Modeling of Reductive Biodegradation of TCE to ETH. Adam Worsztynowicz, Dorota Rzychon, Sebastian Iwaszenko, Tomasz Siobowicz
|
|
|
- Agnes Garrett
- 5 years ago
- Views:
Transcription
1 Modlig of Rduciv Biodgradaio of o ETH Adam Worszyowicz, Doroa Rzycho, Sbasia Iwaszo, Tomasz Siobowicz Isiu for Ecology of Idusrial Aras Kossuha S., Kaowic, Polad l. (+-) 5, fax: (+-) mail: iu@iu.aowic.pl Absrac A rduciv biormdiaio procss of chloriad solv () was modld usig iic approach. Dgradaio of o ETH was cosidrd as a coscuiv s of biochmical rasformaios. Exprimal daa wr usd for procss aalysis ad assssig ordr of ach procss sp. I was assumd, ha biochmical racios corol ovrall quicss of h procss. Accordig o rsuls of xprims modl was dividd io wo pars ad VC ETH covrsio. Small bioracor gas laag, cd durig xprim, was icorporad i modl quaios. Aalyical soluios wr rmid ad calculaios wr compard o xprimal daa. Modl was hacd o iclud biological aur of aalyzd procsss: a logisic quaio was usd o dscrib iic paramr dpdcy o microorgaisms populaio. Calculaios prformd wih hacd modl quaios wr compard o xprimal daa wih saisfacory rsuls. Iroducio Usig ad disposal of volail orgaic compouds (VOC) of rsul i soil ad groud war viromal problms. Chloriad solvs, such as rachloroh (PCE), richloroh (), richloroha (TCA) ad carbo rachlorid (CT) ar cosidrd o b o of h mos viromally dagrous VOCs. Amog fw chologis which ar capabl of rmovig hos compouds from soil ad groudwar, biormdiaio sm o b rlaivly chap ad viromally fridly. Trasformaio of chloriad solv durig biodgradaio procss ca follow ihr rduciv dhalogaio (halorspiraio) or oxidaio racios (arobic ad aarobic oxidaio). A ypical rduciv dchloriaio procss of ca b rad as a s of hr sps, cosqu racios. Th is firs covrd o cis ad ras dichloroh (). is h covrd o viyl chlorid (VC) ad VC is chagd io hyl (ETH) which ds h dgradaio pah. Modlig biodgradaio of o ETH ivolvs aalysis of possibl biochmical racios i a paricular biormdiaio sysm, xprimal daa aalysis, maig rasoabl simplifyig assumpio ad formulaig s of quaios dscribig cosidrd sysm. Oc h quaios ar formulad ad paramrs ar assssd, calculaios ar mad ad modl is vrifid wih xprimal daa. Exprimal Bacgroud A small, pocd bad, coiuous gas rcirculaio bioracor was dvlopd i Isiu for Ecology of Idusrial Aras (Polad) wih coopraio wih Wsighous Savaah Rivr Compay (USA) o cla up a limid (up o cubic mrs) ams of coamiad soil. Th sysm was dsigd o a advaag of aarobic biodgradaio of ad is quippd wih procss moiorig ad corollig sysm. Priodically, sampls of soil gass wr a for laboraory aalysis. As h procss was carrid i aarobic codiios, aig soil sampls was impossibl. Figur prss masurd avrag,, VC ad ETH cocraio chags i soil gass. Th rsuls obaid durig biodgradaio xprim wr uss as a basis for formulaio of mahmaical procss dscripio. I was assumd ha quilibrium i,, VC ad ETH cocraios amog gas, liquid ad solid-adsorbd phass ar maiaid hrough procss duraio. O ha basis, calculaig of oal am of ach compoud ca b do by usig appropria Hry s law ad adsorpio cosas, providig ha volum of ach phas is ow.
2 cocraios [mmol/m ] Figur.,, VC ad ETH ma cocraio i soil gas. VC ETH im, days Modl formulaio Rsuls of xprim prov h coscuiv characr of assumd racios s. Thr diffr priods ca b iifid i h bioracor opraio: Sharp dcras of cocraio (afr shor priod of sabl cocraio) accompaid wih disic icras i DEC cocraio, cocraios of VC ad ETH wr gligibl; Ngligibl cocraios of, clos o zro cocraios of VC ad ETH bu slow icras may b obsrvd a h d of h priod, cocraio d o dcli wh VC d ETH bgu o ris; cocraio gligibl, dcras of cocraio o zro, VC cocraio gaid a maximum ad h droppd o vry small valus. Th cocraio chags of ETH wr similar bu h maximum was highr ad shifd i im. Bcaus o rasformaio was sparad from furhr rasformaio of o ETH hrough VC, h modl was dividd io wo pars: (i) dscripio of o racio ad (ii) dscripio of cosqu o VC ad h o ETH racios. As ETH was a fial produc of h rduciv biodgradaio of ad o sigs of ETH dgradaio producs wr foud, i was assumd ha obsrvd dcras i ETH cocraio was causd by gas laag from h bioracor vssl. Gass (mosly CO ad O) producio durig rduciv dgradaio of sludg was cosidrd as a drivig forc for prssur icras isid h vssl, ad, i cosquc, gas laag. I was assumd ha gas scap oo plac durig whol biormdiaio procss. Chags i gas phas cocraio of chloriad aliphaic compouds ar schmaically illusrad i h figur : Figur. Chags i gas phas cocraio of chloriad aliphaic compouds schma mi = vici m = G c m = v c whr: m i, c i mass ad cocraio of chloriad aliphaic compouds flowig io h racor ovr im v i flow ra of gass io h racor (i his cas h ra of gass graio i sludg dgradaio) m, c mass ad cocraio of chloriad aliphaic compouds flowig of h racor ovr im v flow ra of gass laig from h racor m, c icras i chloriad aliphaic compouds mass co ad cocraio i h racor gas phas ovr im G gas phas volum i h racor.
3 Mass balac quaio for gas volum i h bioracor may b wri i h form: m G c i ci c As h flowig gass dos o coai ay chloriad compouds, c i =. Rarragig abov quaio ad subsiuig ci = : c G c dc c G which shows, ha loos of chloriad aliphaic compouds causd by gas laag ca b dscribd by firs ordr iic quaio. Th formula is also ru i cas of ETH. Th procss of o rduciv biodgradaio, icludig looss(firs par of whol procss), ca b dpicd as follows: c c Assumig ha o dgradaio procss ca b dscribd by zro ordr iics, h followig s of ordiary diffrial quaios ca b formulad: Th iiial valus for is qual is bgiig co i h vssl ad for ad is zro. d ( Aalyical soluios of prsd abov quaio ca b wri as follows: ; ; d d d Compariso bw calculad ad masurd ad cos ovr im ar prsd i h figur Th scod par of h rduciv biodgradaio (dchloriaio of followd by dchloriaio of VC) is prsd o schmaic diagram blow: ) l ; ; VC ETH
4 Figur. Chags i ad cos i h bioracor ovr im. xp cis- xp mod mod co, mol 5 im, days Assumig firs ordr racio modl for as wll as VC dgradaio, h followig quaios ca b obaid: d d ETH VC ETH VC ETH VC VC Thir aalyical soluios ca b wri as follows: ETH ( ) d d ( VC ETH ) VC Compariso bw calculad ad masurd valus is prsd i h figur blow.
5 Figur. Chags i, VC ad ETH cos i h bioracor ovr im. co, mol xp VC VC xp ETH ETH xp xp im, days Modl hacm Assumig ha h ra cosas ar proporioal o umbr of microorgaisms aciv i a giv racio a biological aur of procsss may b icorporad. I was addiioally assumd ha chags i populaio of microorgaisms ovr h im follows h logisic quaio. Applyig appropria modificaios o modl quaios rsuld i br modl fi o xprimal daa (fig 5) Figur 5. Chags i, VC ad ETH cos ovr im logisic apporoach xp VC VC xp ETH ETH xp xp Coclusios Rduciv biormdiaio of ca b modld as a s of coscuiv racios. Though firs ordr iics dos o fi wll o xprimal daa, modl ca b furhr hacd. Maig iic cosa proporioal o logisic quaio rsuls i sigifica improvm of modl fi o xprimal daa. Acowldgms This projc was dsigd, maagd ad implmd udr h dircio of h Isiu for Ecology of Idusrial Aras (IETU) ad h Wsighous Savaah Rivr Compay (WSRC) for h Uid Sas Dparm of Ergy (DOE). WSRC providd chical suppor ad srvd as h IETU's cusomr whil Florida Sa Uivrsiy providd projc maagm suppor o h IETU. All paris coopra udr DOE EM-5 Joi Coordiaig Commi for Eviromal Sysms (JCCES) agrm.
Continous 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
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
, 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
( 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
Modeling 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
Poisson 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 =
Software Development Cost Model based on NHPP Gompertz Distribution
Idia Joural of Scic ad Tchology, Vol 8(12), DOI: 10.17485/ijs/2015/v8i12/68332, Ju 2015 ISSN (Pri) : 0974-6846 ISSN (Oli) : 0974-5645 Sofwar Dvlopm Cos Modl basd o NHPP Gomprz Disribuio H-Chul Kim 1* ad
Poisson 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
Adomian 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
The 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
Part 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
1973 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
Chapter 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
MAT3700. 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...
Fourier 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
Research on the Decomposition of the Economic Impact Factors of Air. Pollution in Hubei Province in China
d raioal Cofrc o ducaio, Maagm ad formaio cholog (CM 5) Rsarch o h Dcomposiio of h coomic mpac Facors of Air olluio i Hubi rovic i Chia Luo Jua, a, Aglia N.lchko, b, H Qiga, c Collg of Mahmaics ad Compur
Page 1. Before-After Control-Impact (BACI) Power Analysis For Several Related Populations (With Unknown Variance Matrix) Richard A.
Pag Bfor-Afr Corol-Impac (BACI) Powr Aalysis For Svral Rlad Populaios (Wih Ukow Variac Marix) Richard A. Hirichs Spmbr 0, 00 Cava: This xprimal dsig ool is a idalizd powr aalysis buil upo svral simplifyig
Analysis of TE (Transverse Electric) Modes of Symmetric Slab Waveguide
Adv. Sudis Thor. Phs., Vol. 6,, o. 7, 33-336 Aalsis of T (Trasvrs lcric Mods of Smmric Slab Wavguid arr Rama SPCTC (Spcrum Tcholog Rsarch Group Dparm of lcrical, lcroic ad Ssms girig Naioal Uivrsi of Malasia
The 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
) 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
Web-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
Practice 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
Mathematical 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
Control 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.
Note 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
2 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
ECE351: 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
ANALYTICAL EXPRESSION FOR THE NON-ISOTHERMAL EFFECTIVENESS FACTOR: The n th -order reaction in a slab geometry
ANALYTICAL XPRSSION FOR T NON-ISOTRMAL FFCTIVNSS FACTOR: Th h -ordr racio i a slab gomry riqu Muñoz Tavra Dparm o Biogirig, Ric Uivrsiy, ouso, TX 775-89 USA muoz@ric.du Absrac Th problm o calculaig h civss
(Reference: sections in Silberberg 5 th ed.)
ALE. Atomic Structur Nam HEM K. Marr Tam No. Sctio What is a atom? What is th structur of a atom? Th Modl th structur of a atom (Rfrc: sctios.4 -. i Silbrbrg 5 th d.) Th subatomic articls that chmists
They must have different numbers of electrons orbiting their nuclei. They must have the same number of neutrons in their nuclei.
37 1 How may utros ar i a uclus of th uclid l? 20 37 54 2 crtai lmt has svral isotops. Which statmt about ths isotops is corrct? Thy must hav diffrt umbrs of lctros orbitig thir ucli. Thy must hav th sam
ECEN620: 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
Linear 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
What 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
Mixing 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
Response 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
The 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
8. 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.
Ring 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
The Impact of Separate Processes on Asset Pricing
Th Impac o Spara Procsss o Ass Pricig DECISION SCIENCES INSTITUTE Th impac o spara procsss o aggrga dividds ad cosumpio o ass pricig wih a ails (Full Papr Submissio) Jacky So Uivrsiy o Macau Uivrsiy o
z 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
ELECTROMAGNETIC 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(
Institute 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
A method for calculating the productivity of cable communications networks
IOP Cofrc Sris: Marials Scic ad Eiri PAPER OPEN ACCESS A mhod for calculai h produciviy of cabl commuicaios works o ci his aricl: S N Shuliki al 6 IOP Cof. Sr.: Mar. Sci. E. Rlad co - Prformac Compariso
Session : Plasmas in Equilibrium
Sssio : Plasmas i Equilibrium Ioizatio ad Coductio i a High-prssur Plasma A ormal gas at T < 3000 K is a good lctrical isulator, bcaus thr ar almost o fr lctros i it. For prssurs > 0.1 atm, collisio amog
EEE 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 =
t=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
Phase 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
5. An object moving along an x-coordinate axis with its scale measured in meters has a velocity of 6t
AP CALCULUS FINAL UNIT WORKSHEETS ACCELERATION, VELOCTIY AND POSITION In problms -, drmin h posiion funcion, (), from h givn informaion.. v (), () = 5. v ()5, () = b g. a (), v() =, () = -. a (), v() =
Phys463.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
Triple Play: From De Morgan to Stirling To Euler to Maclaurin to Stirling
Tripl Play: From D Morga to Stirlig To Eulr to Maclauri to Stirlig Augustus D Morga (186-1871) was a sigificat Victoria Mathmaticia who mad cotributios to Mathmatics History, Mathmatical Rcratios, Mathmatical
STK4080/9080 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
Available online at Energy Procedia 4 (2011) Energy Procedia 00 (2010) GHGT-10
Availabl oli at www.scicdirct.com Ergy Procdia 4 (01 170 177 Ergy Procdia 00 (010) 000 000 Ergy Procdia www.lsvir.com/locat/procdia www.lsvir.com/locat/xxx GHGT-10 Exprimtal Studis of CO ad CH 4 Diffusio
Blackbody Radiation. All bodies at a temperature T emit and absorb thermal electromagnetic radiation. How is blackbody radiation absorbed and emitted?
All bodis at a tmpratur T mit ad absorb thrmal lctromagtic radiatio Blackbody radiatio I thrmal quilibrium, th powr mittd quals th powr absorbd How is blackbody radiatio absorbd ad mittd? 1 2 A blackbody
Logistic equation of Human population growth (generalization to the case of reactive environment).
Logisic quaion of Human populaion growh gnralizaion o h cas of raciv nvironmn. Srg V. Ershkov Insiu for Tim aur Exploraions M.V. Lomonosov's Moscow Sa Univrsi Lninski gor - Moscow 999 ussia -mail: srgj-rshkov@andx.ru
Washington State University
he 3 Ktics ad Ractor Dsig Sprg, 00 Washgto Stat Uivrsity Dpartmt of hmical Egrg Richard L. Zollars Exam # You will hav o hour (60 muts) to complt this xam which cosists of four (4) problms. You may us
Probability & Statistics,
Probability & Statistics, BITS Pilai K K Birla Goa Campus Dr. Jajati Kshari Sahoo Dpartmt of Mathmatics BITS Pilai, K K Birla Goa Campus Poisso Distributio Poisso Distributio: A radom variabl X is said
Economics 8723 Macroeconomic Theory Problem Set 2 Professor Sanjay Chugh Spring 2017
Deparme of Ecoomics The Ohio Sae Uiversiy Ecoomics 8723 Macroecoomic Theory Problem Se 2 Professor Sajay Chugh Sprig 207 Labor Icome Taxes, Nash-Bargaied Wages, ad Proporioally-Bargaied Wages. I a ecoomy
Some 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:
UNIT #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
Chapter4 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
Pupil / Class Record We can assume a word has been learned when it has been either tested or used correctly at least three times.
2 Pupi / Css Rr W ssum wr hs b r wh i hs b ihr s r us rry s hr ims. Nm: D Bu: fr i bus brhr u firs hf hp hm s uh i iv iv my my mr muh m w ih w Tik r pp push pu sh shu sisr s sm h h hir hr hs im k w vry
Physics 160 Lecture 3. R. Johnson April 6, 2015
Physics 6 Lcur 3 R. Johnson April 6, 5 RC Circui (Low-Pass Filr This is h sam RC circui w lookd a arlir h im doma, bu hr w ar rsd h frquncy rspons. So w pu a s wav sad of a sp funcion. whr R C RC Complx
Pricing and Hedging of Long-term Futures and Forward Contracts by a Three-Factor Model
CIRJE-F-68 Pricig ad Hdgig of Log-rm Fuurs ad Forward Coracs by a hr-facor Modl Kichiro Shiraya Mizuho-DL Fiacial chology Co. Ld. Akihiko akahashi Uivrsiy of okyo April 009 CIRJE Discussio Paprs ca b dowloadd
Research Article Modelling of Rehydration of Freeze-dried Dumpling Wrapper
Rsarch Joural of Applid Scics, Egirig ad Tchology 1(5): 556-561, 16 DOI:1.196/rjas.1. 683 ISSN: 4-7459; -ISSN: 4-7467 16 axwll Sciific Publicaio Corp. Submid: Spmbr 1, 15 Accpd: Ocobr 3, 15 Publishd: arch
Principles of Humidity Dalton s law
Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid
DTFT Properties. Example - Determine the DTFT Y ( e ) of n. Let. We can therefore write. From Table 3.1, the DTFT of x[n] is given by 1
![DTFT Properties. Example - Determine the DTFT Y ( e ) of n. Let. We can therefore write. From Table 3.1, the DTFT of x[n] is given by 1](/thumbs/79/79094742.jpg "DTFT Properties. Example - Determine the DTFT Y ( e ) of n. Let. We can therefore write. From Table 3.1, the DTFT of x[n] is given by 1")
DTFT Proprtis Exampl - Dtrmi th DTFT Y of y α µ, α < Lt x α µ, α < W ca thrfor writ y x x From Tabl 3., th DTFT of x is giv by ω X ω α ω Copyright, S. K. Mitra Copyright, S. K. Mitra DTFT Proprtis DTFT
Inference of the Second Order Autoregressive. Model with Unit Roots
Ieraioal Mahemaical Forum Vol. 6 0 o. 5 595-604 Iferece of he Secod Order Auoregressive Model wih Ui Roos Ahmed H. Youssef Professor of Applied Saisics ad Ecoomerics Isiue of Saisical Sudies ad Research
Chapter 2 The Poisson Process
Chapr 2 Th oisso rocss 2. Expoial ad oisso disribuios 2... Th Birh Modl I scods, a oal of popl ar bor. Sarig a ay poi i im, wha is h waiig im for h firs birh? I milliscods, a oal of lpho calls arriv a
Log-periodogram regression with odd Fourier frequencies
Log-priodogram rgrssio wih odd Fourir frqucis Erhard Rschhofr Dparm of Saisics ad Opraios Rsarch, Uivrsiy of Via, Ausria Uivrsiässr. 5, Via, Ausria E-mail: rhard.rschhofr@uivi.ac.a Absrac I his papr, a
BMM3553 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
Microscopic 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,
A THREE COMPARTMENT MATHEMATICAL MODEL OF LIVER
A THREE COPARTENT ATHEATICAL ODEL OF LIVER V. An N. Ch. Paabhi Ramacharyulu Faculy of ahmaics, R D collgs, Hanamonda, Warangal, India Dparmn of ahmaics, Naional Insiu of Tchnology, Warangal, India E-ail:
Fourier 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
UNIT III STANDARD DISTRIBUTIONS
UNIT III STANDARD DISTRIBUTIONS Biomial, Poisso, Normal, Gomric, Uiform, Eoial, Gamma disribuios ad hir roris. Prard by Dr. V. Valliammal Ngaiv biomial disribuios Prard by Dr.A.R.VIJAYALAKSHMI Sadard Disribuios
AR(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
(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
An 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
A 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
Review Answers for E&CE 700T02
Review Aswers for E&CE 700T0 . Deermie he curre soluio, all possible direcios, ad sepsizes wheher improvig or o for he simple able below: 4 b ma c 0 0 0-4 6 0 - B N B N ^0 0 0 curre sol =, = Ch for - -
1 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
Midterm 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
Recovery of Valuable Incompletely-Recorded Return- Stroke Current Derivative Signals
Rcovry of Valuabl Icomplly-Rcordd Rur- Srok Curr Drivaiv Sigals Lakmii Prra Elcrical ad Compur Egirig Dparm Ryrso Uivrsiy Toroo, Caada lakmii.prra@ryrso.ca Ali M. Hussi Elcrical ad Compur Egirig Dparm
THE EFFECT OF SHEAR RATE ON APPARENT VISCOSITY FOR DIFFERENT PULP SUSPENSIONS
5h Iraioal Cofrc o Mchaics ad Marials i Dsig THE EFFECT OF SHEAR RATE ON APPARENT VISCOSITY FOR DIFFERENT PULP SUSPENSIONS SYNOPSIS A. Vaz, C. Gil, R. Simõs, J. Silvy Dparamo d Ciêcia Tcologia do Pl da
Review 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. ()
1. 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
Auto-Tuning of PID Controllers for Second Order Unstable Process Having Dead Time
Joural of Chmical Egirig of Jaa, Vol. 3, No. 4,. 486 497, 1999 Rsarch Par Auo-uig of PID Corollrs for Scod Ordr Usabl Procss Havig Dad im HSIAO-PING HUANG AND CHAN-CHENG CHEN Darm of Chmical Egirig, Naioal
F.Y. Diploma : Sem. II [AE/CH/FG/ME/PT/PG] Applied Mathematics
![F.Y. Diploma : Sem. II [AE/CH/FG/ME/PT/PG] Applied Mathematics](/thumbs/89/97771684.jpg "F.Y. Diploma : Sem. II [AE/CH/FG/ME/PT/PG] Applied Mathematics")
F.Y. Diploma : Sem. II [AE/CH/FG/ME/PT/PG] Applied Mahemaics Prelim Quesio Paper Soluio Q. Aemp ay FIVE of he followig : [0] Q.(a) Defie Eve ad odd fucios. [] As.: A fucio f() is said o be eve fucio if
Solution to 1223 The Evil Warden.
Solutio to 1 Th Evil Ward. This is o of thos vry rar PoWs (I caot thik of aothr cas) that o o solvd. About 10 of you submittd th basic approach, which givs a probability of 47%. I was shockd wh I foud
Advanced 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%
Lecture 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 -
Fourier Series and Parseval s Relation Çağatay Candan Dec. 22, 2013
Fourir Sris nd Prsvl s Rlion Çğy Cndn Dc., 3 W sudy h m problm EE 3 M, Fll3- in som dil o illusr som conncions bwn Fourir sris, Prsvl s rlion nd RMS vlus. Q. ps h signl sin is h inpu o hlf-wv rcifir circui
ON H-TRICHOTOMY IN BANACH SPACES
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
Spring 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
Lecture 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
Final 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
5.1 The Nuclear Atom
Sav My Exams! Th Hom of Rvisio For mor awsom GSE ad lvl rsourcs, visit us at www.savmyxams.co.uk/ 5.1 Th Nuclar tom Qustio Papr Lvl IGSE Subjct Physics (0625) Exam oard Topic Sub Topic ooklt ambridg Itratioal
Decline Curves. Exponential decline (constant fractional decline) Harmonic decline, and Hyperbolic decline.
Dlin Curvs Dlin Curvs ha lo flow ra vs. im ar h mos ommon ools for forasing roduion and monioring wll rforman in h fild. Ths urvs uikly show by grahi mans whih wlls or filds ar roduing as xd or undr roduing.
On 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.
EE 350 Signals and Systems Spring 2005 Sample Exam #2 - Solutions
EE 35 Signals an Sysms Spring 5 Sampl Exam # - Soluions. For h following signal x( cos( sin(3 - cos(5 - T, /T x( j j 3 j 3 j j 5 j 5 j a -, a a -, a a - ½, a 3 /j-j -j/, a -3 -/jj j/, a 5 -½, a -5 -½,
EE 434 Lecture 22. Bipolar Device Models
EE 434 Lcur 22 Bipolar Dvic Modls Quiz 14 Th collcor currn of a BJT was masurd o b 20mA and h bas currn masurd o b 0.1mA. Wha is h fficincy of injcion of lcrons coming from h mir o h collcor? 1 And h numbr