principles, scales and applications
|
|
|
- Johnathan Nicholson
- 6 years ago
- Views:
Transcription
1 Ippen Lecure Kul Lumpur 207 Cellulr Auom n ecohydrulcs modelng: prncples scles nd pplcons Quwen Chen Nnng Hydrulc Reserch Insue Chn
2 PhD Progrm Rver Hydrulcs Por cos nd offshore. Wer resources Hydro-power engneerng Hydrulc srucures NHRI 00 km 5 km 50k m 80 km Chn Nonl Hydrulc Reserch Insue 300 km Nnng Hydrulc Reserch Insue MWR MOT NEA
3 . Prncples n connuous world Connuy nd homogeney n hydrodynmcs V ( ) 2 V V F P V V c c c c c c c u v w Dx D ( ) 2 y D 2 z S f 2 R c x y y x y z 0
4 . Prncples n dsconnuous world Peso-connuy nd homogeney n eco-dynmcs r() r mx C K C dn N rn( ) d K s Mchels-Menen Logsc growh dn d dp d rn NP cp NP Lok-Volerr S.E. Jorgensen Fund. of Ecol. Mod. 994 W.S. Gurney & R. Nsbe Ecol. Dyn. 998
5 . Prncples n dsconnuous world Fcs of quc eco-dynmcs: dsconnuy & heerogeney Dscree se: presence/bsence Locl vs. globl nercons Spl heerogeney Dsconnuous reproducon Dsconnuous predon
6 . Prncples n dsconnuous world Chllenges n lnkng flud dynmcs & eco-dynmcs Dscree se Indvdul dfference Locl nercons Innovve soluon o eco-hydrulcs modellng Cellulr uom: dscree n me nd spce reproduce complex spl-emporl dynmc perns by some smple locl nercon rules beween cells. f ( ) Indvdul bsed: descrbe ndvdul properes & behvours nercons beween ndvduls ndvdul & envronmens. Node (x y ) Node (x + y + ) Node (x + + y + + ) Node (x + y + ) y x (x y ) (x - y - )
7 A mhemcl sysem dscree n spce nd me 2 Conss of regulr lce of cells (uomon) 3 Ech cell hs fne possble ses 4 Cell se updes ccordng o locl nercons 5 Globl complex perns emerge hrough evoluons ) ( f ) ( f Locl behvours Splly explc Pchy phenomen Cellulr Auom. Prncples n dsconnuous world
8 . Prncples n dsconnuous world Cellulr Auom: neghbor scheme D Moore Von Neumnn 2D Moore Exended Moore Lce gs Trngulr Hexgon Mrgolus
9 . Prncples n dsconnuous world Cellulr Auom: nl condon In close uom nl condon s no sensve due o memoryless In open uom exernl governng fcor re ncorpored nl condon mus be correcly se Cellulr Auom: boundry condons In modellng prcce CA mus be fne nd hve boundres b b 0 b 0 Perod boundry Fxed boundry b b c c d b d Adbc boundry Reflecon boundry
![) ( f f: evoluon rules defne cell updng Sochsc Deermnsc Hybrd Usully olsc or ouer olsc rule re used ] [](/docs-images/80/81570782/images/10-0.jpg "~ ~ n kn k n f C n n k n f C ) ( Cellulr Auom: evoluon rules.")
10 ) ( f f: evoluon rules defne cell updng Sochsc Deermnsc Hybrd Usully olsc or ouer olsc rule re used ] [ ~ ~ n kn k n f C n n k n f C ) ( Cellulr Auom: evoluon rules. Prncples n dsconnuous world (Von Neumnn 949)
11 2. Scles n eco-hydrulc model Scles n hydrodynmc model Drec numercl smulon (DNS): x = /2 Kolmogorov lengh scle Lrge eddy smulon (LES): x > /2 x u Reynolds verged N-S smulon (RANS): engneerng scle C r (from Frmn Zl 2002 TUD)
![)] c (cos / 3sn / 3 ) u c / n ( x c ) n ( x ) un ( x](/docs-images/80/81570782/images/12-1.jpg "c ) un ( x ) 2 ( u) ( u) u p u g( ) ( x ) N ( x ) 6")
12 2. Scles n eco-hydrulc model Scles n lce gs model or (wo prcles) (hree prcles) n ( x c ) n ( x ) [ n( x )] c (cos / 3sn / 3 ) u c / n ( x c ) n ( x ) un ( x c ) un ( x ) 2 ( u) ( u) u p u g( ) ( x ) N ( x ) 6 g( ) ( ) 2( ) un un x Boolen se hgh grden Wolfrm 984 Nure 3: ; Wolf-Gldrow 2000 LNM (Wolfrm 984)
13 Populon prey predor 2. Scles n eco-hydrulc model Scles n wo speces dynmc model 800 prey-predor populon dynmcs prey predor : men predon me nervl x: mxmum serchng rdus Qu e l 2008 Eco Inf 3: (cons: 58) Chen nd Myne. 2003SIMPRA : dn d Populon dynmcs Prey Predor rn NP dp d cp NP No x!! 0
14 2. Scles n eco-hydrulc model Scles n wo speces dynmc model Scenro Scenro 2 Men Sdv. Men Sdv. Prey Predor CA revels he embedded srucure sbly Improper spl scle ( x) crees refc perns Chen nd Myne. 2003SIMPRA :
15 2. Scles n eco-hydrulc model Herrchc scles n quc ecosysem Top Down Level + Level 0 BU Level - P.S. Gller e l. 994 Aquc ecology J. Wu & Dvd J.L. Eco Mod 53: 7-26
16 2. Scles n eco-hydrulc model Scles denfcon nd couplng Spl scle nlyss (Gussn feld) ( ) e x x x 0 0 ( x/ L) x x+x : correlon beween wo spl cells L: chrcersc scle of suded sysem level Spl scle nlyss (Wvele nlyss) 2 ( x) f ( x) g( x ) dx 2 ( ) ( ) x dx : scle fcor; : he pon round whch he Wvele s cenred.
17 2. Scles n eco-hydrulc model Scles denfcon nd couplng Hgh frequency componens: Upsclng Smple vergng: Weghed vergng: Power vergng: A( ) N N A( ) A( E') p( E') de' N p A( ) [ A ] N A p Low frequency componens: Downsclng Use up level componens s consrn o he dynmcs of he suded level f ( Neb For B ) Chen e l JHI8(3): ; Chen e l Eco Mod 99(): 73-82
18 3. Applcons n ecohydrulcs Rprn vegeon dynmcs Groundwer Anoxc/Oxc Lnd Inerfce Wer Zhu e l. Nure Geoscence
19 3. Applcons n ecohydrulcs Rprn vegeon dynmcs: flow pln dynmcs Source? N Y Y Norml growh Wek compeor? N Spce? Dormn Bomss+? Y N N N Germnon? Y Sress? Y Sress response Bomss Morly Compeon Wer level velocy Roughness Flow module Updng vegeon N Bomss * Y Colonze Bomss +
20 3. Applcons n ecohydrulcs Rprn vegeon dynmcs flow sress lg by( ) Y( ) / K Y( ) Lgh sress Growh re s < curren growh re Y ( ) ( loss) Y( ) Mddle sress Bomss loss bs sgn( r) sgn( r) ( loss) Y( ) 2 Bomss loss & cern morly Srong sress Ye F. e l. 200 Eco. Info. 5: 08-4 Lu R. e l. 204Scenfc Repor 4: 5507
21 3. Applcons n ecohydrulcs Rprn vegeon dynmcs speces compeon C Bwek Bsrong C B wek C wek B srong C srong srong wek = bomss chnge of wek compeng speces = source consumpon re of wek speces = bomss chnge of wek compeng speces = source consumpon re of srong speces Rprn vegeon dynmcs speces colonzon Ech speces hs mxmum colonzon exend dependng on speces physology nd fled survey resuls
22 3. Applcons n ecohydrulcs Flow Vegeon nercon To ech CA cell defne L b x c y 2 L bx c y 2 Lm m bm x cm y 2 k (xy) To ech CA cell he hydro-envron effec f ( cell) f ( x y) f ( ) L( ) f ( ) L( ) f ( k) L( k) where f: hydro-envronmen fcor nd ssumng homogenous n he cell Summer flood Boom roughness Flow velocy
23 3. Applcons n ecohydrulcs Vegeon Flow nercon Mehod d C d g( n n ) b R pln /3 2 ( k ) z( k ) Mehod 2 FD CdU 2 2 ( k) 3 S z ( k ) JFK Bes Suden Pper IAHR 2009 Vncouver Mehod 3 FD C du 2 2
24 3. Applcons n ecohydrulcs Vegeon Flow nercon p 2.. p.. 3 Rough ( P) rough ( ) n node cell n re() re(). n
25 3. Applcons n ecohydrulcs Flow Pln f () f ( x y ) pln pln c c f ( ) L f ( ) L f ( k) L hydro hydro hydro k Flow edge Tensn polygon Flow node Pln node Ye F. e l. 203 Ecohydrology 6(4): ( x yk xk y ) ( y yk ) x ( xk x ) y L ( x y) 2k ( xk y x yk ) ( yk y ) x ( x xk ) y L ( x y) 2k ( x y x y ) ( y y ) x ( x x ) y Lk ( x y) 2k Pln Flow 8 fhydro ( ) f pln ( n) w( n) n2 wn ( ) / n k
26 3. Applcons n ecohydrulcs Rprn vegeon dynmcs sudy re N Locon Mddle rech of Lng Rver: N 0 25 E Flow condon Flow drecon Pln smplng rnsecs 200 m Hgh ground Chnnel shelf nd brs ~200.2 :20~3720m 3 Vegeon survey Severl rnsecs were surveyed ech rnsec hve 5 squres n S shpe: Rumex Mrmus: Ner wer vergely 3/m 2 relvely ll. Leonurus Heerophyllus: ner he bnk wy from he wer. vergely /m 2 Polygonum Hydropper: In beween vergely 32/m 2 ~35/m 2
27 3. Applcons n ecohydrulcs Rprn vegeon dynmcs modeled speces R. Mrmus P. Hydropper L. Heerophyllus Rumex mrmus Polygonum hydropper Leonurus heerophyllus
28 3. Applcons n ecohydrulcs Rprn vegeon dynmcs flow sress Bomss (g) P. hydropper =824 b=0.2 K= Tme (d) Trnsform o dscree form: Y( ) by( ) Y( ) / K Y( ) Survvl re R. Mrmus P. Hydropper Survvl re Inundon dys Inundon dys
29 3. Applcons n ecohydrulcs Rprn vegeon dynmcs he scles Rpley L funcon x = r/2 = 9 hours
30 Relve wer level 3. Applcons n ecohydrulcs P. hydropper dynmcs n 200 model vldon Relve wer level 200 Enre re Sprng flood
31 I. D. P. C. I. D. P. C. I. D. P. C. I. D. P. C. 3. Applcons n ecohydrulcs P. hydropper rnsec n 200 model vldon Legend: (bove x-xs) smuled mesured
32 Relve wer level 3. Applcons n ecohydrulcs R. mrmus dynmcs n 200 model vldon Relve wer level 200 Enre re Prolonged drough Sprng flood
33 I. D. P. C. I. D. P. C. I. D. P. C. I. D. P. C. 3. Applcons n ecohydrulcs R. mrmus rnsec n 200 model vldon Dsnce (m) Dsnce (m) Dsnce (m) Dsnce (m) Legend: (bove x-xs) smuled mesured
34 3. Applcons n ecohydrulcs Rprn vegeon dynmcs model comprson log ( Y) w w.3704 mw mw d Y: coverge of vegeon (P. hydropper ) by he end of growh perod; : ro of nundon me; mw: mxmum nundon me; w: verged nundon deph; d: ground wer deph. C. Cmporele & Rdolf L. WRR 42: 045
35 3. Applcons n ecohydrulcs CA model Ssc model 50 m 50 m Legend: Chnnel shelf nd brs Flow drecon Smpled rnsecs: Locon nd lengh of pln bel Qudrs wh <5% cover Smuled percen cover: 0% 00%
36 3. Applcons n ecohydrulcs CA model Ssc model 50 m 50 m Legend: Chnnel shelf nd brs Flow drecon Smpled rnsecs: Locon nd lengh of pln bel Qudrs wh <5% cover Smuled percen cover: 0% 00%
37 Relve elevon (m) Relve elevon (m) Relve elevon (m) Relve elevon (m) 3. Applcons n ecohydrulcs Rprn vegeon dynmcs vegeon successon Sprng flood Sprng flood Dry seson We seson Dry seson We seson - -4 Jn Feb Mr Apr My Jun Jul Jn Feb Mr Apr My Jun -Jn -Feb -Mr -Apr -My -Jun -Jul -Jn -Feb -Mr -Apr -My -Jun -Jul Jul 30-2 Sprng flood 30-2 No ppren sprng floods Dry seson We seson - -4 Jn Feb Mr Apr My Jun Jul -JnJn -Feb Feb -Mr Mr -Apr Apr -My My -JunJun -Jul Jul Legend: upper bound consrned by sprng floods lower bound consrned by we seson floods -Jn -Feb -Mr -Apr -My -Jun -Jul -3 0 Dry seson We seson
38 3. Applcons n ecohydrulcs Rprn vegeon dynmcs vegeon successon Ye F. e l. 200 Eco Inf 5: 08-4; Lu R. e l. 204Scenfc Repor 4: 5507
39 3. Applcons n ecohydrulcs Rver mcronverebres nhbn: flow locl movemen N m Hgh ground Chnnel shelf nd brs Velocy Velocy Temperure Temperure Deph 30 Deph Flow drecon Pln smplng rnsecs Flow model Subly & Inercons CA hb Chen e l. 20 Eco. Info 6: Speces presence
40 Bomss (g AFDW m-2 ) 3. Applcons n ecohydrulcs Mcrophyes successon: vercl mxng locl compeon Pomogeon pecnus 400 Chr sper Growh pern Before 968 vrous speces Europhcon 970~989 lge nd Pomogeon pecnus Resoron 990~ Chr sper bck nd domnn Chrophye Pecnus Tme (dys) Chen nd Myne Eco Mod 47: (Cons: 53)
41 3. Applcons n ecohydrulcs Lke lge bloom: flow + wnd drfng lge pchness b 3.5 x 06 R (7.66 NO 0.044*WT 0.4* PO ) / (.2 (NO ) ) C R C 2 2 C C C : 2 hours n lge model; cell sze x: drfng speed Ln e l. 207 Eco. Mod. (submed) y (m) x (m) x 0 7
42 membershp Chl (ug/l) 3. Applcons n ecohydrulcs Cosl lgl bloom: curren lge pchness Delf3D-WAQ numercl module Exernl forcngs fuzzy logc * S + * S N dsnce (m) fuzzy cellulr uom 4 Chlorophyll- concenron (mg/m3) 02-Apr :00:00 7 x S dsnce (m) x L M H BLOOM II RCA Observons TIN (mg/l) Noordwk rnsec dsnce (km) Chen nd Myne 2006 Eco. Mod 99: 73-8 (Cons: 55)
43 3. Applcons n ecohydrulcs Splly-explc evluon of CA model R. Cosnz Ecol. Mod. 989 F F w n [ ] w 2 2 s 2w n w n w F e w e w k ( w) k ( w) s F = 0.66 Chen nd Myne 2003 Eco. Mod 62: (Cons: 42)
44 Fnl remrks () Through herrchcl scle couplng he flud dynmcs s lnked o quc eco-dynmcs (2) The dopon of cellulr uom offers novel pproch o descrbe quc eco-dynmcs feured by spl heerogeney locl nercons nd dscree processes (3) The developed ecohydrulc models provde brod rnge of pplcons wh promsng poenl.
45 The persons & he ph Prof. Arhur Myne Dr. Tony Mnns Ruonn L Fe Ye Koen Blncker Yuqng Ln Ru Hn Xoqng Zhng Qngru Yng
46 For more nformon 34 Huugun NHRI Chn
47
Supporting information How to concatenate the local attractors of subnetworks in the HPFP
n Effcen lgorh for Idenfyng Prry Phenoype rcors of Lrge-Scle Boolen Newor Sng-Mo Choo nd Kwng-Hyun Cho Depren of Mhecs Unversy of Ulsn Ulsn 446 Republc of Kore Depren of Bo nd Brn Engneerng Kore dvnced
ISSN 075-7 : (7) 0 007 C ( ), E-l: ssolos@glco FPGA LUT FPGA EM : FPGA, LUT, EM,,, () FPGA (feldprogrble ge rrs) [, ] () [], () [] () [5] [6] FPGA LUT (Look-Up-Tbles) EM (Ebedded Meor locks) [7, 8] LUT
Hidden Markov Model. a ij. Observation : O1,O2,... States in time : q1, q2,... All states : s1, s2,..., sn
Hdden Mrkov Model S S servon : 2... Ses n me : 2... All ses : s s2... s 2 3 2 3 2 Hdden Mrkov Model Con d Dscree Mrkov Model 2 z k s s s s s s Degree Mrkov Model Hdden Mrkov Model Con d : rnson roly from
MODELLING AND EXPERIMENTAL ANALYSIS OF MOTORCYCLE DYNAMICS USING MATLAB
MODELLING AND EXPERIMENTAL ANALYSIS OF MOTORCYCLE DYNAMICS USING MATLAB P. Florn, P. Vrání, R. Čermá Fculy of Mechncl Engneerng, Unversy of Wes Bohem Asrc The frs pr of hs pper s devoed o mhemcl modellng
Macroscopic quantum effects generated by the acoustic wave in a molecular magnet
Cudnovsky-Fes-09034 Mcroscopc qunum effecs genered by e cousc wve n moleculr mgne Gwng-Hee Km ejong Unv., Kore Eugene M. Cudnovksy Lemn College, CUNY Acknowledgemens D. A. Grnn Lemn College, CUNY Oulne
Background and Motivation: Importance of Pressure Measurements
Imornce of Pressre Mesremens: Pressre s rmry concern for mny engneerng lcons e.g. lf nd form drg. Cvon : Pressre s of fndmenl mornce n ndersndng nd modelng cvon. Trblence: Velocy-Pressre-Grden ensor whch
Comparison between LETKF and EnVAR with observation localization
Comprson beeen LETKF nd EnVAR h observon loclzon * Sho Yoo Msru Kun Kzums Aonsh Se Orguch Le Duc Tuy Kb 3 Tdsh Tsuyu Meeorologcl Reserch Insue JAMSTEC 3 Meeorologcl College 6..7 D Assmlon Semnr n RIKEN/AICS
HEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD
Journal of Appled Mahemacs and Compuaonal Mechancs 3, (), 45-5 HEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD Sansław Kukla, Urszula Sedlecka Insue of Mahemacs,
Existence and Uniqueness Results for Random Impulsive Integro-Differential Equation
Global Journal of Pure and Appled Mahemacs. ISSN 973-768 Volume 4, Number 6 (8), pp. 89-87 Research Inda Publcaons hp://www.rpublcaon.com Exsence and Unqueness Resuls for Random Impulsve Inegro-Dfferenal
Physics 201 Lecture 2
Physcs 1 Lecure Lecure Chper.1-. Dene Poson, Dsplcemen & Dsnce Dsngush Tme nd Tme Inerl Dene Velocy (Aerge nd Insnneous), Speed Dene Acceleron Undersnd lgebrclly, hrough ecors, nd grphclly he relonshps
Review: Transformations. Transformations - Viewing. Transformations - Modeling. world CAMERA OBJECT WORLD CSE 681 CSE 681 CSE 681 CSE 681
Revew: Trnsforons Trnsforons Modelng rnsforons buld cople odels b posonng (rnsforng sple coponens relve o ech oher ewng rnsforons plcng vrul cer n he world rnsforon fro world coordnes o cer coordnes Perspecve
J i-1 i. J i i+1. Numerical integration of the diffusion equation (I) Finite difference method. Spatial Discretization. Internal nodes.
umercal negraon of he dffuson equaon (I) Fne dfference mehod. Spaal screaon. Inernal nodes. R L V For hermal conducon le s dscree he spaal doman no small fne spans, =,,: Balance of parcles for an nernal
THE EXISTENCE OF SOLUTIONS FOR A CLASS OF IMPULSIVE FRACTIONAL Q-DIFFERENCE EQUATIONS
Europen Journl of Mhemcs nd Compuer Scence Vol 4 No, 7 SSN 59-995 THE EXSTENCE OF SOLUTONS FOR A CLASS OF MPULSVE FRACTONAL Q-DFFERENCE EQUATONS Shuyun Wn, Yu Tng, Q GE Deprmen of Mhemcs, Ynbn Unversy,
Numerical Simulations of Femtosecond Pulse. Propagation in Photonic Crystal Fibers. Comparative Study of the S-SSFM and RK4IP
Appled Mhemcl Scences Vol. 6 1 no. 117 5841 585 Numercl Smulons of Femosecond Pulse Propgon n Phoonc Crysl Fbers Comprve Sudy of he S-SSFM nd RK4IP Mourd Mhboub Scences Fculy Unversy of Tlemcen BP.119
Simplified Variance Estimation for Three-Stage Random Sampling
Deprmen of ppled Sscs Johnnes Kepler Unversy Lnz IFS Reserch Pper Seres 04-67 Smplfed rnce Esmon for Three-Sge Rndom Smplng ndres Quember Ocober 04 Smplfed rnce Esmon for Three-Sge Rndom Smplng ndres Quember
Reinforcement Learning for a New Piano Mover s Problem
Renforcemen Lernng for New Pno Mover s Problem Yuko ISHIWAKA Hkode Nonl College of Technology, Hkode, Hokkdo, Jpn Tomohro YOSHIDA Murorn Insue of Technology, Murorn, Hokkdo, Jpn nd Yuknor KAKAZU Reserch
Chapter Lagrangian Interpolation
Chaper 5.4 agrangan Inerpolaon Afer readng hs chaper you should be able o:. dere agrangan mehod of nerpolaon. sole problems usng agrangan mehod of nerpolaon and. use agrangan nerpolans o fnd deraes and
MODEL SOLUTIONS TO IIT JEE ADVANCED 2014
MODEL SOLUTIONS TO IIT JEE ADVANCED Pper II Code PART I 6 7 8 9 B A A C D B D C C B 6 C B D D C A 7 8 9 C A B D. Rhc(Z ). Cu M. ZM Secon I K Z 8 Cu hc W mu hc 8 W + KE hc W + KE W + KE W + KE W + KE (KE
FINANCIAL ECONOMETRICS
FINANCIAL ECONOMETRICS SPRING 07 WEEK IV NONLINEAR MODELS Prof. Dr. Burç ÜLENGİN Nonlner NONLINEARITY EXISTS IN FINANCIAL TIME SERIES ESPECIALLY IN VOLATILITY AND HIGH FREQUENCY DATA LINEAR MODEL IS DEFINED
ANOTHER CATEGORY OF THE STOCHASTIC DEPENDENCE FOR ECONOMETRIC MODELING OF TIME SERIES DATA
Tn Corn DOSESCU Ph D Dre Cner Chrsn Unversy Buchres Consnn RAISCHI PhD Depren of Mhecs The Buchres Acdey of Econoc Sudes ANOTHER CATEGORY OF THE STOCHASTIC DEPENDENCE FOR ECONOMETRIC MODELING OF TIME SERIES
Chapters 2 Kinematics. Position, Distance, Displacement
Chapers Knemacs Poson, Dsance, Dsplacemen Mechancs: Knemacs and Dynamcs. Knemacs deals wh moon, bu s no concerned wh he cause o moon. Dynamcs deals wh he relaonshp beween orce and moon. The word dsplacemen
Origin Destination Transportation Models: Methods
In Jr. of Mhemcl Scences & Applcons Vol. 2, No. 2, My 2012 Copyrgh Mnd Reder Publcons ISSN No: 2230-9888 www.journlshub.com Orgn Desnon rnsporon Models: Mehods Jyo Gup nd 1 N H. Shh Deprmen of Mhemcs,
A capacitor consists of two conducting plates, separated by an insulator. Conduction plates: e.g., Aluminum foil Insulator: air, mica, ceramic, etc
3//7 haper 6 apacors and Inducors Makng preparaon for dynamc crcus, whch hae far more applcaons han he sac crcus we hae learned so far. 6. apacors Sore energy n elecrc feld nsulaor onducng plaes A capacor
DCDM BUSINESS SCHOOL NUMERICAL METHODS (COS 233-8) Solutions to Assignment 3. x f(x)
DCDM BUSINESS SCHOOL NUMEICAL METHODS (COS -8) Solutons to Assgnment Queston Consder the followng dt: 5 f() 8 7 5 () Set up dfference tble through fourth dfferences. (b) Wht s the mnmum degree tht n nterpoltng
Calculus 241, section 12.2 Limits/Continuity & 12.3 Derivatives/Integrals notes by Tim Pilachowski r r r =, with a domain of real ( )
Clculu 4, econ Lm/Connuy & Devve/Inel noe y Tm Plchow, wh domn o el Wh we hve o : veco-vlued uncon, ( ) ( ) ( ) j ( ) nume nd ne o veco The uncon, nd A w done wh eul uncon ( x) nd connuy e he componen
CH.3. COMPATIBILITY EQUATIONS. Continuum Mechanics Course (MMC) - ETSECCPB - UPC
CH.3. COMPATIBILITY EQUATIONS Connuum Mechancs Course (MMC) - ETSECCPB - UPC Overvew Compably Condons Compably Equaons of a Poenal Vecor Feld Compably Condons for Infnesmal Srans Inegraon of he Infnesmal
Research Article Oscillatory Criteria for Higher Order Functional Differential Equations with Damping
Journl of Funcon Spces nd Applcons Volume 2013, Arcle ID 968356, 5 pges hp://dx.do.org/10.1155/2013/968356 Reserch Arcle Oscllory Crer for Hgher Order Funconl Dfferenl Equons wh Dmpng Pegung Wng 1 nd H
Advanced Electromechanical Systems (ELE 847)
(ELE 847) Dr. Smr ouro-rener Topc 1.4: DC moor speed conrol Torono, 2009 Moor Speed Conrol (open loop conrol) Consder he followng crcu dgrm n V n V bn T1 T 5 T3 V dc r L AA e r f L FF f o V f V cn T 4
Minimum Squared Error
Minimum Squred Error LDF: Minimum Squred-Error Procedures Ide: conver o esier nd eer undersood prolem Percepron y i > for ll smples y i solve sysem of liner inequliies MSE procedure y i = i for ll smples
Notes on the stability of dynamic systems and the use of Eigen Values.
Noes on he sabl of dnamc ssems and he use of Egen Values. Source: Macro II course noes, Dr. Davd Bessler s Tme Seres course noes, zarads (999) Ineremporal Macroeconomcs chaper 4 & Techncal ppend, and Hamlon
Minimum Squared Error
Minimum Squred Error LDF: Minimum Squred-Error Procedures Ide: conver o esier nd eer undersood prolem Percepron y i > 0 for ll smples y i solve sysem of liner inequliies MSE procedure y i i for ll smples
4.8 Improper Integrals
4.8 Improper Inegrls Well you ve mde i hrough ll he inegrion echniques. Congrs! Unforunely for us, we sill need o cover one more inegrl. They re clled Improper Inegrls. A his poin, we ve only del wih inegrls
EEM 486: Computer Architecture
EEM 486: Compuer Archecure Lecure 4 ALU EEM 486 MIPS Arhmec Insrucons R-ype I-ype Insrucon Exmpe Menng Commen dd dd $,$2,$3 $ = $2 + $3 sub sub $,$2,$3 $ = $2 - $3 3 opernds; overfow deeced 3 opernds;
The Finite Element Method for the Analysis of Non-Linear and Dynamic Systems
Swss Federal Insue of Page 1 The Fne Elemen Mehod for he Analyss of Non-Lnear and Dynamc Sysems Prof. Dr. Mchael Havbro Faber Dr. Nebojsa Mojslovc Swss Federal Insue of ETH Zurch, Swzerland Mehod of Fne
How to create a. Rain Garden. in 6 easy steps
How o cree Rin Grden in 6 esy seps 1 design Firs nd foremos, his is grden for your yrd. So pick rcive plns h you like. Mos of he plns lised like full sun o pril shde. Rin grdens cn lso work in shdy res,
Dual Approximate Dynamic Programming for Large Scale Hydro Valleys
Dual Approxmae Dynamc Programmng for Large Scale Hydro Valleys Perre Carpener and Jean-Phlppe Chanceler 1 ENSTA ParsTech and ENPC ParsTech CMM Workshop, January 2016 1 Jon work wh J.-C. Alas, suppored
Lecture 4: Trunking Theory and Grade of Service (GOS)
Lecure 4: Trunkng Theory nd Grde of Servce GOS 4.. Mn Problems nd Defnons n Trunkng nd GOS Mn Problems n Subscrber Servce: lmed rdo specrum # of chnnels; mny users. Prncple of Servce: Defnon: Serve user
Experimental Design and the Analysis of Variance
Expermenl Desgn nd he nlyss of Vrnce Comprng > Groups - Numerc Responses Exenson of Mehods used o Compre Groups Independen Smples nd Pred D Desgns Norml nd non-norml d dsruons D Desgn Independen Smples
6. Gas dynamics. Ideal gases Speed of infinitesimal disturbances in still gas
6. Gs dynmics Dr. Gergely Krisóf De. of Fluid echnics, BE Februry, 009. Seed of infiniesiml disurbnces in sill gs dv d, dv d, Coninuiy: ( dv)( ) dv omenum r r heorem: ( ( dv) ) d 3443 4 q m dv d dv llievi
A NEW TECHNIQUE FOR SOLVING THE 1-D BURGERS EQUATION
S19 A NEW TECHNIQUE FOR SOLVING THE 1-D BURGERS EQUATION by Xaojun YANG a,b, Yugu YANG a*, Carlo CATTANI c, and Mngzheng ZHU b a Sae Key Laboraory for Geomechancs and Deep Underground Engneerng, Chna Unversy
Motion in Two Dimensions
Phys 1 Chaper 4 Moon n Two Dmensons adzyubenko@csub.edu hp://www.csub.edu/~adzyubenko 005, 014 A. Dzyubenko 004 Brooks/Cole 1 Dsplacemen as a Vecor The poson of an objec s descrbed by s poson ecor, r The
[ ] 2. [ ]3 + (Δx i + Δx i 1 ) / 2. Δx i-1 Δx i Δx i+1. TPG4160 Reservoir Simulation 2018 Lecture note 3. page 1 of 5
![[ ] 2. [ ]3 + (Δx i + Δx i 1 ) / 2. Δx i-1 Δx i Δx i+1. TPG4160 Reservoir Simulation 2018 Lecture note 3. page 1 of 5](/thumbs/85/92299540.jpg "[ ] 2. [ ]3 + (Δx i + Δx i 1 ) / 2. Δx i-1 Δx i Δx i+1. TPG4160 Reservoir Simulation 2018 Lecture note 3. page 1 of 5")
TPG460 Reservor Smulaon 08 page of 5 DISCRETIZATIO OF THE FOW EQUATIOS As we already have seen, fne dfference appromaons of he paral dervaves appearng n he flow equaons may be obaned from Taylor seres
EVALUATION OF FORCE COEFFICIENTS FOR A 2-D ANGLE SECTION USING REALIZABLE k-ε TURBULENCE MODEL
The Sevenh Asa-Pacfc Conference on Wnd Engneerng, November 8-, 009, Tape, Tawan EVALUATION OF FORCE COEFFICIENTS FOR A -D ANGLE SECTION USING REALIZABLE k-ε TURBULENCE MODEL S. Chra Ganapah, P. Harkrshna,
OPERATOR-VALUED KERNEL RECURSIVE LEAST SQUARES ALGORITHM
3rd Europen Sgnl Processng Conference EUSIPCO OPERATOR-VALUED KERNEL RECURSIVE LEAST SQUARES ALGORITM P. O. Amblrd GIPSAlb/CNRS UMR 583 Unversé de Grenoble Grenoble, Frnce. Kdr LIF/CNRS UMR 779 Ax-Mrselle
Visual Robot Homing using Sarsa(λ), Whole Image Measure, and Radial Basis Function.
Vsul Robo Homng usng Srs(λ, Whole Imge Mesure, nd Rdl Bss Funcon. Abdulrhmn Alhhn, Kevn Burn, Sefn Wermer Hybrd Inellgen Sysems Reserch Group, School of Compung nd echnology, Unversy of Sunderlnd, SR6
2.1 Constitutive Theory
Secon.. Consuve Theory.. Consuve Equaons Governng Equaons The equaons governng he behavour of maerals are (n he spaal form) dρ v & ρ + ρdv v = + ρ = Conservaon of Mass (..a) d x σ j dv dvσ + b = ρ v& +
II The Z Transform. Topics to be covered. 1. Introduction. 2. The Z transform. 3. Z transforms of elementary functions
II The Z Trnsfor Tocs o e covered. Inroducon. The Z rnsfor 3. Z rnsfors of eleenry funcons 4. Proeres nd Theory of rnsfor 5. The nverse rnsfor 6. Z rnsfor for solvng dfference equons II. Inroducon The
Predict Global Earth Temperature using Linier Regression
Predict Globl Erth Temperture using Linier Regression Edwin Swndi Sijbt (23516012) Progrm Studi Mgister Informtik Sekolh Teknik Elektro dn Informtik ITB Jl. Gnesh 10 Bndung 40132, Indonesi 23516012@std.stei.itb.c.id
Motion Feature Extraction Scheme for Content-based Video Retrieval
oon Feure Exrcon Scheme for Conen-bsed Vdeo Rerevl Chun Wu *, Yuwen He, L Zho, Yuzhuo Zhong Deprmen of Compuer Scence nd Technology, Tsnghu Unversy, Bejng 100084, Chn ABSTRACT Ths pper proposes he exrcon
A NEW INTERPRETATION OF INTERVAL-VALUED FUZZY INTERIOR IDEALS OF ORDERED SEMIGROUPS
ScInLhore),7),9-37,4 ISSN 3-536; CODEN: SINTE 8 9 A NEW INTERPRETATION O INTERVAL-VALUED UZZY INTERIOR IDEALS O ORDERED SEMIGROUPS Hdy Ullh Khn, b, Nor Hnz Srmn, Asghr Khn c nd z Muhmmd Khn d Deprmen of
Electromagnetic Transient Simulation of Large Power Transformer Internal Fault
Inernonl Conference on Advnces n Energy nd Envronmenl Scence (ICAEES 5) Elecromgnec Trnsen Smulon of rge Power Trnsformer Inernl Ful Jun u,, Shwu Xo,, Qngsen Sun,c, Huxng Wng,d nd e Yng,e School of Elecrcl
To Possibilities of Solution of Differential Equation of Logistic Function
Arnold Dávd, Frnše Peller, Rená Vooroosová To Possbles of Soluon of Dfferenl Equon of Logsc Funcon Arcle Info: Receved 6 My Acceped June UDC 7 Recommended con: Dávd, A., Peller, F., Vooroosová, R. ().
Magnetostatics Bar Magnet. Magnetostatics Oersted s Experiment
Mgneosics Br Mgne As fr bck s 4500 yers go, he Chinese discovered h cerin ypes of iron ore could rc ech oher nd cerin mels. Iron filings "mp" of br mgne s field Crefully suspended slivers of his mel were
2/20/2013. EE 101 Midterm 2 Review
//3 EE Mderm eew //3 Volage-mplfer Model The npu ressance s he equalen ressance see when lookng no he npu ermnals of he amplfer. o s he oupu ressance. I causes he oupu olage o decrease as he load ressance
Software Reliability Growth Models Incorporating Fault Dependency with Various Debugging Time Lags
Sofwre Relbly Growh Models Incorporng Ful Dependency wh Vrous Debuggng Tme Lgs Chn-Yu Hung 1 Chu-T Ln 1 Sy-Yen Kuo Mchel R. Lyu 3 nd Chun-Chng Sue 4 1 Deprmen of Compuer Scence Nonl Tsng Hu Unversy Hsnchu
Query Data With Fuzzy Information In Object- Oriented Databases An Approach The Semantic Neighborhood Of Hedge Algebras
(IJCSIS) Inernonl Journl of Compuer Scence nd Informon Secury, Vol 9, No 5, My 20 Query D Wh Fuzzy Informon In Obec- Orened Dbses An Approch The Semnc Neghborhood Of edge Algebrs Don Vn Thng Kore-VeNm
Chapter 2 Linear Mo on
Chper Lner M n .1 Aerge Velcy The erge elcy prcle s dened s The erge elcy depends nly n he nl nd he nl psns he prcle. Ths mens h prcle srs rm pn nd reurn bck he sme pn, s dsplcemen, nd s s erge elcy s
Contraction Mapping Principle Approach to Differential Equations
epl Journl of Science echnology 0 (009) 49-53 Conrcion pping Principle pproch o Differenil Equions Bishnu P. Dhungn Deprmen of hemics, hendr Rn Cmpus ribhuvn Universiy, Khmu epl bsrc Using n eension of
INVESTIGATION OF HABITABILITY INDICES OF YTU GULET SERIES IN VARIOUS SEA STATES
Brodogrdnj/Shpuldng Volume 65 Numer 3, 214 Ferd Ckc Muhsn Aydn ISSN 7-215X eissn 1845-5859 INVESTIGATION OF HABITABILITY INDICES OF YTU GULET SERIES IN VARIOUS SEA STATES UDC 629.5(5) Professonl pper Summry
Mechanics Physics 151
Mechancs Physcs 5 Lecure 9 Hamlonan Equaons of Moon (Chaper 8) Wha We Dd Las Tme Consruced Hamlonan formalsm H ( q, p, ) = q p L( q, q, ) H p = q H q = p H = L Equvalen o Lagrangan formalsm Smpler, bu
National Exams December 2015 NOTES: 04-BS-13, Biology. 3 hours duration
Naonal Exams December 205 04-BS-3 Bology 3 hours duraon NOTES: f doub exss as o he nerpreaon of any queson he canddae s urged o subm wh he answer paper a clear saemen of any assumpons made 2 Ths s a CLOSED
Density Matrix Description of NMR BCMB/CHEM 8190
Densy Marx Descrpon of NMR BCMBCHEM 89 Operaors n Marx Noaon Alernae approach o second order specra: ask abou x magnezaon nsead of energes and ranson probables. If we say wh one bass se, properes vary
Let s treat the problem of the response of a system to an applied external force. Again,
Page 33 QUANTUM LNEAR RESPONSE FUNCTON Le s rea he problem of he response of a sysem o an appled exernal force. Agan, H() H f () A H + V () Exernal agen acng on nernal varable Hamlonan for equlbrum sysem
Mechanics Physics 151
Mechancs Physcs 5 Lecure 9 Hamlonan Equaons of Moon (Chaper 8) Wha We Dd Las Tme Consruced Hamlonan formalsm Hqp (,,) = qp Lqq (,,) H p = q H q = p H L = Equvalen o Lagrangan formalsm Smpler, bu wce as
The Mathematics of Harmonic Oscillators
Th Mhcs of Hronc Oscllors Spl Hronc Moon In h cs of on-nsonl spl hronc oon (SHM nvolvng sprng wh sprng consn n wh no frcon, you rv h quon of oon usng Nwon's scon lw: con wh gvs: 0 Ths s sos wrn usng h
Variants of Pegasos. December 11, 2009
Inroducon Varans of Pegasos SooWoong Ryu bshboy@sanford.edu December, 009 Youngsoo Cho yc344@sanford.edu Developng a new SVM algorhm s ongong research opc. Among many exng SVM algorhms, we wll focus on
Energy Storage Devices
Energy Sorage Deces Objece of Lecure Descrbe he consrucon of a capacor and how charge s sored. Inroduce seeral ypes of capacors Dscuss he elecrcal properes of a capacor The relaonshp beween charge, olage,
PARABOLA. moves such that PM. = e (constant > 0) (eccentricity) then locus of P is called a conic. or conic section.
wwwskshieducioncom PARABOLA Le S be given fixed poin (focus) nd le l be given fixed line (Direcrix) Le SP nd PM be he disnce of vrible poin P o he focus nd direcrix respecively nd P SP moves such h PM
Developing Communication Strategy for Multi-Agent Systems with Incremental Fuzzy Model
(IJACSA) Inernonl Journl of Advnced Compuer Scence nd Applcons, Developng Communcon Sregy for Mul-Agen Sysems wh Incremenl Fuzzy Model Sm Hmzeloo, Mnsoor Zolghdr Jhrom Deprmen of Compuer Scence nd Engneerng
September 20 Homework Solutions
College of Engineering nd Compuer Science Mechnicl Engineering Deprmen Mechnicl Engineering A Seminr in Engineering Anlysis Fll 7 Number 66 Insrucor: Lrry Creo Sepember Homework Soluions Find he specrum
Overview of Calculus I
Overview of Clculus I Prof. Jim Swift Northern Arizon University There re three key concepts in clculus: The limit, the derivtive, nd the integrl. You need to understnd the definitions of these three things,
Implementation of Quantized State Systems in MATLAB/Simulink
SNE T ECHNICAL N OTE Implemenaon of Quanzed Sae Sysems n MATLAB/Smulnk Parck Grabher, Mahas Rößler 2*, Bernhard Henzl 3 Ins. of Analyss and Scenfc Compung, Venna Unversy of Technology, Wedner Haupsraße
Numerical Simulation of the Dispersion of a Plume of Exhaust Gases from Diesel and Petrol Engine Vehicles
World Academy of Scence, Engneerng and Technology 67 01 Numercal Smulaon of he Dsperson of a Plume of Exhaus Gases from Desel and Perol Engne Vehcles H. ZAHLOUL, and M. MERIEM-BENZIANE Absrac The obecve
Question Details Int Vocab 1 [ ] Question Details Int Vocab 2 [ ]
![Question Details Int Vocab 1 [ ] Question Details Int Vocab 2 [ ]](/thumbs/92/109283538.jpg "Question Details Int Vocab 1 [ ] Question Details Int Vocab 2 [ ]")
/3/5 Assignmen Previewer 3 Bsic: Definie Inegrls (67795) Due: Wed Apr 5 5 9: AM MDT Quesion 3 5 6 7 8 9 3 5 6 7 8 9 3 5 6 Insrucions Red ody's Noes nd Lerning Gols. Quesion Deils In Vocb [37897] The chnge
22.615, MHD Theory of Fusion Systems Prof. Freidberg Lecture 9: The High Beta Tokamak
.65, MHD Theory of Fusion Sysems Prof. Freidberg Lecure 9: The High e Tokmk Summry of he Properies of n Ohmic Tokmk. Advnges:. good euilibrium (smll shif) b. good sbiliy ( ) c. good confinemen ( τ nr )
Approximate Analytic Solution of (2+1) - Dimensional Zakharov-Kuznetsov(Zk) Equations Using Homotopy
Arcle Inernaonal Journal of Modern Mahemacal Scences, 4, (): - Inernaonal Journal of Modern Mahemacal Scences Journal homepage: www.modernscenfcpress.com/journals/jmms.aspx ISSN: 66-86X Florda, USA Approxmae
Statistics and Probability Letters
Sttstcs nd Probblty Letters 79 (2009) 105 111 Contents lsts vlble t ScenceDrect Sttstcs nd Probblty Letters journl homepge: www.elsever.com/locte/stpro Lmtng behvour of movng verge processes under ϕ-mxng
7.3 Problem 7.3. ~B(~x) = ~ k ~ E(~x)=! but we also have a reected wave. ~E(~x) = ~ E 2 e i~ k 2 ~x i!t. ~B R (~x) = ~ k R ~ E R (~x)=!
7. Problem 7. We hve two semi-innite slbs of dielectric mteril with nd equl indices of refrction n >, with n ir g (n ) of thickness d between them. Let the surfces be in the x; y lne, with the g being
Lecture 9: Dynamic Properties
Shor Course on Molecular Dynamcs Smulaon Lecure 9: Dynamc Properes Professor A. Marn Purdue Unversy Hgh Level Course Oulne 1. MD Bascs. Poenal Energy Funcons 3. Inegraon Algorhms 4. Temperaure Conrol 5.
ADORO TE DEVOTE (Godhead Here in Hiding) te, stus bat mas, la te. in so non mor Je nunc. la in. tis. ne, su a. tum. tas: tur: tas: or: ni, ne, o:
R TE EVTE (dhd H Hdg) L / Mld Kbrd gú s v l m sl c m qu gs v nns V n P P rs l mul m d lud 7 súb Fí cón ví f f dó, cru gs,, j l f c r s m l qum t pr qud ct, us: ns,,,, cs, cut r l sns m / m fí hó sn sí
Robustness Experiments with Two Variance Components
Naonal Insue of Sandards and Technology (NIST) Informaon Technology Laboraory (ITL) Sascal Engneerng Dvson (SED) Robusness Expermens wh Two Varance Componens by Ana Ivelsse Avlés avles@ns.gov Conference
Multi-load Optimal Design of Burner-inner-liner Under Performance Index Constraint by Second-Order Polynomial Taylor Series Method
, 0005 (06) DOI: 0.05/ mecconf/06700005 ICMI 06 Mul-lod Opml Desgn of Burner-nner-lner Under Performnce Index Consrn by Second-Order Polynoml ylor Seres Mehod U Goqo, Wong Chun Nm, Zheng Mn nd ng Kongzheng
Tutorial 4. b a. h(f) = a b a ln 1. b a dx = ln(b a) nats = log(b a) bits. = ln λ + 1 nats. = log e λ bits. = ln 1 2 ln λ + 1. nats. = ln 2e. bits.
Tutoril 4 Exercises on Differentil Entropy. Evlute the differentil entropy h(x) f ln f for the following: () The uniform distribution, f(x) b. (b) The exponentil density, f(x) λe λx, x 0. (c) The Lplce
KRASNOSEL SKII TYPE FIXED POINT THEOREM FOR NONLINEAR EXPANSION
Fixed Point Theory, 13(2012), No. 1, 285-291 http://www.mth.ubbcluj.ro/ nodecj/sfptcj.html KRASNOSEL SKII TYPE FIXED POINT THEOREM FOR NONLINEAR EXPANSION FULI WANG AND FENG WANG School of Mthemtics nd
4. Eccentric axial loading, cross-section core
. Eccentrc xl lodng, cross-secton core Introducton We re strtng to consder more generl cse when the xl force nd bxl bendng ct smultneousl n the cross-secton of the br. B vrtue of Snt-Vennt s prncple we
Midterm Exam. Thursday, April hour, 15 minutes
Economcs of Grow, ECO560 San Francsco Sae Unvers Mcael Bar Sprng 04 Mderm Exam Tursda, prl 0 our, 5 mnues ame: Insrucons. Ts s closed boo, closed noes exam.. o calculaors of an nd are allowed. 3. Sow all
STURM-LIOUVILLE BOUNDARY VALUE PROBLEMS
STURM-LIOUVILLE BOUNDARY VALUE PROBLEMS Throughout, we let [, b] be bounded intervl in R. C 2 ([, b]) denotes the spce of functions with derivtives of second order continuous up to the endpoints. Cc 2
CHM Physical Chemistry I Chapter 1 - Supplementary Material
CHM 3410 - Physicl Chemistry I Chpter 1 - Supplementry Mteril For review of some bsic concepts in mth, see Atkins "Mthemticl Bckground 1 (pp 59-6), nd "Mthemticl Bckground " (pp 109-111). 1. Derivtion
THE PREDICTION OF COMPETITIVE ENVIRONMENT IN BUSINESS
THE PREICTION OF COMPETITIVE ENVIRONMENT IN BUSINESS INTROUCTION The wo dmensonal paral dfferenal equaons of second order can be used for he smulaon of compeve envronmen n busness The arcle presens he
Response 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
THERMODYNAMICS 1. The First Law and Other Basic Concepts (part 2)
Company LOGO THERMODYNAMICS The Frs Law and Oher Basc Conceps (par ) Deparmen of Chemcal Engneerng, Semarang Sae Unversy Dhon Harano S.T., M.T., M.Sc. Have you ever cooked? Equlbrum Equlbrum (con.) Equlbrum
Math 113 Exam 1-Review
Mth 113 Exm 1-Review September 26, 2016 Exm 1 covers 6.1-7.3 in the textbook. It is dvisble to lso review the mteril from 5.3 nd 5.5 s this will be helpful in solving some of the problems. 6.1 Are Between
Math 124B January 24, 2012
Mth 24B Jnury 24, 22 Viktor Grigoryn 5 Convergence of Fourier series Strting from the method of seprtion of vribes for the homogeneous Dirichet nd Neumnn boundry vue probems, we studied the eigenvue probem
Adaptive and Coordinated Traffic Signal Control Based on Q-Learning and MULTIBAND Model
Adpve nd Coordned Trffc Sgnl Conrol Bsed on Q-Lernng nd MULTIBAND Model Shoufeng Lu,. Trffc nd Trnsporon College Chngsh Unversy of Scence nd Technology Chngsh, Chn slusf@gml.com Xmn Lu, nd Shqng D. Shngh
Applied Statistics Qualifier Examination
Appled Sttstcs Qulfer Exmnton Qul_june_8 Fll 8 Instructons: () The exmnton contns 4 Questons. You re to nswer 3 out of 4 of them. () You my use ny books nd clss notes tht you mght fnd helpful n solvng
Mangel, M. and N. Wolf Predator diet breadth and prey population dynamics. Pg in Whales, Whaling, and Ocean Ecosystems (JA Estes, DP
Mngel, M. nd N. Wolf. 26. Predor de bredh nd prey populon dynmcs. Pg 279-285 n Whles, Whlng, nd Ocen Ecosysems (JA Eses, DP Demser, DF Dok, TM Wllms nd RL Brownell, Jr. edors). Unversy of Clforn Press,
Density Matrix Description of NMR BCMB/CHEM 8190
Densy Marx Descrpon of NMR BCMBCHEM 89 Operaors n Marx Noaon If we say wh one bass se, properes vary only because of changes n he coeffcens weghng each bass se funcon x = h< Ix > - hs s how we calculae
e t dt e t dt = lim e t dt T (1 e T ) = 1
Improper Inegrls There re wo ypes of improper inegrls - hose wih infinie limis of inegrion, nd hose wih inegrnds h pproch some poin wihin he limis of inegrion. Firs we will consider inegrls wih infinie
Pen Tip Position Estimation Using Least Square Sphere Fitting for Customized Attachments of Haptic Device
for Cuomed Ahmen of Hp Deve Mno KOEDA nd Mhko KAO Deprmen of Compuer Sene Ful of Informon Sene nd Ar Ok Elero-Communon Unver Kok 30-70, Shjonwe, Ok, 575-0063, JAPA {koed, 0809@oeu.jp} Ar In h pper, mehod
Solubilities and Thermodynamic Properties of SO 2 in Ionic
Solubltes nd Therodync Propertes of SO n Ionc Lquds Men Jn, Yucu Hou, b Weze Wu, *, Shuhng Ren nd Shdong Tn, L Xo, nd Zhgng Le Stte Key Lbortory of Checl Resource Engneerng, Beng Unversty of Checl Technology,