wih h subss Θ ad Θ for posii rspcily gai alus of μ. By Ψ is dod h s of coiuous fucios h : R [ dfid such ha for all H Γ hr xis a fucio f Θ ad a cosa k > wih h propris hs kf s H s ad hh s H s s. Rmark.. Th s Ψ is o mpy as w ca cosidr ν ν h = f = ad H = ν >. W will mphasiz h oio of skw-oluio smiflows by mas of oluio smiflows ad oluio cocycls as iroducd by us i [4]. Thy aurally graliz oios as opraors smigroups oluio opraors or skwproduc smiflows. A skw-oluio smiflow dpds o hr ariabils corary o a skwproduc smiflow which dpds oly o wo ad hc h sudy of asympoic bhaiors for skw-oluio smiflows i h ouiform copyrigh FACULTY of EGIEERIG HUEDOARA ROAIA 5
2 ACTA TECHICA CORVIIESIS BULLETI of EGIEERIG sig ariss as aural rlai o h hird ariabil. I his papr w will also cosidr h dfiiios ad characrizaios of som asympoic propris by mas of h s of fucios Θ Γ ad Ψ. SKEW-EVOLUTIO SEIFLOWS L us cosidr X d a mric spac V a ral or complx Baach spac V is opological dual ad BV h family of liar V-alud boudd opraors dfid o V. Th orm of cors ad opraors is. I wha follows w will do Y = X V ad w will cosidr h s T = { R }. By I is dsigd h idiy opraor o V. Dfiiio.. A mappig ϕ : T X X wih h propris: s ϕ x = x x R X ; s ϕ s ϕ s x = ϕ x ss T x X is calld oluio smiflow o X. Dfiiio.. A mappig : T X BV wih h propris: c x = I x R X ; c s ϕs x sx = x ss T x X is calld oluio cocycl or h oluio smiflow ϕ. Dfiiio.. Th mappig C : T Y Y Csx = ϕsx s x whr ϕ is a oluio smiflow o X ad h mappig is a oluio cocycl or ϕ is calld skw-oluio smiflow o Y. Th x xampl mphasizs a skw-oluio smiflow grad by a sysm of diffrial quaios. Exampl.. L us cosidr h sysm of diffrial quaios u = si u w = cos w z = cos z. L us dfi h spacs X = R ad V = R which is dowd wih h orm = whr = V. Th mappig ϕ : T R ϕ s x = - s x is a oluio smiflow o R. Th mappig : T X B V sx Us W s Zs = whr U s=uu - s W s=ww - s Z s=zz - s s T ad u w ad z whr R ar h soluios of h gi sysm of diffrial quaios is a oluio cocycl or h oluio smiflow ϕ o h mric spac R. W obai ha C = ϕ is a skw-oluio. Th followig asympoic bhaiors of skwoluio smiflow ar usful i characrizig h propry of H-richoomy as wll as hir characrizaios. Dfiiio.. A skw-oluio smiflow C = ϕ is said o ha xpoial growh if hr xiss a odcrasig fucio g : R [ wih h propry lim g = such ha: x g s s x ss T x Y. Proposiio.. A skw-oluio smiflow C = ϕ has xpoial growh if ad oly if hr xis som cosas ad ω > such ha: x s s x ω ss T x Y. Proof. cssiy. L s ad b h igr par of h ral umbr - s. W obai succssily x g x... [ g] x ω s s x s x for all ss T ad all x Y whr w ha dod = g > ad ω = l >. Sufficicy. I is obaid immdialy if w ωu cosidr gu = u. ω Dfiiio.. A skw-oluio smiflow C = ϕ is said o b wih xpoial dcay if hr xiss a odcrasig fucio g : R [ wih h propry lim g = such ha: 54 9/Fascicul /Jauary arch/tom II
3 ACTA TECHICA CORVIIESIS BULLETI of EGIEERIG s x g s x ss T x Y. H s s x P x x P x ; Proposiio.. A skw-oluio smiflow C = ϕ has xpoial dcay if ad oly if hr xis som cosas ad ω > such ha: H s s x P x P x x ; ω s s x x ss T x Y. Proof. cssiy. L s. Thr xiss a aural umbr such ha. W ha followig rlaios s x... [ g] g s s x x ω s x x ω for all ss T ad all x Y whr w ha cosidrd h cosas = g > ad ω = l >. Sufficicy. I follows immdialy for ωu gu = u O THE PROPERTY OF H-TRICHOTOY A gral cocp of xpoial richoomy is mphasizd i his scio. Dfiiio.. A mappig P:Y Y gi by Px=x Px whr Px is a projcio o Y x = {x} V ad x X is calld projcor o Y. Dfiiio.. A skw-oluio smiflow C = ϕ is said o b H-richoomic if hr xis som mappigs : projcors familis {P k } k followig codiios hold: R ad hr {} such ha R for ach projcor P k k {} h rlaio P ϕ sx s x = s xpx holds for all s T ad all x X; for all x X h projcios P x P x ad P x saisfy h codiios P xp xp x=i ad P i xp j x= for all i j {} i j; followig iqualiis x P x s H s x P x ad s xp x Hs xp x hold for all ss T for all x Y ad all H Γ. ν Rmark.. I h paricular cas H = ν > h xpoial richoomy for skw-oluio smiflows dfid ad characrizd by us i [] for oluio opraors is obaid i a ouiform sig. Rmark.. i A projcor P o Y wih propry is also calld iaria rlai o h skwoluio smiflow C = ϕ ; ii If hr projcors familis {P k } k {} saisfy rlaios ad of Dfiiio. hy ar usually said o b compaibl wih h skwoluio smiflow C. I wha follows w will do a skw-oluio smiflow C k = ϕ k k {} whr k s x = sx P k x s T x Y. Exampl.. L us cosidr h skw-oluio smiflow gi i Exampl.. W obai for h oluio cocycl : T X BV followig rlaios = s x si s si cos cos s s si si s s = cos s cos s si si s s L us dfi h projcors P x= P x= ad P x=. As followig rlaio holds cos - s cos s - si si s - s - 5s 4 s T w ha ha 9/Fascicul /Jauary arch/tom II 55
4 ACTA TECHICA CORVIIESIS BULLETI of EGIEERIG H s x P x s s x T Y whr w ha dod H = ad 5s 4 s =. Accordig o h iqualiy si s si s cos - cos s - s s - s T i follows ha s x P x H s s x T Y whr w ha cosidrd H = s s =. Also as - si si s - s s s T w ha s xp x sh s x T Y ad as - si si s - s - s - s T w obai H s s xp x ad s x T Y whr i boh cass w ha dod u u H u = ad u =. As a rmark w ca cosidr wihou ay loss of graliy h fucio dod H = mi{h H H }. I follows ha h skw-oluio smiflow C = ϕ is H-richoomic. Th x mai rsul of his papr ca b cosidrd as a igral characrizaio for h cocp of H-richoomy. Thorm.. L H Γ ad h Ψ. A skwoluio smiflow C = ϕ is H-richoomic if ad oly if hr xis som mappigs : R som fucios f f Θ ad hr projcors familis {P k } k {} compaibl wih C such ha h skw-oluio smiflow C has xpoial growh ad h skw-oluio smiflow C has xpoial dcay ad such ha followig codiios hold: i ii H h τ τx dτ P x ; h τ x dτ x ; H τ iii f τ s τ x dτ s x ; s i f τ τ x dτ x s for all s s T ad all x Y V wih. Proof. cssiy. As h skw-oluio smiflow C is H-richoomic i implis ha h rlaios of Dfiiio. hold. i Thr xis a fucio f Θ ad a cosa k > wih h propry hs kf sh s. L us do f = ν >. W obai s x s s H s s x x for all ss T ad for all x Y whr w ha cosidrd h fucio : R u u = k. hu W obai furhr H k h τ τ P x τ x τ x d τ d τ whr w ha dod u = kν u u. ii Thr xis a fucio f Θ ad a cosa k > wih h propry kfs Hs s. L us h cosidr f = ν >. W ha s x x H s s k x h k h ν s s s x x 56 9/Fascicul /Jauary arch/tom II
5 ACTA TECHICA CORVIIESIS BULLETI of EGIEERIG for all ss T ad for all x Y whr w ha dod h νu fucio : R u = k u. iii ad i ar obaid by a similar argumaio accordig o Proposiio. ad Proposiio.. Sufficicy. i L ad s [ ]. As H Γ ad h Ψ hr xiss a cosa α > such ha α s hs H for all s T. Th as h skw-oluio smiflow C has xpoial growh accordig o Proposiio. hr xis som cosas ad ω > such ha followig rlaios hold α ω α ω α τ x x = α τ x dτ α τ ω τ τ ϕ τ x τ x dτ α τ P x τ ϕ τ P x x dτ By akig suprmum rlai o w ha α x P x for all ad all x Y whr α ω u = u u. O h ohr had for [ ] ad x Y w obai ω α x ˆ whr w ha dod ˆ follows ha α ω =. Hc i α x [ ˆ ] for all T ad for all x Y. Furhr if w cosidr H u = fu ad u = [ u ˆ ]fu νu whr fu = Θ ad u w obai rlaio. ii W ha cosidrd H Γ ad h Ψ hc hr xiss a cosa β > such ha β s hs H for all s T. As h skwoluio smiflow C has xpoial growh accordig o Dfiiio. hr xiss a odcrasig fucio g : [ wih R h propry lim g = such ha s x g s x ss T x Y. W will do βτ K = g τdτ. W obai succssily followig rlaios β τ K P x = g τ x dτ β τ β τ x dτ x for all T ad for all x Y. Accordig o Dfiiio. his rlaio is quial wih β s s x x K for all ss T ad for all x Y. If w ak H u = fu ad u ufu = u for fu = Θ ad u rlaio is obaid. iii ad i ca simmilarly b prod. COCLUSIO I h las dcads a gra progrss cocrig h sudy of asympoic bhaiors for oluio quaios ca b obsrd. Th possibiliy of rducig h oauoomous cas i h sudy of oluioary familis or skw-produc flows o h auoomous cas of oluio smigroups o Baach spacs is cosidrd a impora way oward irsig applicaios. Th sudy of h asympoic bhaior of liar skw-produc smiflows has b usd i h hory of oluio quaios i ifii dimsioal spacs. Th approach from h poi of iw of asympoic propris for h oluio 9/Fascicul /Jauary arch/tom II 57
6 ACTA TECHICA CORVIIESIS BULLETI of EGIEERIG smigroup associad o h liar skw-produc smiflows was ssial. Isad i our sudy w ha cosidrd mor gral characrizaios for h asympoic propris of h soluios of oluio quaios dscribd by mas of skw-oluio smiflows which graliz h abo oios. Also h approach was o rsraid by cosidrig i h dfiiios xpoials. As a rmark i Dfiiio. w ha h dfiiios for H-sabiliy H-isabiliy H-growh ad H-dcay characrizd rspcily by Thorm. which xds oward applicaios i girig ad coomics h sudy of oluio quaios. AUTHORS & AFFILIATIO CODRUTA STOICA IHAIL EGA DEPARTET OF ATHEATICS AD COPUTER SCIECE UIVERSITY AUREL VLAICU OF ARAD ROAIA DEPARTET OF ATHEATICS WEST UIVERSITY OF TIISOARA ROAIA ACKOWLEDGET This work is fiacially suppord by h Rsarch Gra CCSIS P II ID 8 of h Romaia iisry of Educaio Rsarch ad Ioaio. REFERECES [] S. ELAYDI O. HAJEK Expoial richoomy of diffrial sysms J. ah. Aal. Appl []. EGA O H-sabiliy of oluio opraors Prpri Sris i ahmaics Ws Uirsiy of Timisoara []. EGA C. STOICA O uiform xpoial richoomy of oluio opraors i Baach spacs Igral Equaios Opraor Thory 6 o [4]. EGA C. STOICA Expoial isabiliy of skw-oluio smiflows i Baach spacs Sudia Ui. Babs-Bolyai ah. LIII o [5] R.J. SACKER G.R. SELL Exisc of dichoomis ad iaria spliigs for liar diffrial sysms III J. Diffrial Equaios /Fascicul /Jauary arch/tom II
Numerical Simulation for the 2-D Heat Equation with Derivative Boundary Conditions
IOSR Joural of Applid Chmisr IOSR-JAC -ISSN: 78-576.Volum 9 Issu 8 Vr. I Aug. 6 PP 4-8 www.iosrjourals.org Numrical Simulaio for h - Ha Equaio wih rivaiv Boudar Codiios Ima. I. Gorial parm of Mahmaics
More informationResponse of LTI Systems to Complex Exponentials
3 Fourir sris coiuous-im Rspos of LI Sysms o Complx Expoials Ouli Cosidr a LI sysm wih h ui impuls rspos Suppos h ipu sigal is a complx xpoial s x s is a complx umbr, xz zis a complx umbr h or h h w will
More information1973 AP Calculus BC: Section I
97 AP Calculus BC: Scio I 9 Mius No Calculaor No: I his amiaio, l dos h aural logarihm of (ha is, logarihm o h bas ).. If f ( ) =, h f ( ) = ( ). ( ) + d = 7 6. If f( ) = +, h h s of valus for which f
More informationFourier Series: main points
BIOEN 3 Lcur 6 Fourir rasforms Novmbr 9, Fourir Sris: mai pois Ifii sum of sis, cosis, or boh + a a cos( + b si( All frqucis ar igr mulipls of a fudamal frqucy, o F.S. ca rprs ay priodic fucio ha w ca
More informationPoisson Arrival Process
1 Poisso Arrival Procss Arrivals occur i) i a mmorylss mar ii) [ o arrival durig Δ ] = λδ + ( Δ ) P o [ o arrival durig Δ ] = 1 λδ + ( Δ ) P o P j arrivals durig Δ = o Δ for j = 2,3, ( ) o Δ whr lim =
More informationPart B: Transform Methods. Professor E. Ambikairajah UNSW, Australia
Par B: rasform Mhods Profssor E. Ambikairaah UNSW, Ausralia Chapr : Fourir Rprsaio of Sigal. Fourir Sris. Fourir rasform.3 Ivrs Fourir rasform.4 Propris.4. Frqucy Shif.4. im Shif.4.3 Scalig.4.4 Diffriaio
More informationThe Development of Suitable and Well-founded Numerical Methods to Solve Systems of Integro- Differential Equations,
Shiraz Uivrsiy of Tchology From h SlcdWorks of Habibolla Laifizadh Th Dvlopm of Suiabl ad Wll-foudd Numrical Mhods o Solv Sysms of Igro- Diffrial Equaios, Habibolla Laifizadh, Shiraz Uivrsiy of Tchology
More informationPoisson Arrival Process
Poisso Arrival Procss Arrivals occur i) i a mmylss mar ii) [ o arrival durig Δ ] = λδ + ( Δ ) P o [ o arrival durig Δ ] = λδ + ( Δ ) P o P j arrivals durig Δ = o Δ f j = 2,3, o Δ whr lim =. Δ Δ C C 2 C
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 informationChapter 3 Linear Equations of Higher Order (Page # 144)
Ma Modr Dirial Equaios Lcur wk 4 Jul 4-8 Dr Firozzama Darm o Mahmaics ad Saisics Arizoa Sa Uivrsi This wk s lcur will covr har ad har 4 Scios 4 har Liar Equaios o Highr Ordr Pag # 44 Scio Iroducio: Scod
More information2 Dirac delta function, modeling of impulse processes. 3 Sine integral function. Exponential integral function
Chapr VII Spcial Fucios Ocobr 7, 7 479 CHAPTER VII SPECIAL FUNCTIONS Cos: Havisid sp fucio, filr fucio Dirac dla fucio, modlig of impuls procsss 3 Si igral fucio 4 Error fucio 5 Gamma fucio E Epoial igral
More information( A) ( B) ( C) ( D) ( E)
d Smsr Fial Exam Worksh x 5x.( NC)If f ( ) d + 7, h 4 f ( ) d is 9x + x 5 6 ( B) ( C) 0 7 ( E) divrg +. (NC) Th ifii sris ak has h parial sum S ( ) for. k Wha is h sum of h sris a? ( B) 0 ( C) ( E) divrgs
More informationWhat Is the Difference between Gamma and Gaussian Distributions?
Applid Mahmaics,,, 85-89 hp://ddoiorg/6/am Publishd Oli Fbruary (hp://wwwscirporg/joural/am) Wha Is h Diffrc bw Gamma ad Gaussia Disribuios? iao-li Hu chool of Elcrical Egirig ad Compur cic, Uivrsiy of
More informationNote 6 Frequency Response
No 6 Frqucy Rpo Dparm of Mchaical Egirig, Uivriy Of Sakachwa, 57 Campu Driv, Sakaoo, S S7N 59, Caada Dparm of Mchaical Egirig, Uivriy Of Sakachwa, 57 Campu Driv, Sakaoo, S S7N 59, Caada. alyical Exprio
More informationRing of Large Number Mutually Coupled Oscillators Periodic Solutions
Iraioal Joural of horical ad Mahmaical Physics 4, 4(6: 5-9 DOI: 59/jijmp446 Rig of arg Numbr Muually Coupld Oscillaors Priodic Soluios Vasil G Aglov,*, Dafika z Aglova Dparm Nam of Mahmaics, Uivrsiy of
More informationFrom Fourier Series towards Fourier Transform
From Fourir Sris owards Fourir rasform D D d D, d wh lim Dparm of Elcrical ad Compur Eiri D, d wh lim L s Cosidr a fucio G d W ca xprss D i rms of Gw D G Dparm of Elcrical ad Compur Eiri D G G 3 Dparm
More informationECE351: Signals and Systems I. Thinh Nguyen
ECE35: Sigals ad Sysms I Thih Nguy FudamalsofSigalsadSysms x Fudamals of Sigals ad Sysms co. Fudamals of Sigals ad Sysms co. x x] Classificaio of sigals Classificaio of sigals co. x] x x] =xt s =x
More informationISSN: [Bellale* et al., 6(1): January, 2017] Impact Factor: 4.116
IESRT INTERNTIONL OURNL OF ENGINEERING SCIENCES & RESERCH TECHNOLOGY HYBRID FIED POINT THEOREM FOR NONLINER DIFFERENTIL EQUTIONS Sidhshwar Sagram Bllal*, Gash Babrwa Dapk * Dparm o Mahmaics, Daaad Scic
More informationLinear Systems Analysis in the Time Domain
Liar Sysms Aalysis i h Tim Domai Firs Ordr Sysms di vl = L, vr = Ri, d di L + Ri = () d R x= i, x& = x+ ( ) L L X() s I() s = = = U() s E() s Ls+ R R L s + R u () = () =, i() = L i () = R R Firs Ordr Sysms
More informationMAT3700. Tutorial Letter 201/2/2016. Mathematics III (Engineering) Semester 2. Department of Mathematical sciences MAT3700/201/2/2016
MAT3700/0//06 Tuorial Lr 0//06 Mahmaics III (Egirig) MAT3700 Smsr Dparm of Mahmaical scics This uorial lr coais soluios ad aswrs o assigms. BARCODE CONTENTS Pag SOLUTIONS ASSIGNMENT... 3 SOLUTIONS ASSIGNMENT...
More informationMathematical Preliminaries for Transforms, Subbands, and Wavelets
Mahmaical Prlimiaris for rasforms, Subbads, ad Wavls C.M. Liu Prcpual Sigal Procssig Lab Collg of Compur Scic Naioal Chiao-ug Uivrsiy hp://www.csi.cu.du.w/~cmliu/courss/comprssio/ Offic: EC538 (03)5731877
More informationMixing time with Coupling
Mixig im wih Couplig Jihui Li Mig Zhg Saisics Dparm May 7 Goal Iroducio o boudig h mixig im for MCMC wih couplig ad pah couplig Prsig a simpl xampl o illusra h basic ida Noaio M is a Markov chai o fii
More information(A) 1 (B) 1 + (sin 1) (C) 1 (sin 1) (D) (sin 1) 1 (C) and g be the inverse of f. Then the value of g'(0) is. (C) a. dx (a > 0) is
[STRAIGHT OBJECTIVE TYPE] l Q. Th vlu of h dfii igrl, cos d is + (si ) (si ) (si ) Q. Th vlu of h dfii igrl si d whr [, ] cos cos Q. Vlu of h dfii igrl ( si Q. L f () = d ( ) cos 7 ( ) )d d g b h ivrs
More information3.2. Derivation of Laplace Transforms of Simple Functions
3. aplac Tarform 3. PE TRNSFORM wid rag of girig ym ar modld mahmaically by uig diffrial quaio. I gral, h diffrial quaio of h ordr ym i wri: d y( a d d d y( dy( a a y( f( (3. d Which i alo ow a a liar
More informationPractice papers A and B, produced by Edexcel in 2009, with mark schemes. Practice Paper A. 5 cosh x 2 sinh x = 11,
Prai paprs A ad B, produd by Edl i 9, wih mark shms Prai Papr A. Fid h valus of for whih 5 osh sih =, givig your aswrs as aural logarihms. (Toal 6 marks) k. A = k, whr k is a ral osa. 9 (a) Fid valus of
More informationSome Applications of the Poisson Process
Applid Maaics, 24, 5, 3-37 Publishd Oli Novbr 24 i SciRs. hp://www.scirp.org/oural/a hp://dx.doi.org/.4236/a.24.59288 So Applicaios of Poisso Procss Kug-Ku s Dpar of Maaics, Ka Uivrsiy, Uio, USA Eail:
More informationWeb-appendix 1: macro to calculate the range of ( ρ, for which R is positive definite
Wb-basd Supplmary Marials for Sampl siz cosidraios for GEE aalyss of hr-lvl clusr radomizd rials by Sv Trsra, Big Lu, oh S. Prissr, Tho va Achrbrg, ad Gorg F. Borm Wb-appdix : macro o calcula h rag of
More information) and furthermore all X. The definition of the term stationary requires that the distribution fulfills the condition:
Assigm Thomas Aam, Spha Brumm, Haik Lor May 6 h, 3 8 h smsr, 357, 7544, 757 oblm For R b X a raom variabl havig ormal isribuio wih ma µ a variac σ (his is wri as ~ (,) X. by: R a. Is X ) a urhrmor all
More informationChapter 11 INTEGRAL EQUATIONS
hapr INTERAL EQUATIONS hapr INTERAL EUATIONS Dcmbr 4, 8 hapr Igral Eqaios. Normd Vcor Spacs. Eclidia vcor spac. Vcor spac o coios cios ( ). Vcor Spac L ( ) 4. achy-byaowsi iqaliy 5. iowsi iqaliy. Liar
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 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 informationIntrinsic formulation for elastic line deformed on a surface by an external field in the pseudo-galilean space 3. Nevin Gürbüz
risic formuaio for asic i form o a surfac by a xra fi i h psuo-aia spac Nvi ürbüz Eskişhir Osmaazi Uivrsiy Mahmaics a Compur Scics Dparm urbuz@ouur Absrac: his papr w riv irisic formuaio for asic i form
More informationOn (h, k) trichotomy for skew-evolution semiflows in Banach spaces
Stud. Univ. Babeş-Bolyai Math. 56(2011), No. 4, 147 156 On (h, k) trichotomy for skew-evolution semiflows in Banach spaces Codruţa Stoica and Mihail Megan Abstract. In this paper we define the notion of
More information, then the old equilibrium biomass was greater than the new B e. and we want to determine how long it takes for B(t) to reach the value B e.
SURPLUS PRODUCTION (coiud) Trasiio o a Nw Equilibrium Th followig marials ar adapd from lchr (978), o h Rcommdd Radig lis caus () approachs h w quilibrium valu asympoically, i aks a ifii amou of im o acually
More informationFIXED FUZZY POINT THEOREMS IN FUZZY METRIC SPACE
Mohia & Samaa, Vol. 1, No. II, December, 016, pp 34-49. ORIGINAL RESEARCH ARTICLE OPEN ACCESS FIED FUZZY POINT THEOREMS IN FUZZY METRIC SPACE 1 Mohia S. *, Samaa T. K. 1 Deparme of Mahemaics, Sudhir Memorial
More informationThe geometry of surfaces contact
Applid ad ompuaioal Mchaics (007 647-656 h gomry of surfacs coac J. Sigl a * J. Švíglr a a Faculy of Applid Scics UWB i Pils Uivrzií 0 00 Pils zch public civd 0 Spmbr 007; rcivd i rvisd form 0 Ocobr 007
More information1.7 Vector Calculus 2 - Integration
cio.7.7 cor alculus - Igraio.7. Ordiary Igrals o a cor A vcor ca b igrad i h ordiary way o roduc aohr vcor or aml 5 5 d 6.7. Li Igrals Discussd hr is h oio o a dii igral ivolvig a vcor ucio ha gras a scalar.
More informationSome Properties of Semi-E-Convex Function and Semi-E-Convex Programming*
The Eighh Ieraioal Symposium o Operaios esearch ad Is Applicaios (ISOA 9) Zhagjiajie Chia Sepember 2 22 29 Copyrigh 29 OSC & APOC pp 33 39 Some Properies of Semi-E-Covex Fucio ad Semi-E-Covex Programmig*
More informationEXISTENCE THEORY OF RANDOM DIFFERENTIAL EQUATIONS D. S. Palimkar
Ieraioal Joural of Scieific ad Research Publicaios, Volue 2, Issue 7, July 22 ISSN 225-353 EXISTENCE THEORY OF RANDOM DIFFERENTIAL EQUATIONS D S Palikar Depare of Maheaics, Vasarao Naik College, Naded
More informationCalculus Limits. Limit of a function.. 1. One-Sided Limits...1. Infinite limits 2. Vertical Asymptotes...3. Calculating Limits Using the Limit Laws.
Limi of a fucio.. Oe-Sided..... Ifiie limis Verical Asympoes... Calculaig Usig he Limi Laws.5 The Squeeze Theorem.6 The Precise Defiiio of a Limi......7 Coiuiy.8 Iermediae Value Theorem..9 Refereces..
More informationPhase plane method is an important graphical methods to deal with problems related to a second-order autonomous system.
NCTU Dpam of Elcical ad Compu Egiig Sio Cous
More informationEEE 303: Signals and Linear Systems
33: Sigls d Lir Sysms Orhogoliy bw wo sigls L us pproim fucio f () by fucio () ovr irvl : f ( ) = c( ); h rror i pproimio is, () = f() c () h rgy of rror sigl ovr h irvl [, ] is, { }{ } = f () c () d =
More informationFourier Techniques Chapters 2 & 3, Part I
Fourir chiqus Chaprs & 3, Par I Dr. Yu Q. Shi Dp o Elcrical & Compur Egirig Nw Jrsy Isiu o chology Email: shi@i.du usd or h cours: , 4 h Ediio, Lahi ad Dog, Oord
More informationS n. = n. Sum of first n terms of an A. P is
PROGREION I his secio we discuss hree impora series amely ) Arihmeic Progressio (A.P), ) Geomeric Progressio (G.P), ad 3) Harmoic Progressio (H.P) Which are very widely used i biological scieces ad humaiies.
More informationInfinite Continued Fraction (CF) representations. of the exponential integral function, Bessel functions and Lommel polynomials
Ifii Coiu Fraio CF rraio of h oial igral fuio l fuio a Lol olyoial Coiu Fraio CF rraio a orhogoal olyoial I hi io w rall h rlaio bw ifi rurry rlaio of olyoial orroig orhogoaliy a aroria ifii oiu fraio
More informationBE.430 Tutorial: Linear Operator Theory and Eigenfunction Expansion
BE.43 Tuorial: Liear Operaor Theory ad Eigefucio Expasio (adaped fro Douglas Lauffeburger) 9//4 Moivaig proble I class, we ecouered parial differeial equaios describig rasie syses wih cheical diffusio.
More informationChapter 7 INTEGRAL EQUATIONS
hapr 7 INTERAL EQUATIONS hapr 7 INTERAL EUATIONS hapr 7 Igral Eqaios 7. Normd Vcor Spacs. Eclidia vcor spac. Vcor spac o coios cios ( ). Vcor Spac L ( ) 4. ach-baowsi iqali 5. iowsi iqali 7. Liar Opraors
More informationChapter4 Time Domain Analysis of Control System
Chpr4 im Domi Alyi of Corol Sym Rouh biliy cririo Sdy rror ri rpo of h fir-ordr ym ri rpo of h cod-ordr ym im domi prformc pcificio h rliohip bw h prformc pcificio d ym prmr ri rpo of highr-ordr ym Dfiiio
More informationResearch Article A Generalized Nonlinear Sum-Difference Inequality of Product Form
Joural of Applied Mahemaics Volume 03, Aricle ID 47585, 7 pages hp://dx.doi.org/0.55/03/47585 Research Aricle A Geeralized Noliear Sum-Differece Iequaliy of Produc Form YogZhou Qi ad Wu-Sheg Wag School
More informationMidterm exam 2, April 7, 2009 (solutions)
Univrsiy of Pnnsylvania Dparmn of Mahmaics Mah 26 Honors Calculus II Spring Smsr 29 Prof Grassi, TA Ashr Aul Midrm xam 2, April 7, 29 (soluions) 1 Wri a basis for h spac of pairs (u, v) of smooh funcions
More informationAn Indian Journal FULL PAPER. Trade Science Inc. A stage-structured model of a single-species with density-dependent and birth pulses ABSTRACT
[Typ x] [Typ x] [Typ x] ISSN : 974-7435 Volum 1 Issu 24 BioTchnology 214 An Indian Journal FULL PAPE BTAIJ, 1(24), 214 [15197-1521] A sag-srucurd modl of a singl-spcis wih dnsiy-dpndn and birh pulss LI
More information, R we have. x x. ) 1 x. R and is a positive bounded. det. International Journal of Basic & Applied Sciences IJBAS-IJENS Vol:10 No:06 11
raioal Joral of asic & ppli Scics JS-JENS Vol: No:6 So Dirichl ors a Pso Diffrial Opraors wih Coiioall Epoial Cov cio aa. M. Kail Dpar of Mahaics; acl of Scic; Ki laziz Uivrsi Jah Sai raia Eail: fkail@ka..sa
More informationModeling of the CML FD noise-to-jitter conversion as an LPTV process
Modlig of h CML FD ois-o-ir covrsio as a LPV procss Marko Alksic. Rvisio hisory Vrsio Da Comms. //4 Firs vrsio mrgd wo docums. Cyclosaioary Nois ad Applicaio o CML Frqucy Dividr Jir/Phas Nois Aalysis fil
More informationECEN620: Network Theory Broadband Circuit Design Fall 2014
ECE60: work Thory Broadbad Circui Dig Fall 04 Lcur 6: PLL Trai Bhavior Sam Palrmo Aalog & Mixd-Sigal Cr Txa A&M Uivriy Aoucm, Agda, & Rfrc HW i du oday by 5PM PLL Trackig Rpo Pha Dcor Modl PLL Hold Rag
More informationAdvanced Engineering Mathematics, K.A. Stroud, Dexter J. Booth Engineering Mathematics, H.K. Dass Higher Engineering Mathematics, Dr. B.S.
Rfrc: (i) (ii) (iii) Advcd Egirig Mhmic, K.A. Sroud, Dxr J. Booh Egirig Mhmic, H.K. D Highr Egirig Mhmic, Dr. B.S. Grwl Th mhod of m Thi coi of h followig xm wih h giv coribuio o h ol. () Mid-rm xm : 3%
More informationChapter 5 The Laplace Transform. x(t) input y(t) output Dynamic System
EE 422G No: Chapr 5 Inrucor: Chung Chapr 5 Th Laplac Tranform 5- Inroducion () Sym analyi inpu oupu Dynamic Sym Linar Dynamic ym: A procor which proc h inpu ignal o produc h oupu dy ( n) ( n dy ( n) +
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 informationTAKA KUSANO. laculty of Science Hrosh tlnlersty 1982) (n-l) + + Pn(t)x 0, (n-l) + + Pn(t)Y f(t,y), XR R are continuous functions.
Iera. J. Mah. & Mah. Si. Vol. 6 No. 3 (1983) 559-566 559 ASYMPTOTIC RELATIOHIPS BETWEEN TWO HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS TAKA KUSANO laculy of Sciece Hrosh llersy 1982) ABSTRACT. Some asympoic
More informationBMM3553 Mechanical Vibrations
BMM3553 Mhaial Vibraio Chapr 3: Damp Vibraio of Sigl Dgr of From Sym (Par ) by Ch Ku Ey Nizwa Bi Ch Ku Hui Fauly of Mhaial Egirig mail: y@ump.u.my Chapr Dripio Ep Ouom Su will b abl o: Drmi h aural frquy
More informationIdeal Amplifier/Attenuator. Memoryless. where k is some real constant. Integrator. System with memory
Liear Time-Ivaria Sysems (LTI Sysems) Oulie Basic Sysem Properies Memoryless ad sysems wih memory (saic or dyamic) Causal ad o-causal sysems (Causaliy) Liear ad o-liear sysems (Lieariy) Sable ad o-sable
More informationMIHAIL MEGAN and LARISA BIRIŞ
ANALELE ŞTIINŢIFICE ALE UNIVERSITĂŢII AL.I. CUZA DIN IAŞI (S.N.) MATEMATICĂ, Tomul LIV, 2008, f.2 POINTWISE EXPONENTIAL TRICHOTOMY OF LINEAR SKEW-PRODUCT SEMIFLOWS BY MIHAIL MEGAN and LARISA BIRIŞ Abstract.
More information1 Notes on Little s Law (l = λw)
Copyrigh c 26 by Karl Sigma Noes o Lile s Law (l λw) We cosider here a famous ad very useful law i queueig heory called Lile s Law, also kow as l λw, which assers ha he ime average umber of cusomers i
More informationLecture 4: Laplace Transforms
Lur 4: Lapla Transforms Lapla and rlad ransformaions an b usd o solv diffrnial quaion and o rdu priodi nois in signals and imags. Basially, hy onvr h drivaiv opraions ino mulipliaion, diffrnial quaions
More informationPrakash Chandra Rautaray 1, Ellipse 2
Prakash Chadra Rauara, Ellise / Ieraioal Joural of Egieerig Research ad Alicaios (IJERA) ISSN: 48-96 www.ijera.com Vol. 3, Issue, Jauar -Februar 3,.36-337 Degree Of Aroimaio Of Fucios B Modified Parial
More informationOn Stability of Quintic Functional Equations in Random Normed Spaces
J. COMPUTATIONAL ANALYSIS AND APPLICATIONS, VOL. 3, NO.4, 07, COPYRIGHT 07 EUDOXUS PRESS, LLC O Sabiliy of Quiic Fucioal Equaios i Radom Normed Spaces Afrah A.N. Abdou, Y. J. Cho,,, Liaqa A. Kha ad S.
More informationSupplement for SADAGRAD: Strongly Adaptive Stochastic Gradient Methods"
Suppleme for SADAGRAD: Srogly Adapive Sochasic Gradie Mehods" Zaiyi Che * 1 Yi Xu * Ehog Che 1 iabao Yag 1. Proof of Proposiio 1 Proposiio 1. Le ɛ > 0 be fixed, H 0 γi, γ g, EF (w 1 ) F (w ) ɛ 0 ad ieraio
More informationELECTROMAGNETIC COMPATIBILITY HANDBOOK 1. Chapter 12: Spectra of Periodic and Aperiodic Signals
ELECTOMAGNETIC COMPATIBILITY HANDBOOK Chapr : Spcra of Priodic ad Apriodic Sigals. Drmi whhr ach of h followig fucios ar priodic. If hy ar priodic, provid hir fudamal frqucy ad priod. a) x 4cos( 5 ) si(
More informationPhys463.nb Conductivity. Another equivalent definition of the Fermi velocity is
39 Anohr quival dfiniion of h Fri vlociy is pf vf (6.4) If h rgy is a quadraic funcion of k H k L, hs wo dfiniions ar idical. If is NOT a quadraic funcion of k (which could happ as will b discussd in h
More informationDEFLECTIONS OF THIN PLATES: INFLUENCE OF THE SLOPE OF THE PLATE IN THE APLICATION OF LINEAR AND NONLINEAR THEORIES
Procdigs of COBEM 5 Coprigh 5 b BCM 8h Iraioal Cogrss of Mchaical Egirig Novmbr 6-, 5, Ouro Pro, MG DEFLECIONS OF HIN PLES: INFLUENCE OF HE SLOPE OF HE PLE IN HE PLICION OF LINER ND NONLINER HEORIES C..
More informationLINEAR 2 nd ORDER DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS
Diol Bgyoko (0) I.INTRODUCTION LINEAR d ORDER DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS I. Dfiiio All suh diffril quios s i h sdrd or oil form: y + y + y Q( x) dy d y wih y d y d dx dx whr,, d
More informationOn the approximation of the constant of Napier
Stud. Uiv. Babş-Bolyai Math. 560, No., 609 64 O th approximatio of th costat of Napir Adri Vrscu Abstract. Startig from som oldr idas of [] ad [6], w show w facts cocrig th approximatio of th costat of
More informationAdomian Decomposition Method for Dispersion. Phenomena Arising in Longitudinal Dispersion of. Miscible Fluid Flow through Porous Media
dv. Thor. ppl. Mch. Vol. 3 o. 5 - domia Dcomposiio Mhod for Disprsio Phoma risig i ogiudial Disprsio of Miscibl Fluid Flow hrough Porous Mdia Ramakaa Mhr ad M.N. Mha Dparm of Mahmaics S.V. Naioal Isiu
More informationH is equal to the surface current J S
Chapr 6 Rflcion and Transmission of Wavs 6.1 Boundary Condiions A h boundary of wo diffrn mdium, lcromagnic fild hav o saisfy physical condiion, which is drmind by Maxwll s quaion. This is h boundary condiion
More informationOn the Frame Properties of System of Exponents with Piecewise Continuous Phase
Alid Mahmaics 3 4 848-853 h://dxdoiorg/436/am3456 Publishd Oli May 3 (h://wwwscirorg/joural/am) O h Fram Proris of Sysm of Exos wih Picwis Coiuous Phas Sad Mohammadali Farahai Tofig Isa ajafov Isiu of
More informationFolding of Hyperbolic Manifolds
It. J. Cotmp. Math. Scics, Vol. 7, 0, o. 6, 79-799 Foldig of Hyprbolic Maifolds H. I. Attiya Basic Scic Dpartmt, Collg of Idustrial Educatio BANE - SUEF Uivrsity, Egypt hala_attiya005@yahoo.com Abstract
More information82A Engineering Mathematics
Class Nos 5: Sod Ordr Diffrial Eqaio No Homoos 8A Eiri Mahmais Sod Ordr Liar Diffrial Eqaios Homoos & No Homoos v q Homoos No-homoos q ar iv oios fios o h o irval I Sod Ordr Liar Diffrial Eqaios Homoos
More informationSTK4080/9080 Survival and event history analysis
STK48/98 Survival ad eve hisory aalysis Marigales i discree ime Cosider a sochasic process The process M is a marigale if Lecure 3: Marigales ad oher sochasic processes i discree ime (recap) where (formally
More informationAnalysis of Non-Sinusoidal Waveforms Part 2 Laplace Transform
Aalyi o No-Siuoidal Wavorm Par Laplac raorm I h arlir cio, w lar ha h Fourir Sri may b wri i complx orm a ( ) C jω whr h Fourir coici C i giv by o o jωo C ( ) d o I h ymmrical orm, h Fourir ri i wri wih
More informationAn Analytical Study on Fractional Partial Differential Equations by Laplace Transform Operator Method
Iraioal Joural o Applid Egirig Rsarch ISSN 973-456 Volum 3 Numbr (8 pp 545-549 Rsarch Idia Publicaios hp://wwwripublicaiocom A Aalical Sud o Fracioal Parial Dirial Euaios b aplac Trasorm Opraor Mhod SKElaga
More informationChapter Five. More Dimensions. is simply the set of all ordered n-tuples of real numbers x = ( x 1
Chatr Fiv Mor Dimsios 51 Th Sac R W ar ow rard to mov o to sacs of dimsio gratr tha thr Ths sacs ar a straightforward gralizatio of our Euclida sac of thr dimsios Lt b a ositiv itgr Th -dimsioal Euclida
More informationControl Systems. Transient and Steady State Response.
Corol Sym Trai a Say Sa Ro chibum@oulch.ac.kr Ouli Tim Domai Aalyi orr ym Ui ro Ui ram ro Ui imul ro Chibum L -Soulch Corol Sym Tim Domai Aalyi Afr h mahmaical mol of h ym i obai, aalyi of ym rformac i.
More informationEÜFBED - Fen Bilimleri Enstitüsü Dergisi Cilt-Sayı: 6-2 Yıl:
EÜED - ilimlri Esiüsü Drgisi Cil-Saı: 6- Yıl: 3 75-86 75 ON SEMIGOUP GENEAED Y OUIE- ESSEL ANSOM AND IESZ POENIAL ASSOCIAED WIH SEMIGOUP OUIE- ESSEL DÖNÜŞÜMÜ AAINDAN ÜEİLEN SEMİGUU VE - SEMİGUP AAINDAN
More information15. Numerical Methods
S K Modal' 5. Numrical Mhod. Th quaio + 4 4 i o b olvd uig h Nwo-Rapho mhod. If i ak a h iiial approimaio of h oluio, h h approimaio uig hi mhod will b [EC: GATE-7].(a (a (b 4 Nwo-Rapho iraio chm i f(
More information1. Solve by the method of undetermined coefficients and by the method of variation of parameters. (4)
7 Differeial equaios Review Solve by he mehod of udeermied coefficies ad by he mehod of variaio of parameers (4) y y = si Soluio; we firs solve he homogeeous equaio (4) y y = 4 The correspodig characerisic
More informationMean Square Convergent Finite Difference Scheme for Stochastic Parabolic PDEs
America Joural of Compuaioal Mahemaics, 04, 4, 80-88 Published Olie Sepember 04 i SciRes. hp://www.scirp.org/joural/ajcm hp://dx.doi.org/0.436/ajcm.04.4404 Mea Square Coverge Fiie Differece Scheme for
More informationz 1+ 3 z = Π n =1 z f() z = n e - z = ( 1-z) e z e n z z 1- n = ( 1-z/2) 1+ 2n z e 2n e n -1 ( 1-z )/2 e 2n-1 1-2n -1 1 () z
Sris Expasio of Rciprocal of Gamma Fuctio. Fuctios with Itgrs as Roots Fuctio f with gativ itgrs as roots ca b dscribd as follows. f() Howvr, this ifiit product divrgs. That is, such a fuctio caot xist
More informationReview Topics from Chapter 3&4. Fourier Series Fourier Transform Linear Time Invariant (LTI) Systems Energy-Type Signals Power-Type Signals
Rviw opics from Chapr 3&4 Fourir Sris Fourir rasform Liar im Ivaria (LI) Sysms Ergy-yp Sigals Powr-yp Sigals Fourir Sris Rprsaio for Priodic Sigals Dfiiio: L h sigal () b a priodic sigal wih priod. ()
More informationFourier transform. Continuous-time Fourier transform (CTFT) ω ω
Fourier rasform Coiuous-ime Fourier rasform (CTFT P. Deoe ( he Fourier rasform of he sigal x(. Deermie he followig values, wihou compuig (. a (0 b ( d c ( si d ( d d e iverse Fourier rasform for Re { (
More informationAssessing Reliable Software using SPRT based on LPETM
Iraioal Joural of Compur Applicaios (75 888) Volum 47 No., Ju Assssig Rliabl Sofwar usig SRT basd o LETM R. Saya rasad hd, Associa rofssor Dp. of CS &Egg. AcharyaNagarjua Uivrsiy D. Hariha Assisa rofssor
More informationA note on deviation inequalities on {0, 1} n. by Julio Bernués*
A oe o deviaio iequaliies o {0, 1}. by Julio Berués* Deparameo de Maemáicas. Faculad de Ciecias Uiversidad de Zaragoza 50009-Zaragoza (Spai) I. Iroducio. Le f: (Ω, Σ, ) IR be a radom variable. Roughly
More informationOutline. Overlook. Controllability measures. Observability measures. Infinite Gramians. MOR: Balanced truncation based on infinite Gramians
Ouli Ovrlook Corollabiliy masurs Obsrvabiliy masurs Ifii Gramias MOR: alacd rucaio basd o ifii Gramias Ovrlook alacd rucaio: firs balacig h ruca. Giv a I sysm: / y u d d For covic of discussio w do h sysm
More informationState-Space Model. In general, the dynamic equations of a lumped-parameter continuous system may be represented by
Sae-Space Model I geeral, he dyaic equaio of a luped-paraeer coiuou ye ay be repreeed by x & f x, u, y g x, u, ae equaio oupu equaio where f ad g are oliear vecor-valued fucio Uig a liearized echique,
More informationApproximate solutions for the time-space fractional nonlinear of partial differential equations using reduced differential transform method
Global Joral o Pr ad Applid Mahmaics ISSN 97-768 Volm Nmbr 6 7 pp 5-6 sarch Idia Pblicaios hp://wwwripblicaiocom Approima solios or h im-spac racioal oliar o parial dirial qaios sig rdcd dirial rasorm
More informationFurther Results on Pair Sum Graphs
Applid Mathmatis, 0,, 67-75 http://dx.doi.org/0.46/am.0.04 Publishd Oli Marh 0 (http://www.sirp.org/joural/am) Furthr Rsults o Pair Sum Graphs Raja Poraj, Jyaraj Vijaya Xavir Parthipa, Rukhmoi Kala Dpartmt
More informationPURE MATHEMATICS A-LEVEL PAPER 1
-AL P MATH PAPER HONG KONG EXAMINATIONS AUTHORITY HONG KONG ADVANCED LEVEL EXAMINATION PURE MATHEMATICS A-LEVEL PAPER 8 am am ( hours) This papr must b aswrd i Eglish This papr cosists of Sctio A ad Sctio
More informationL-functions and Class Numbers
L-fucios ad Class Numbers Sude Number Theory Semiar S. M.-C. 4 Sepember 05 We follow Romyar Sharifi s Noes o Iwasawa Theory, wih some help from Neukirch s Algebraic Number Theory. L-fucios of Dirichle
More informationFRACTIONAL SYNCHRONIZATION OF CHAOTIC SYSTEMS WITH DIFFERENT ORDERS
THE PUBLISHING HOUSE PROCEEINGS OF THE ROMANIAN ACAEMY, Series A, OF THE ROMANIAN ACAEMY Volume 1, Number 4/01, pp 14 1 FRACTIONAL SYNCHRONIZATION OF CHAOTIC SYSTEMS WITH IFFERENT ORERS Abolhassa RAZMINIA
More informationOption Pricing Model With Continuous Dividends
Avacs i Naural Scic Vol. 8 No. 3 5 pp. -5 DOI:.3968/736 ISSN 75-786 [PRIN] ISSN 75-787 [ONLINE] www.cscaaa. www.cscaaa.org Opio Pricig Mol Wih Coiuous Divi ZHENG Yigchu [a] ; YANG Yufg [a] ; ZHANG Shougag
More informationApproximating Solutions for Ginzburg Landau Equation by HPM and ADM
Available a hp://pvamu.edu/aam Appl. Appl. Mah. ISSN: 193-9466 Vol. 5, No. Issue (December 1), pp. 575 584 (Previously, Vol. 5, Issue 1, pp. 167 1681) Applicaios ad Applied Mahemaics: A Ieraioal Joural
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 information