THE PRINCIPLE OF THE ACTIVE JMC SCATTERER. Seppo Uosukainen
|
|
- Joleen Porter
- 8 years ago
- Views:
Transcription
1 THE PRINCIPLE OF THE ACTIVE JC SCATTERER Seppo Uoukaie VTT Buildig ad Tapot Ai Hadlig Techology ad Acoutic P. O. Bo 1803, FIN VTT, Filad ABSTRACT The piciple of fomulatig the JC method to poduce ecoday ouce that fuctio a active cattee o a hypothetical catteig uface i etablihed, to be applied, e.g., i cocet hall. The eamiatio i baed o the modified JC method, to eue that the logic doe ot lead to the eed of chagig the pimay ouce. The actively eflectig plae eve a a eample of the JC fomulatio fo the active cattee. The olutio fo the actively eflectig plae wok o the local cotol piciple: each eflectig ubaea eed ifomatio of the pimay field oly at that ubaea. The olutio ca alo apply to piecemeal plaa uface ad to mooth cove uface, appoimately. 1. INTRODUCTION The JC method i uitable fo fomulatig the poblem of active oie cotol with the geeal ytem theoy. oe geeally, the method applie to the ehapig of acoutic o ay othe field [1], [2], [3], to wave ecotuctio [3], ad to wave popagatio poblem [4], [5]. It ame oigiate fom the fit thee pioee of the method: Jeel, agiate, ad Caévet [2] (the JC goup). Uoukaie peeted the modified JC method [6]. The modified JC method diffe fom the oigial oe o that i the fome the pimay ouce ae ot chaged i ay cae. The pupoe of thi pape i to etablih, at a geeal level ad epecially applied to acoutic field, the piciple of fomulatig the JC method to poduce ecoday ouce that fuctio a active cattee o a hypothetical catteig uface. A a eample, a actively eflectig plae i itoduced. The eamiatio i baed o the modified JC method, to eue that the logic doe ot lead to the eed of chagig the pimay ouce. A moe detailed peetatio ha bee give by Uoukaie [7]. 2. ODIFIED JC ETHOD I the oigial ituatio thee i a detemiitic field (of ay type) i which liea opeato L (typically a diffeetial opeato) coect ouce S ad field F via LF = S. (1) Itead of field F, field F i deied, which ca be obtaied fom the oigial field uig opeato a F = F. (2) I the oigial JC method, opeato alo weight the oigial ouce to ouce S. I the modified JC method, the oigial ouce alway emai uchaged. Both i the oigial ad modified JC method, thee i a eed fo additioal ouce S uch that field equatio (1) fo the modified field i valid. The field equatio of deied field F with the oigial ouce uchaged i Joit Baltic-Nodic Acoutic eetig 2004, 8-10 Jue 2004, aieham, Ålad BNA2004-1
2 L F = S + S. (3) The epeio above, togethe with equatio (1) ad (2), yield fo the ecoday ouce i the modified JC method whee S = L F S = LF LF = F, (4) = L( I), (5) whee I i the idetity opeato Geeal fomulatio 3. JC FORULATION OF THE ACTIVE SCATTERER A hypothetical catteig obtacle with it bouday uface A i defied accodig to Figue 1. e 1 1 = 0 1 = 10 A Figue 1. A hypothetical catteig obtacle. The modified field i aumed to be the um of oigial field F ad ome eta field F (catteed field) F = F + F F ( ) = F ( ), whee i a patial coodiate vecto, ad ad ae opeato. It i uppoed that opeato map vecto o the othe ide of uface A, i.e., i iide i outide A if i outide A A if i iide A =, if i at A, ee Figue 1. It i futhe uppoed that eta field F vaihe iide A ad obey the homogeeou field equatio outide A, F = 0 iide A LF = 0 outide A. The latte fomula, togethe with equatio (1) ad (3), implicate that the oly poible place fo the ecoday ouce ae o uface A. (6) (7) (8) Joit Baltic-Nodic Acoutic eetig 2004, 8-10 Jue 2004, aieham, Ålad BNA2004-2
3 The fact that the modified field geeally obey equatio (2) yield = I +, (9) whee opeato opeate o that F ( ) = F ( ). (10) The ecoday ouce, accodig to the modified JC method, ae ow a tated i equatio (4), whee, accodig to equatio (5) ad (9), = L( I) = L, (11) o S ( ) = L F( ) = L F( ). (12) Accodig to equatio (6) ad (8), opeato ha to be of the fom =, (13) 0ε( whee 0 i a cotiuou fuctio of patial coodiate, ε( 1 10 ) i a tep fuctio, ad whee it i uppoed that bouday A i fomed of a cotat 1 uface 1 = 10, ee Figue 1. The ecoday ouce o A ae due to the dicotiuity of at 1 = 10. Equatio (8) ca be witte outide A, utilizig equatio (6) ad (8), a L F ( ) = L F( ) = L 0 F( ) = 0 outide A. (14) Due to the cotiuity of 0, thi mut hold alo at A. Becaue F vaihe iide A, accodig to equatio (8), the equatio above i valid eveywhee, i.e., L F ( ) 0. (15) 0 = Now the ecoday ouce ae, accodig to equatio (12), (13), ad (15), S ( ) = L = L ( 0ε( F ( ) ) = L( 0F ( ) ) ε( + L( ε( ) ( ε( )) F ( ) at A F( ) The fial geeal olutio above deped o the oigial field at A, opeato 0, ad the field opeato opeatig o the tep fuctio at A Applicatio to acoutic field I acoutic field i flowle ad homogeou ideal fluid field F, ouce S, ad opeato L coectig them ae (16) Q0 L = t p F = u q S =, f ρ0 t (17) Joit Baltic-Nodic Acoutic eetig 2004, 8-10 Jue 2004, aieham, Ålad BNA2004-3
4 whee t i time, Q 0 ad ρ 0 ae the compeibility ad the deity of the upetubed fluid, p ad u ae the oud peue ad the paticle velocity of the acoutic field, ad q ad f ae the moopole ad dipole ditibutio pe uit volume. Opeato L opeatig o the tep fuctio yield ow 0 ε( 0 e L ( ε( ) = = δ(, (18) ε( 0 ) 0 e 0 whee δ( 1 10 ) i the Diac delta fuctio ad e i a uit outwad omal vecto o uface A, ee Figue 1. The ecoday ouce ae ow, accodig to equatio (16), (17), ad (18), q S = = δ f 0 e p u e u u ( e e 0 = δ = δ u ( 1 10) p pe ( 1 10) 0 p pi, (19) whee opeato 0 ha bee divided ito two opeato, p opeatig o the oud peue, ad u opeatig o the paticle velocity p p p 0 = u u, (20) u ad whee I i idetic dyadic (I a = a I = a). Itegatig epeio (19) with epect to 1 yield uface ecoday ouce ditibutio S o A a q S = = f u u e p pe = u p u e pi u at A. (21) The olutio above fo the acoutic field deped o the oigial oud peue ad the omal compoet of the oigial paticle velocity at A, ad opeato Reflectig plae Dyadic K poducig the eflectio tafomatio of the oigial field with epect to the plae = 0 ca be peeted a [8] K = I 2e e = e e + e e + e e, (22) y y z z whee e i a uit vecto i -diectio (omal to the eflectig plae), ee Figue 2. The dyadic of the eflectio tafomatio ivet the omal compoet (with epect to the eflectig plae) of the vecto a oppoite without chagig the othe compoet i ay way. The eflectio tafomatio opeate o both the actual field vecto ad coodiate vecto, ee Figue 2. The tafomed field may be itepeted to be caued by a mio image of the oigial ouce with epect to the uface. The tegth of the mio image ad it ditace fom the eflectig uface ae equal to thoe of the oigial ouce. Joit Baltic-Nodic Acoutic eetig 2004, 8-10 Jue 2004, aieham, Ålad BNA2004-4
5 eflectig plae F () F ( K ) K F ( K ) K image d d ouce 0 Figue 2. The effect of the eflectio tafomatio to field vecto F ad co-odiate vecto. If the eflectig uface i ot ideal, the amplitude of the eflected field i malle tha that of the oigial field o the eflectig uface. The eflectio may alo chage the phae of the field. Thi ca be take ito accout with comple eflectio coefficiet R. The eflectio coefficiet mut be popely choe to eue that the eflected field atifie the homogeeou field equatio i the half pace > 0. Oe poibility i to ue a eflectio coefficiet idepedet of the agle of icidece. With a eflectio coefficiet choe a tated above, the eflected acoutic field (ubcipt ) obey ( ) = Rp( K ) ( ) = RK u( K ). p (23) u Accodig to the peetatio of the patial vaiable i the eflectio tafomatio, the popagatio diectio with epect to the omal of the plate i chaged ito the oppoite, emaiig oigial i lateal diectio. Opeato ad, defied i equatio (6), (7), (13), ad (20), ae ow 0 = 0 = = K. ε( ) p u 1 = R K The ecoday ouce deitie, accodig to equatio (21), (22), ad (24), ae ow q uu K u = u e S = = e R e = R at = 0. (25) f p pi pi pe The olutio above wok o the local cotol piciple: the ecoday ouce tegth at ay poit o A deped o the oigial field oly at the ame poit. The plaa ecoday ouce epeio i the equatio above appoimately applie to piecemeal plaa uface ad eve to mooth cove uface. I thoe cae the uit vecto i -diectio ha to be eplaced with a uit vecto omal to the uface. (24) Joit Baltic-Nodic Acoutic eetig 2004, 8-10 Jue 2004, aieham, Ålad BNA2004-5
6 4. CONCLUSIONS The piciple of fomulatig the JC method to poduce ecoday ouce that fuctio a active cattee o a hypothetical catteig uface wa etablihed. The piciple ca be applied, e.g., i the active cotol of the acoutical popetie of cocet hall. The eamiatio wa baed o the modified JC method, to eue that the logic doe ot lead to the eed of chagig the pimay ouce. A a eample of the cattee, a actively eflectig plae wa itoduced. The olutio wok o the local cotol piciple: each eflectig ubaea eed ifomatio of the pimay field oly at that ubaea. The olutio ca alo apply to piecemeal plaa uface ad to mooth cove uface. 5. REFERENCES [1] Jeel,. J.., ad Agevie, O. L. "Active acoutic atteuatio of a comple oie ouce," Ite-Noie 80, Poceedig, iami, Floida, , [2] Jeel,. J.. "Active oie eductio a a epeimetal applicatio of the geeal ytem theoy," Ite- Noie 83, Poceedig, Edibugh, , [3] Illéyi, A., ad Jeel,. "Decodig/ecodig the ouce ifomatio fom/ito oud field: aothe way of udetadig active oie cotol," Ite-Noie 88, Poceedig, Avigo, , [4] Caévet, G. "Acoutic Popagatio i Apeiodic Taitio Laye ad Waveguide," J. Acout. Soc. Am. 67: , [5] agiate, G., ad Chale, S. "Abobig bouday coditio fo acoutic wave ad Huyge piciple," 16th Iteatioal Coge o Acoutic, Poceedig, Wahigto, , [6] Uoukaie, S. "odified JC ethod i Active Cotol of Soud," Acutica Uited with Acta Acutica 83: , [7] Uoukaie, S. "Active Soud Scattee Baed o the JC ethod," J. Soud Vib. 267: , [8] Lidell, I., ethod fo Electomagetic Field Aalyi, Claedo Pe, Ofod, Joit Baltic-Nodic Acoutic eetig 2004, 8-10 Jue 2004, aieham, Ålad BNA2004-6
Two degree of freedom systems. Equations of motion for forced vibration Free vibration analysis of an undamped system
wo degee of feedom systems Equatios of motio fo foced vibatio Fee vibatio aalysis of a udamped system Itoductio Systems that equie two idepedet d coodiates to descibe thei motio ae called two degee of
More informationChapter 30: Magnetic Fields Due to Currents
d Chapte 3: Magnetic Field Due to Cuent A moving electic chage ceate a magnetic field. One of the moe pactical way of geneating a lage magnetic field (.1-1 T) i to ue a lage cuent flowing though a wie.
More informationChapter 12 Static Equilibrium and Elasticity
Chapte Static Equilibium ad Elaticity Coceptual Poblem [SSM] Tue o fale: (a) i 0 i ufficiet fo tatic equilibium to eit. i (b) i 0 i eceay fo tatic equilibium to eit. i (c) I tatic equilibium, the et toque
More informationHANDOUT E.17 - EXAMPLES ON BODE PLOTS OF FIRST AND SECOND ORDER SYSTEMS
Lecture 7,8 Augut 8, 00 HANDOUT E7 - EXAMPLES ON BODE PLOTS OF FIRST AND SECOND ORDER SYSTEMS Example Obtai the Bode plot of the ytem give by the trafer fuctio ( We covert the trafer fuctio i the followig
More informationConfidence Intervals for Linear Regression Slope
Chapter 856 Cofidece Iterval for Liear Regreio Slope Itroductio Thi routie calculate the ample ize eceary to achieve a pecified ditace from the lope to the cofidece limit at a tated cofidece level for
More informationLearning Objectives. Chapter 2 Pricing of Bonds. Future Value (FV)
Leaig Objectives Chapte 2 Picig of Bods time value of moey Calculate the pice of a bod estimate the expected cash flows detemie the yield to discout Bod pice chages evesely with the yield 2-1 2-2 Leaig
More informationUnderstanding Financial Management: A Practical Guide Guideline Answers to the Concept Check Questions
Udestadig Fiacial Maagemet: A Pactical Guide Guidelie Aswes to the Cocept Check Questios Chapte 4 The Time Value of Moey Cocept Check 4.. What is the meaig of the tems isk-etu tadeoff ad time value of
More informationReport 4668-1b 30.10.2010. Measurement report. Sylomer - field test
Report 4668-1b Meaurement report Sylomer - field tet Report 4668-1b 2(16) Contet 1 Introduction... 3 1.1 Cutomer... 3 1.2 The ite and purpoe of the meaurement... 3 2 Meaurement... 6 2.1 Attenuation of
More informationEffect of Unemployment Insurance Tax On Wages and Employment: A Partial Equilibrium Analysis
Effect of Unemployment nuance Tax On Wage and Employment: atial Equilibium nalyi Deegha Raj dhikai, Oklahoma Employment Secuity Commiion ynn Gay, Oklahoma Employment Secuity Commiion Jackie Bun, Texa &
More informationChapter 5 Additional Applications of Newton s Laws
Chapte 5 Additioal Applicatio of Newto Law Coceptual Poble [SSM] Vaiou object lie o the bed of a tuc that i oi alo a taiht hoizotal oad. If the tuc aduall peed up, what foce act o the object to caue the
More informationAnnuities and loan. repayments. Syllabus reference Financial mathematics 5 Annuities and loan. repayments
8 8A Futue value of a auity 8B Peset value of a auity 8C Futue ad peset value tables 8D Loa epaymets Auities ad loa epaymets Syllabus efeece Fiacial mathematics 5 Auities ad loa epaymets Supeauatio (othewise
More informationThe Essence of the Electromagnetic Wave is Not Energy
The Eence of the Electomagnetic Wave i Not Enegy Zeng Qingping Ai Foce Rada Academy Pofeo cienceum@yahoocn Abtact The cutomay opinion i: electic ave o light ave i enegy, TYang expeiment i the intefeence
More informationFinance Practice Problems
Iteest Fiace Pactice Poblems Iteest is the cost of boowig moey. A iteest ate is the cost stated as a pecet of the amout boowed pe peiod of time, usually oe yea. The pevailig maket ate is composed of: 1.
More informationSkills Needed for Success in Calculus 1
Skills Needed fo Success in Calculus Thee is much appehension fom students taking Calculus. It seems that fo man people, "Calculus" is snonmous with "difficult." Howeve, an teache of Calculus will tell
More informationHeat (or Diffusion) equation in 1D*
Heat (or Diffusio) equatio i D* Derivatio of the D heat equatio Separatio of variables (refresher) Worked eamples *Kreysig, 8 th Ed, Sectios.4b Physical assumptios We cosider temperature i a log thi wire
More informationPeriodic Review Probabilistic Multi-Item Inventory System with Zero Lead Time under Constraints and Varying Order Cost
Ameica Joual of Applied Scieces (8: 3-7, 005 ISS 546-939 005 Sciece Publicatios Peiodic Review Pobabilistic Multi-Item Ivetoy System with Zeo Lead Time ude Costaits ad Vayig Ode Cost Hala A. Fegay Lectue
More informationTime Value of Money: The case of Arithmetic and Geometric growth and their Applications
CHAPTER TE SPECIAL TOPICS I FIACE Time Value of Moey: The cae of Aithmetic a Geometic owth a thei Applicatio I. Itouctio Kowlee of how iteet compou i a coetoe of fiace a i iteal i fiacial eciio at the
More informationMoney Math for Teens. Introduction to Earning Interest: 11th and 12th Grades Version
Moey Math fo Tees Itoductio to Eaig Iteest: 11th ad 12th Gades Vesio This Moey Math fo Tees lesso is pat of a seies ceated by Geeatio Moey, a multimedia fiacial liteacy iitiative of the FINRA Ivesto Educatio
More informationBuilding Blocks Problem Related to Harmonic Series
TMME, vol3, o, p.76 Buildig Blocks Problem Related to Harmoic Series Yutaka Nishiyama Osaka Uiversity of Ecoomics, Japa Abstract: I this discussio I give a eplaatio of the divergece ad covergece of ifiite
More informationCooley-Tukey. Tukey FFT Algorithms. FFT Algorithms. Cooley
Cooley Cooley-Tuey Tuey FFT Algorithms FFT Algorithms Cosider a legth- sequece x[ with a -poit DFT X[ where Represet the idices ad as +, +, Cooley Cooley-Tuey Tuey FFT Algorithms FFT Algorithms Usig these
More informationEkkehart Schlicht: Economic Surplus and Derived Demand
Ekkehart Schlicht: Ecoomic Surplus ad Derived Demad Muich Discussio Paper No. 2006-17 Departmet of Ecoomics Uiversity of Muich Volkswirtschaftliche Fakultät Ludwig-Maximilias-Uiversität Müche Olie at http://epub.ub.ui-mueche.de/940/
More informationPricing Strategies of Electronic B2B Marketplaces with Two-Sided Network Externalities
-7695-145-9 $17. c IEEE 1 Poceedig of the 5th Aual Hawaii Iteatioal Cofeece o Sytem Sciece HICSS-5-7695-145-9 $17. IEEE Poceedig of the 5th Hawaii Iteatioal Cofeece o Sytem Sciece - Picig Stategie of Electoic
More informationOn k-connectivity and Minimum Vertex Degree in Random s-intersection Graphs
O k-coectivity ad Miimum Vertex Degree i Radom -Iterectio Graph Ju Zhao Oma Yağa Virgil Gligor CyLab ad Dept. of ECE Caregie Mello Uiverity Email: {juzhao, oyaga, virgil}@adrew.cmu.edu Abtract Radom -iterectio
More informationThe dinner table problem: the rectangular case
The ie table poblem: the ectagula case axiv:math/009v [mathco] Jul 00 Itouctio Robeto Tauaso Dipatimeto i Matematica Uivesità i Roma To Vegata 00 Roma, Italy tauaso@matuiomait Decembe, 0 Assume that people
More informationSoving Recurrence Relations
Sovig Recurrece Relatios Part 1. Homogeeous liear 2d degree relatios with costat coefficiets. Cosider the recurrece relatio ( ) T () + at ( 1) + bt ( 2) = 0 This is called a homogeeous liear 2d degree
More informationTopic 5: Confidence Intervals (Chapter 9)
Topic 5: Cofidece Iterval (Chapter 9) 1. Itroductio The two geeral area of tatitical iferece are: 1) etimatio of parameter(), ch. 9 ) hypothei tetig of parameter(), ch. 10 Let X be ome radom variable with
More informationCHAPTER 4: NET PRESENT VALUE
EMBA 807 Corporate Fiace Dr. Rodey Boehe CHAPTER 4: NET PRESENT VALUE (Assiged probles are, 2, 7, 8,, 6, 23, 25, 28, 29, 3, 33, 36, 4, 42, 46, 50, ad 52) The title of this chapter ay be Net Preset Value,
More informationThe Binomial Multi- Section Transformer
4/15/21 The Bioial Multisectio Matchig Trasforer.doc 1/17 The Bioial Multi- Sectio Trasforer Recall that a ulti-sectio atchig etwork ca be described usig the theory of sall reflectios as: where: Γ ( ω
More information4.4 VOLUME AND SURFACE AREA
160 CHAPTER 4 Geomety 4.4 VOLUME AND SURFACE AREA Textbook Refeence Section 8.4 CLAST OBJECTIVES Calculate volume and uface aea Infe fomula fo meauing geometic figue Select applicable fomula fo computing
More informationSolutions to Problems: Chapter 7
Solution to Poblem: Chapte 7 P7-1. P7-2. P7-3. P7-4. Authoized and available hae LG 2; Baic a. Maximum hae available fo ale Authoized hae 2,000,000 Le: Shae outtanding 1,400,000 Available hae 600,000 b.
More informationUsing Model Checking to Analyze Network Vulnerabilities
Uing Model Checking to Analyze Netwok Vulneabilitie Ronald W. Ritchey Paul Ammann * National Secuity Team Infomation and Softwae Engineeing Depatment Booz Allen & Hamilton Geoge Maon Univeity Fall Chuch,
More informationAN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM
AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,
More informationDerivation of Annuity and Perpetuity Formulae. A. Present Value of an Annuity (Deferred Payment or Ordinary Annuity)
Aity Deivatios 4/4/ Deivatio of Aity ad Pepetity Fomlae A. Peset Vale of a Aity (Defeed Paymet o Odiay Aity 3 4 We have i the show i the lecte otes ad i ompodi ad Discoti that the peset vale of a set of
More informationChapter 6: Variance, the law of large numbers and the Monte-Carlo method
Chapter 6: Variace, the law of large umbers ad the Mote-Carlo method Expected value, variace, ad Chebyshev iequality. If X is a radom variable recall that the expected value of X, E[X] is the average value
More informationSolving Logarithms and Exponential Equations
Solvig Logarithms ad Epoetial Equatios Logarithmic Equatios There are two major ideas required whe solvig Logarithmic Equatios. The first is the Defiitio of a Logarithm. You may recall from a earlier topic:
More informationFramework for Computation Offloading in Mobile Cloud Computing
Famewok fo Computatio Offloadig i Mobile Cloud Computig Deja Kovachev ad Ralf Klamma Depatmet of Ifomatio Sytem ad Databae RWTH Aache Uiveity Abtact The iheetly limited poceig powe ad battey lifetime of
More informationSmall Hydropower Plant with variable speed PM generator
Witold MAZGAJ, Zbigniew SZULAR, Tomaz WĘGEL, Tadeuz SOBCZYK Politechnika Kakowka, ntytut Elektomechanicznych Pzemian Enegii Small Hydopowe Plant with vaiable peed PM geneato Abtact. Thi pape peent a new
More informationVector Calculus: Are you ready? Vectors in 2D and 3D Space: Review
Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.-7. find the vecto defined
More informationStandardized Coefficients
Standadized Coefficient Ta. How do ou decide which of the X ae mot impotant fo detemining? In thi handout, we dicu one poile (and contoveial) anwe to thi quetion - the tandadized egeion coefficient. Fomula.
More informationANNUITIES SOFTWARE ASSIGNMENT TABLE OF CONTENTS... 1 ANNUITIES SOFTWARE ASSIGNMENT... 2 WHAT IS AN ANNUITY?... 2 EXAMPLE 1... 2 QUESTIONS...
ANNUITIES SOFTWARE ASSIGNMENT TABLE OF CONTENTS ANNUITIES SOFTWARE ASSIGNMENT TABLE OF CONTENTS... 1 ANNUITIES SOFTWARE ASSIGNMENT... WHAT IS AN ANNUITY?... EXAMPLE 1... QUESTIONS... EXAMPLE BRANDON S
More information580.439 Course Notes: Nonlinear Dynamics and Hodgkin-Huxley Equations
58.439 Couse Notes: Noliea Dyamics ad Hodgki-Huxley Equatios Readig: Hille (3 d ed.), chapts 2,3; Koch ad Segev (2 d ed.), chapt 7 (by Rizel ad Emetout). Fo uthe eadig, S.H. Stogatz, Noliea Dyamics ad
More informationA probabilistic proof of a binomial identity
A probabilistic proof of a biomial idetity Joatho Peterso Abstract We give a elemetary probabilistic proof of a biomial idetity. The proof is obtaied by computig the probability of a certai evet i two
More informationIncremental calculation of weighted mean and variance
Icremetal calculatio of weighted mea ad variace Toy Fich faf@cam.ac.uk dot@dotat.at Uiversity of Cambridge Computig Service February 009 Abstract I these otes I eplai how to derive formulae for umerically
More informationLesson 17 Pearson s Correlation Coefficient
Outlie Measures of Relatioships Pearso s Correlatio Coefficiet (r) -types of data -scatter plots -measure of directio -measure of stregth Computatio -covariatio of X ad Y -uique variatio i X ad Y -measurig
More informationThe force between electric charges. Comparing gravity and the interaction between charges. Coulomb s Law. Forces between two charges
The foce between electic chages Coulomb s Law Two chaged objects, of chage q and Q, sepaated by a distance, exet a foce on one anothe. The magnitude of this foce is given by: kqq Coulomb s Law: F whee
More informationThe Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C
Geneal Physics - PH Winte 6 Bjoen Seipel The Electic Potential, Electic Potential Enegy and Enegy Consevation Electic Potential Enegy U is the enegy of a chaged object in an extenal electic field (Unit
More informationGauss Law. Physics 231 Lecture 2-1
Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing
More informationA note on profit maximization and monotonicity for inbound call centers
A note on profit maximization and monotonicity for inbound call center Ger Koole & Aue Pot Department of Mathematic, Vrije Univeriteit Amterdam, The Netherland 23rd December 2005 Abtract We conider an
More informationClustering Process to Solve Euclidean TSP
Cluteig Poce to Solve Euclidea TSP Abdulah Faja *Ifomatic Depatmet, Faculty of Egieeig Uiveita Widyatama Badug Idoeia # Faculty of Ifomatio ad Commuicatio Techology Uiveiti Tekikal Malayia Melaka #*abd.faja@gmail.com,
More informationv = x t = x 2 x 1 t 2 t 1 The average speed of the particle is absolute value of the average velocity and is given Distance travelled t
Chapter 2 Motion in One Dimenion 2.1 The Important Stuff 2.1.1 Poition, Time and Diplacement We begin our tudy of motion by conidering object which are very mall in comparion to the ize of their movement
More information1D STEADY STATE HEAT
D SEADY SAE HEA CONDUCION () Pabal alukda Aociate Pofeo Depatment of Mecanical Engineeing II Deli E-mail: pabal@mec.iitd.ac.in Palukda/Mec-IID emal Contact eitance empeatue ditibution and eat flow line
More information3D BUILDING MODEL RECONSTRUCTION FROM POINT CLOUDS AND GROUND PLANS
3D BUILDING MODEL RECONSTRUCTION FROM POINT CLOUDS AND GROUND PLANS George Voelma ad Sader Dijkma Departmet of Geodey Delft Uiverity of Techology The Netherlad g.voelma@geo.tudelft.l KEY WORDS: Buildig
More informationProperties of MLE: consistency, asymptotic normality. Fisher information.
Lecture 3 Properties of MLE: cosistecy, asymptotic ormality. Fisher iformatio. I this sectio we will try to uderstad why MLEs are good. Let us recall two facts from probability that we be used ofte throughout
More informationTrigonometric Form of a Complex Number. The Complex Plane. axis. ( 2, 1) or 2 i FIGURE 6.44. The absolute value of the complex number z a bi is
0_0605.qxd /5/05 0:45 AM Page 470 470 Chapter 6 Additioal Topics i Trigoometry 6.5 Trigoometric Form of a Complex Number What you should lear Plot complex umbers i the complex plae ad fid absolute values
More informationSysteem en Regeltechniek FMT / Mechatronica. Stabiliteit van regelsystemen
Syteem e Regeltechiek FMT / Mechatroica Deel 4: Blok 9: Stabiliteit va regelyteme De PID regelaar i het frequetie omei Gert va Schothort Philip Cetre for Techical Traiig (CTT) Philip Cetre for Iutrial
More informationUniform Rectilinear Motion
Engineeing Mechanics : Dynamics Unifom Rectilinea Motion Fo paticle in unifom ectilinea motion, the acceleation is zeo and the elocity is constant. d d t constant t t 11-1 Engineeing Mechanics : Dynamics
More informationStrategic Remanufacturing Decision in a Supply Chain with an External Local Remanufacturer
Assoiatio fo Ifomatio Systems AIS Eletoi Libay (AISeL) WHICEB 013 Poeedigs Wuha Iteatioal Cofeee o e-busiess 5-5-013 Stategi Remaufatuig Deisio i a Supply Chai with a Exteal Loal Remaufatue Xu Tiatia Shool
More informationPipe Flow Calculations
Pipe Flow Calculation R. Shankar Subramanian epartment o Chemical and Biomolecular Engineering Clarkon Univerity We begin with ome reult that we hall ue when making riction lo calculation or teady, ully
More informationMath 114- Intermediate Algebra Integral Exponents & Fractional Exponents (10 )
Math 4 Math 4- Itermediate Algebra Itegral Epoets & Fractioal Epoets (0 ) Epoetial Fuctios Epoetial Fuctios ad Graphs I. Epoetial Fuctios The fuctio f ( ) a, where is a real umber, a 0, ad a, is called
More informationForces & Magnetic Dipoles. r r τ = μ B r
Foces & Magnetic Dipoles x θ F θ F. = AI τ = U = Fist electic moto invented by Faaday, 1821 Wie with cuent flow (in cup of Hg) otates aound a a magnet Faaday s moto Wie with cuent otates aound a Pemanent
More informationTI-83, TI-83 Plus or TI-84 for Non-Business Statistics
TI-83, TI-83 Plu or TI-84 for No-Buie Statitic Chapter 3 Eterig Data Pre [STAT] the firt optio i already highlighted (:Edit) o you ca either pre [ENTER] or. Make ure the curor i i the lit, ot o the lit
More informationPurchase and rental subsidies in durable-good oligopolies* 1
Hacienda Pública Epañola / Review of Public Economic, 3-(/05): -40 05, Intituto de Etudio Ficale DOI: 0.7866/HPE-RPE.5.. Puchae and ental ubidie in duable-good oligopolie* AMAGOIA SAGASTA JOSÉ M. USATEGUI
More informationChapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere.
Chapte.3 What is the magnitude of a point chage whose electic field 5 cm away has the magnitude of.n/c. E E 5.56 1 11 C.5 An atom of plutonium-39 has a nuclea adius of 6.64 fm and atomic numbe Z94. Assuming
More informationCoordinate Systems L. M. Kalnins, March 2009
Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean
More informationS. Tanny MAT 344 Spring 1999. be the minimum number of moves required.
S. Tay MAT 344 Sprig 999 Recurrece Relatios Tower of Haoi Let T be the miimum umber of moves required. T 0 = 0, T = 7 Iitial Coditios * T = T + $ T is a sequece (f. o itegers). Solve for T? * is a recurrece,
More informationGCSE STATISTICS. 4) How to calculate the range: The difference between the biggest number and the smallest number.
GCSE STATISTICS You should kow: 1) How to draw a frequecy diagram: e.g. NUMBER TALLY FREQUENCY 1 3 5 ) How to draw a bar chart, a pictogram, ad a pie chart. 3) How to use averages: a) Mea - add up all
More informationVISCOSITY OF BIO-DIESEL FUELS
VISCOSITY OF BIO-DIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use
More informationScal abil it y of ANSYS 16 applicat ions and Hardware select ion.
Technical white pape Scal abil it y of ANSYS 16 applicat ion and Hadwae elect ion. On multi-coe and floating point acceleato poceo ytem Table of Content Ab t a ct... 2 Tet configuation detail... 2 Meage
More informationA technical guide to 2014 key stage 2 to key stage 4 value added measures
A technical guide to 2014 key tage 2 to key tage 4 value added meaure CONTENTS Introduction: PAGE NO. What i value added? 2 Change to value added methodology in 2014 4 Interpretation: Interpreting chool
More informationTaking DCOP to the Real World: Efficient Complete Solutions for Distributed Multi-Event Scheduling
Taig DCOP to the Real World: Efficiet Complete Solutios for Distributed Multi-Evet Schedulig Rajiv T. Maheswara, Milid Tambe, Emma Bowrig, Joatha P. Pearce, ad Pradeep araatham Uiversity of Souther Califoria
More informationVoltage ( = Electric Potential )
V-1 of 9 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage
More informationLong-Term Trend Analysis of Online Trading --A Stochastic Order Switching Model
Asia Pacific Maagemet Review (24) 9(5), 893-924 Log-Tem Ted Aalysis of Olie Tadig --A Stochastic Ode Switchig Model Shalig Li * ad Zili Ouyag ** Abstact Olie bokeages ae eplacig bokes ad telephoes with
More informationFLUID MECHANICS. TUTORIAL No.4 FLOW THROUGH POROUS PASSAGES
FLUID MECHANICS TUTORIAL No.4 FLOW THROUGH POROUS PASSAGES In thi tutorial you will continue the work on laminar flow and develop Poieuille' equation to the form known a the Carman - Kozeny equation. Thi
More informationGraphs of Equations. A coordinate system is a way to graphically show the relationship between 2 quantities.
Gaphs of Equations CHAT Pe-Calculus A coodinate sstem is a wa to gaphicall show the elationship between quantities. Definition: A solution of an equation in two vaiables and is an odeed pai (a, b) such
More informationIlona V. Tregub, ScD., Professor
Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation
More informationOverview on S-Box Design Principles
Overview o S-Box Desig Priciples Debdeep Mukhopadhyay Assistat Professor Departmet of Computer Sciece ad Egieerig Idia Istitute of Techology Kharagpur INDIA -721302 What is a S-Box? S-Boxes are Boolea
More informationOutput Analysis (2, Chapters 10 &11 Law)
B. Maddah ENMG 6 Simulatio 05/0/07 Output Aalysis (, Chapters 10 &11 Law) Comparig alterative system cofiguratio Sice the output of a simulatio is radom, the comparig differet systems via simulatio should
More informationOn the Optimality and Interconnection of Valiant Load-Balancing Networks
O the Optimality ad Itecoectio of Valiat Load-Balacig Netwoks Moshe Babaioff ad Joh Chuag School of Ifomatio Uivesity of Califoia at Bekeley Bekeley, Califoia 94720 4600 {moshe,chuag}@sims.bekeley.edu
More informationOptical Illusion. Sara Bolouki, Roger Grosse, Honglak Lee, Andrew Ng
Optical Illuion Sara Bolouki, Roger Groe, Honglak Lee, Andrew Ng. Introduction The goal of thi proect i to explain ome of the illuory phenomena uing pare coding and whitening model. Intead of the pare
More informationOur aim is to show that under reasonable assumptions a given 2π-periodic function f can be represented as convergent series
8 Fourier Series Our aim is to show that uder reasoable assumptios a give -periodic fuctio f ca be represeted as coverget series f(x) = a + (a cos x + b si x). (8.) By defiitio, the covergece of the series
More informationHow To Solve The Homewor Problem Beautifully
Egieerig 33 eautiful Homewor et 3 of 7 Kuszmar roblem.5.5 large departmet store sells sport shirts i three sizes small, medium, ad large, three patters plaid, prit, ad stripe, ad two sleeve legths log
More informationIrreducible polynomials with consecutive zero coefficients
Irreducible polyomials with cosecutive zero coefficiets Theodoulos Garefalakis Departmet of Mathematics, Uiversity of Crete, 71409 Heraklio, Greece Abstract Let q be a prime power. We cosider the problem
More informationMore examples for Hypothesis Testing
More example for Hypothei Tetig Part I: Compoet 1. Null ad alterative hypothee a. The ull hypothee (H 0 ) i a tatemet that the value of a populatio parameter (mea) i equal to ome claimed value. Ex H 0:
More informationMechanics 1: Motion in a Central Force Field
Mechanics : Motion in a Cental Foce Field We now stud the popeties of a paticle of (constant) ass oving in a paticula tpe of foce field, a cental foce field. Cental foces ae ve ipotant in phsics and engineeing.
More informationLecture 16: Color and Intensity. and he made him a coat of many colours. Genesis 37:3
Lectue 16: Colo and Intensity and he made him a coat of many colous. Genesis 37:3 1. Intoduction To display a pictue using Compute Gaphics, we need to compute the colo and intensity of the light at each
More informationUnit 11 Using Linear Regression to Describe Relationships
Unit 11 Uing Linear Regreion to Decribe Relationhip Objective: To obtain and interpret the lope and intercept of the leat quare line for predicting a quantitative repone variable from a quantitative explanatory
More informationTwo Dimensional FEM Simulation of Ultrasonic Wave Propagation in Isotropic Solid Media using COMSOL
Excerpt from the Proceeding of the COMSO Conference 0 India Two Dimenional FEM Simulation of Ultraonic Wave Propagation in Iotropic Solid Media uing COMSO Bikah Ghoe *, Krihnan Balaubramaniam *, C V Krihnamurthy
More informationProbabilistic Engineering Mechanics. Do Rosenblatt and Nataf isoprobabilistic transformations really differ?
Probabilistic Egieerig Mechaics 4 (009) 577 584 Cotets lists available at ScieceDirect Probabilistic Egieerig Mechaics joural homepage: wwwelseviercom/locate/probegmech Do Roseblatt ad Nataf isoprobabilistic
More informationOverview of some probability distributions.
Lecture Overview of some probability distributios. I this lecture we will review several commo distributios that will be used ofte throughtout the class. Each distributio is usually described by its probability
More informationI. Chi-squared Distributions
1 M 358K Supplemet to Chapter 23: CHI-SQUARED DISTRIBUTIONS, T-DISTRIBUTIONS, AND DEGREES OF FREEDOM To uderstad t-distributios, we first eed to look at aother family of distributios, the chi-squared distributios.
More informationContact Us The College of Management - Academic Studies (COMAS ) Office of International Programs 7 Yitzhak Rabin Blvd. Rishon LeZion 7502501 Israel
m a g o P Study hip e t I ad g i e i D m oga P l a ig atio i p e t A I el fo e a I i Lead g i De Cotact U The College of Maagemet - Academic Studie (COMAS ) Office of Iteatioal Pogam 7 Yitzhak Rabi Blvd.
More informationAP Calculus BC 2003 Scoring Guidelines Form B
AP Calculus BC Scorig Guidelies Form B The materials icluded i these files are iteded for use by AP teachers for course ad exam preparatio; permissio for ay other use must be sought from the Advaced Placemet
More informationLECTURE 13: Cross-validation
LECTURE 3: Cross-validatio Resampli methods Cross Validatio Bootstrap Bias ad variace estimatio with the Bootstrap Three-way data partitioi Itroductio to Patter Aalysis Ricardo Gutierrez-Osua Texas A&M
More informationINFORMATION Technology (IT) infrastructure management
IEEE TRANSACTIONS ON CLOUD COMPUTING, VOL. 2, NO. 1, MAY 214 1 Buine-Driven Long-term Capacity Planning for SaaS Application David Candeia, Ricardo Araújo Santo and Raquel Lope Abtract Capacity Planning
More informationNow here is the important step
LINEST i Excel The Excel spreadsheet fuctio "liest" is a complete liear least squares curve fittig routie that produces ucertaity estimates for the fit values. There are two ways to access the "liest"
More informationLecture 13. Lecturer: Jonathan Kelner Scribe: Jonathan Pines (2009)
18.409 A Algorithmist s Toolkit October 27, 2009 Lecture 13 Lecturer: Joatha Keler Scribe: Joatha Pies (2009) 1 Outlie Last time, we proved the Bru-Mikowski iequality for boxes. Today we ll go over the
More informationBreakeven Holding Periods for Tax Advantaged Savings Accounts with Early Withdrawal Penalties
Beakeve Holdig Peiods fo Tax Advataged Savigs Accouts with Ealy Withdawal Pealties Stephe M. Hoa Depatmet of Fiace St. Boavetue Uivesity St. Boavetue, New Yok 4778 Phoe: 76-375-209 Fax: 76-375-29 e-mail:
More informationPhysics 235 Chapter 5. Chapter 5 Gravitation
Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus
More informationSAMPLE QUESTIONS FOR FINAL EXAM. (1) (2) (3) (4) Find the following using the definition of the Riemann integral: (2x + 1)dx
SAMPLE QUESTIONS FOR FINAL EXAM REAL ANALYSIS I FALL 006 3 4 Fid the followig usig the defiitio of the Riema itegral: a 0 x + dx 3 Cosider the partitio P x 0 3, x 3 +, x 3 +,......, x 3 3 + 3 of the iterval
More informationWorked Examples. v max =?
Exaple iction + Unifo Cicula Motion Cicula Hill A ca i diing oe a ei-cicula hill of adiu. What i the fatet the ca can die oe the top of the hill without it tie lifting off of the gound? ax? (1) Copehend
More information