NON-LINEAR CONTROL OF WHEELED MOBILE ROBOTS

Size: px
Start display at page:

Download "NON-LINEAR CONTROL OF WHEELED MOBILE ROBOTS"

Transcription

1 NON-LINEAR CONTROL OF WHEELED MOBILE ROBOTS Maria Isabl Ribiro Pdro Lima Institto Sprior Técnico (IST) Institto d Sistmas Robótica (ISR) A.Roisco Pais, 49- Lisboa PORTUGAL May. all rights rsrd - Pdro Lima, M. Isabl Ribiro

2 Cors Otlin taas PLANEAMENTO DE TAREFAS PLANEAMENTO DE MOVIMENTO mapa global actalização do mapa MAPA DO MUNDO FUSÃO SENSORIAL Trajctória dsjada (pos+l+ac) mapa local Caractrísticas do mio nolnt Dtcção d obstáclos AUTO-LOCALIZAÇÃO (long baslin, short baslin, fatr matching) Trajctória stimada (pos+l+ac) CONDUÇÃO (sgir trajctória /itar obstáclos) CONTROLO Posição /o locidads dsjadas informação procssada a partir dos dados dos snsors Informação niada aos actadors SENSORES Sonar, lasr, isão, ncodrs, giroscópios VEÍCULO ACTUADORES Motors, rodas, hélics, sprf ciis d dflcção - Pdro Lima, M. Isabl Ribiro

3 Gidanc Path Plannr targt path or trajctory obstacls Gidanc joint st points (.g., whl locitis) Joint Controllr oprati on point joint torqs (.g., motor inpts) joint stat fdback Vhicl postr stimat Localization snsor masrmnts GUIDANCE tak tak th th robot robot from from th th crrnt crrnt postr postr to to th th dsird dsird postr, postr, possibly possibly following following a pr-dtrmind pr-dtrmind path path or or trajctory, trajctory, whil whil aoiding aoiding obstacls obstacls - Pdro Lima, M. Isabl Ribiro

4 Gidanc Mthodologis Som Gidanc mthodologis Stat(postr)-fdback mthods: postr stabilization (initial and final postrs gin; no path or trajctory pr-dtrmind; obstacls not considrd; may lad to larg nxpctd paths) trajctory tracking (rqirs pr-plannd path) irtal hicl tracking (rqirs pr-plannd trajctory) Potntial-Fild lik mthods potntial filds (holonomic hicls) gnralizd potntial filds (non-holonomic hicls) modifid potntial filds (non-holonomic hicls) Vctor Fild Histogram (VHF) lik mthods narnss diagram naigation (holonomic hicls) frzon (non-holonomic hicls) NON-LINEAR CONTROL DESIGN FOR MOBILE ROBOTS - Pdro Lima, M. Isabl Ribiro 4

5 Control of Mobil Robots Thr distintic problms: Trajctory Tracking or Postr Tracking Path Following Point Stabilization - Pdro Lima, M. Isabl Ribiro 5

6 Trajctory Tracking Vhicl of nicycl typ x! cosθ y! sinθ θ! ω kinmatic modl z (x,y, θ) ω position and orintation with rspct to a fixd fram linar locity anglar locity Is a simplifid modl, bt Captrs th nonholonomy proprty which charactrizs most WMR and is th cor of th difficltis inold in th control of ths hicls Th trajctory tracking problm for a WMR of th nicycl typ is sally formlatd with th introdction of a irtal rnc hicl to b trackd. rnc hicl y θ y {} B θ x x - Pdro Lima, M. Isabl Ribiro 6

7 Trajctory Tracking Kinmatic modl of th Rfrnc Vhicl x! y! θ! ω cosθ sinθ z (x,y, θ ) ω (t) (t) Bondd Bondd driatis Do not tnd to zro as t tnds to infinity Control Objcti Dri th rrors x x θ, y y, - θ to zro Exprss th rrors in th {B} fram cosθ sinθ sinθ cosθ x x y y θ θ Diffrntiating Introdcing th chang of inpts + ω ω cos - Pdro Lima, M. Isabl Ribiro 7

8 8 - Pdro Lima, M. Isabl Ribiro Trajctory Tracking + + ω ω sin! non-linar dynamic systm control ariabls Qstion? Is it possibl to dsign a fdback law f() sch that th rror conrgs to zro? Is this law linar or non-linar? Two diffrnt soltions: Linar fdback control Nonlinar fdback control

9 9 - Pdro Lima, M. Isabl Ribiro Trajctory Tracking LINEAR FEEDBACK CONTROL + + ω ω sin! linariz abot th qilibrim point + ω ω (t) (t)! linar tim-arying dynamic systm (t) (t) ω ω Assming linar tim inariant dynamic systm Is it possibl to dsign a linar fdback law f() sch that th rror conrgs to zro? Is th dynamic systm controllabl?

10 Trajctory Tracking Γ c ω ω ω If ω th SLIT is non-controllabl th rnc robot at rst k th rror cannot b takn to zro in finit tim othrwis K K K K K K K Kij Chosn by pol placmnt ndtrmind systm closd loop pols (s + ξa)(s + ξas + a ) k k sgn( ) k - Pdro Lima, M. Isabl Ribiro ξa If r tnds to zro, k incrass withoth bond k k k ξa a ωr

11 Trajctory Tracking To aoid th prios problm: Th closd-loop pols dpnd on th als of r and w r closd loop pols (s + ξa)(s + ξas + a ) a + w b k k sgn( r ) k k k k ξ b ξ w w + b + b - Pdro Lima, M. Isabl Ribiro

12 Trajctory Tracking NONLINEAR FEEDBACK CONTROL! ω ω + sin + k k ( 4,w sin ) k (,w ) k 4 positi constant k continos fnction strictly positi in RxR-(,) k continos fnction strictly positi in RxR-(,) S th analogy with th linar contol Proprty: This control globally asymptotically stabilizis th origin dmonstration sing Lyapno stability thory k k 4 ( b,w ) k (,w ) ξ w + b - Pdro Lima, M. Isabl Ribiro

13 Path Following Objcti: Str th hicl at a constant forward spd along a prdfind gomtric path that is gin in a tim-fr paramtrization. θ Path y {} B " θ d x Approach: Th controllr shold compt Th distanc of th hicl to th path Th orintation rror btwn th hicl s main axis and th tangnt to th path Th controllr shold act on th anglar locity to dri both to zro - Pdro Lima, M. Isabl Ribiro

14 Path Following y {} B θ Path " η T η N M θ d x M is th orthogonal projction of th robot s position P on th path M xists and is niqly dfind if th path satisfis som conditions ( P, η T, ηn ) Srrt-Frnt fram moing along th path. η T Th ctor is th tangnt ctor to th path in th closst point to th hicl Th ctor η N is th normal " is th distanc btwn P and M s is th signd crilinar distanc along th path, from som initial path to th point M θ d (s) is th angl btwn th hicl s x-axis and th tang to th path at th point M. c(s) is th path s cratr at th point M, assmd niformly bondd and diffrntiabl θ θ θ is th orintation rror d - Pdro Lima, M. Isabl Ribiro 4

15 Path Following A nw st of stat coordinats for th mobil robot ( s, ", θ) Thy coincid with x,y,θ in th particlar cas whr th path coincids with th x-axis Th rror dynamics can b drid writing th hicl kinmatic modl in th Srrt-Frnt fram:! cos θ s c(s) " "! sinθ! cos θc(s) θ w c(s) " PROBLEM FORMULATION Gin a path in th x-y plan and th mobil robot translational locity, (t), (assmd to b bondd) togthr with its tim-driati d(t)/dt, th path following problm consists of finding a (smooth) fdback control law ω k(s, ", θ,(t)) sch that lim" (t) t lim θ(t) t - Pdro Lima, M. Isabl Ribiro 5

16 Path Following! cos θ s c(s) " "! sin θ! cos θc(s) θ w c(s) " cos θc(s) w c(s)" cos s! θ c(s) " "! sin θ! θ Two diffrnt soltions: Linar fdback control Nonlinar fdback control LINEAR FEEDBACK CONTROL Linariz th dynamics arond th qilibrim point (", θ ) "! (t) (t) θ(t)! θ(t) (t) Linarization of th last two qations - Pdro Lima, M. Isabl Ribiro 6

17 Path Following If (t)ct Th linar systm is CONTROLLABLE ASYMPTOTICALY STABILIZABLE BY LINEAR STATE FEEDBACK Linar stabilizing fdback k k " θ k >, k >! Closd-loop diffrntial qation "! + k "! + k " transformation " "' γ γ t dτ Distanc gon by point M along th path " '' ' + k" + k " s + ξas + a - Pdro Lima, M. Isabl Ribiro Dsird closd-loop characristic qation 7

18 Path Following NONLINEAR FEEDBACK CONTROL cos s! θ c(s) " "! sin θ! θ Nonlinar control law k " sin θ θ k() θ with k > k(. ) continos fnction strictly positi In ordr to ha th two (linar and nonlinar) controllrs bha similarly nar ", θ chos k() k with k k ξa a - Pdro Lima, M. Isabl Ribiro 8

19 Path Following Proprty Undr th assmption lim (t) t th non-linar control sinθ k " θ k() θ asymptotically stabilizs (", θ ) proidd that th hicl s initial configration is sch that " ( ) + θ() < k lim sp(c(s) Condition to garant that -c(s)l rmains positi Th hicl s location along th path is charactrizd by th al of s (th distanc gon along th path) Dpnds on (t) This dgr of frdom can b sd to stabiliz s abot a prscribd al s d - Pdro Lima, M. Isabl Ribiro 9

20 Point Stabilization Gin An arbitrary postr z d (x,y, θ) Find A control law ω k(z z d,t) which stabilizs asymptotically z-z d abot zro, whatr th initial robot s postr z() COROLLARY Thr is no smooth control law k(z) that can sol th point stabilization problm for th considrd class of systms. ALTERNATIVES Smooth (diffrntiabl) tim-arying nonlinar fdback k(z,t) Picwis continos control laws k(z) Tim-arying picwis continos control laws k(z,t) - Pdro Lima, M. Isabl Ribiro

21 Rfrncs C. Candas d Wit, H. Khnnof, C. Samson, O. Sordaln, Nonlinar Control Dsign for Mobil Robots in Rcnt Dlopmnts in Mobil Robots, World Scintific, 99. Rading assignmnt Carlos Candas d Wit, Brno Siciliano and Gorgs Bastin (Eds), "Thory of Robot Control", Pdro Lima, M. Isabl Ribiro

Traffic Flow Analysis (2)

Traffic Flow Analysis (2) Traffic Flow Analysis () Statistical Proprtis. Flow rat distributions. Hadway distributions. Spd distributions by Dr. Gang-Ln Chang, Profssor Dirctor of Traffic safty and Oprations Lab. Univrsity of Maryland,

More information

The Matrix Exponential

The Matrix Exponential Th Matrix Exponntial (with xrciss) 92.222 - Linar Algbra II - Spring 2006 by D. Klain prliminary vrsion Corrctions and commnts ar wlcom! Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial

More information

3 Distance in Graphs. Brief outline of this lecture

3 Distance in Graphs. Brief outline of this lecture Distance in Graphs While the preios lectre stdied jst the connectiity properties of a graph, now we are going to inestigate how long (short, actally) a connection in a graph is. This natrally leads to

More information

Non-Homogeneous Systems, Euler s Method, and Exponential Matrix

Non-Homogeneous Systems, Euler s Method, and Exponential Matrix Non-Homognous Systms, Eulr s Mthod, and Exponntial Matrix W carry on nonhomognous first-ordr linar systm of diffrntial quations. W will show how Eulr s mthod gnralizs to systms, giving us a numrical approach

More information

CPS 220 Theory of Computation REGULAR LANGUAGES. Regular expressions

CPS 220 Theory of Computation REGULAR LANGUAGES. Regular expressions CPS 22 Thory of Computation REGULAR LANGUAGES Rgular xprssions Lik mathmatical xprssion (5+3) * 4. Rgular xprssion ar built using rgular oprations. (By th way, rgular xprssions show up in various languags:

More information

AP Calculus AB 2008 Scoring Guidelines

AP Calculus AB 2008 Scoring Guidelines AP Calculus AB 8 Scoring Guidlins Th Collg Board: Conncting Studnts to Collg Succss Th Collg Board is a not-for-profit mmbrship association whos mission is to connct studnts to collg succss and opportunity.

More information

The example is taken from Sect. 1.2 of Vol. 1 of the CPN book.

The example is taken from Sect. 1.2 of Vol. 1 of the CPN book. Rsourc Allocation Abstract This is a small toy xampl which is wll-suitd as a first introduction to Cnts. Th CN modl is dscribd in grat dtail, xplaining th basic concpts of C-nts. Hnc, it can b rad by popl

More information

(Analytic Formula for the European Normal Black Scholes Formula)

(Analytic Formula for the European Normal Black Scholes Formula) (Analytic Formula for th Europan Normal Black Schols Formula) by Kazuhiro Iwasawa Dcmbr 2, 2001 In this short summary papr, a brif summary of Black Schols typ formula for Normal modl will b givn. Usually

More information

Waves and Vibration in Civil Engineering

Waves and Vibration in Civil Engineering Wavs and Vibration An ntrodction to Wavs and Vibration in ivil Enginring ntrodction to spctral lmnts and soil-strctr intraction Matthias Baitsch Vitnams Grman Univrsity Ho hi Min ity Yvona olová lova Tchnical

More information

CUTTING METHODS AND CARTESIAN ROBOTS KESME YÖNTEMLERİ VE KARTEZYEN ROBOTLAR

CUTTING METHODS AND CARTESIAN ROBOTS KESME YÖNTEMLERİ VE KARTEZYEN ROBOTLAR ournal of Naval Scinc and Enginring 2009, Vol. 5, No.2, pp. 35-42 CUTTING METHODS AND CARTESIAN ROBOTS Asst. Prof. Ugur SIMSIR, Lt.Cdr. Turkish Naval Acady Mchanical Enginring Dpartnt Tuzla, Istanbul,Turkiy

More information

by John Donald, Lecturer, School of Accounting, Economics and Finance, Deakin University, Australia

by John Donald, Lecturer, School of Accounting, Economics and Finance, Deakin University, Australia Studnt Nots Cost Volum Profit Analysis by John Donald, Lcturr, School of Accounting, Economics and Financ, Dakin Univrsity, Australia As mntiond in th last st of Studnt Nots, th ability to catgoris costs

More information

Projections - 3D Viewing. Overview Lecture 4. Projection - 3D viewing. Projections. Projections Parallel Perspective

Projections - 3D Viewing. Overview Lecture 4. Projection - 3D viewing. Projections. Projections Parallel Perspective Ovrviw Lctur 4 Projctions - 3D Viwing Projctions Paralll Prspctiv 3D Viw Volum 3D Viwing Transformation Camra Modl - Assignmnt 2 OFF fils 3D mor compl than 2D On mor dimnsion Displa dvic still 2D Analog

More information

Sharp bounds for Sándor mean in terms of arithmetic, geometric and harmonic means

Sharp bounds for Sándor mean in terms of arithmetic, geometric and harmonic means Qian t al. Journal of Inqualitis and Applications (015) 015:1 DOI 10.1186/s1660-015-0741-1 R E S E A R C H Opn Accss Sharp bounds for Sándor man in trms of arithmtic, gomtric and harmonic mans Wi-Mao Qian

More information

CPU. Rasterization. Per Vertex Operations & Primitive Assembly. Polynomial Evaluator. Frame Buffer. Per Fragment. Display List.

CPU. Rasterization. Per Vertex Operations & Primitive Assembly. Polynomial Evaluator. Frame Buffer. Per Fragment. Display List. Elmntary Rndring Elmntary rastr algorithms for fast rndring Gomtric Primitivs Lin procssing Polygon procssing Managing OpnGL Stat OpnGL uffrs OpnGL Gomtric Primitivs ll gomtric primitivs ar spcifid by

More information

A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES OF MIDDLE EAST TECHNICAL UNIVERSITY ÖMER GÖKSU

A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES OF MIDDLE EAST TECHNICAL UNIVERSITY ÖMER GÖKSU SHAFT TRANSDUCERLESS VECTOR CONTROL OF THE INTERIOR PERMANENT MAGNET MOTOR WITH SPEED AND POSITION ESTIMATION USING HIGH FREQUENCY SIGNAL INJECTION AND FLUX OBSERVER METHODS A THESIS SUBMITTED TO THE GRADUATE

More information

OXYGEN TRANSFER MEASUREMENTS AT SURFACE AERATORS IN WASTE WATER AS BASIS FOR ENERGY SAVING IN AERATION

OXYGEN TRANSFER MEASUREMENTS AT SURFACE AERATORS IN WASTE WATER AS BASIS FOR ENERGY SAVING IN AERATION OXYGEN TRANSFER MEASUREMENTS AT SURFACE AERATORS IN WASTE WATER AS BASIS FOR ENERGY SAVING IN AERATION Ditr Lomp Hochschu Brmrhavn Grmany Ahmt Nuru-Bruns Achim, Grmany ABSTRACT Oxygn transfr masurmnts

More information

ME 612 Metal Forming and Theory of Plasticity. 6. Strain

ME 612 Metal Forming and Theory of Plasticity. 6. Strain Mtal Forming and Thory of Plasticity -mail: azsnalp@gyt.du.tr Makin Mühndisliği Bölümü Gbz Yüksk Tknoloji Enstitüsü 6.1. Uniaxial Strain Figur 6.1 Dfinition of th uniaxial strain (a) Tnsil and (b) Comprssiv.

More information

International Association of Scientific Innovation and Research (IASIR) (An Association Unifying the Sciences, Engineering, and Applied Research)

International Association of Scientific Innovation and Research (IASIR) (An Association Unifying the Sciences, Engineering, and Applied Research) Intrnational Association of Scintific Innovation and Rsarch (IASIR) (An Association Unifing th Scincs, Enginring, and Applid Rsarch) ISSN (Print): 79-000 ISSN (Onlin): 79-009 Intrnational Journal of Enginring,

More information

Constraint-Based Analysis of Gene Deletion in a Metabolic Network

Constraint-Based Analysis of Gene Deletion in a Metabolic Network Constraint-Basd Analysis of Gn Dltion in a Mtabolic Ntwork Abdlhalim Larhlimi and Alxandr Bockmayr DFG-Rsarch Cntr Mathon, FB Mathmatik und Informatik, Fri Univrsität Brlin, Arnimall, 3, 14195 Brlin, Grmany

More information

AN OPTIMAL MARKETING AND ENGINEERING DESIGN MODEL FOR PRODUCT DEVELOPMENT USING ANALYTICAL TARGET CASCADING

AN OPTIMAL MARKETING AND ENGINEERING DESIGN MODEL FOR PRODUCT DEVELOPMENT USING ANALYTICAL TARGET CASCADING Procdings of th TMCE 2004, April 2-6, 2004, Lausann, Switzrland, Editd by Horáth and Xirouchakis 2004 Millprss, Rottrdam, ISBN AN OPTIMAL MARKETING AND ENGINEERING DESIGN MODEL FOR PRODUCT DEVELOPMENT

More information

Policies for Simultaneous Estimation and Optimization

Policies for Simultaneous Estimation and Optimization Policis for Simultanous Estimation and Optimization Migul Sousa Lobo Stphn Boyd Abstract Policis for th joint idntification and control of uncrtain systms ar prsntd h discussion focuss on th cas of a multipl

More information

1754 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 5, MAY 2007

1754 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 5, MAY 2007 1754 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 5, MAY 007 On th Fasibility of Distributd Bamforming in Wirlss Ntworks R. Mudumbai, Studnt Mmbr, IEEE, G. Barriac, Mmbr, IEEE, and U. Madhow,

More information

Whole Systems Approach to CO 2 Capture, Transport and Storage

Whole Systems Approach to CO 2 Capture, Transport and Storage Whol Systms Approach to CO 2 Captur, Transport and Storag N. Mac Dowll, A. Alhajaj, N. Elahi, Y. Zhao, N. Samsatli and N. Shah UKCCS Mting, July 14th 2011, Nottingham, UK Ovrviw 1 Introduction 2 3 4 Powr

More information

Introduction to Finite Element Modeling

Introduction to Finite Element Modeling Introduction to Finit Elmnt Modling Enginring analysis of mchanical systms hav bn addrssd by driving diffrntial quations rlating th variabls of through basic physical principls such as quilibrium, consrvation

More information

On Resilience of Multicommodity Dynamical Flow Networks

On Resilience of Multicommodity Dynamical Flow Networks On Rsilinc of Multicommodity Dynamical Flow Ntworks Gusta Nilsson, Giacomo Como, and Enrico Loisari bstract Dynamical flow ntworks with htrognous routing ar analyzd in trms of stability and rsilinc to

More information

A Theoretical Model of Public Response to the Homeland Security Advisory System

A Theoretical Model of Public Response to the Homeland Security Advisory System A Thortical Modl of Public Rspons to th Homland Scurity Advisory Systm Amy (Wnxuan) Ding Dpartmnt of Information and Dcision Scincs Univrsity of Illinois Chicago, IL 60607 wxding@uicdu Using a diffrntial

More information

Principles of Humidity Dalton s law

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

More information

QUANTITATIVE METHODS CLASSES WEEK SEVEN

QUANTITATIVE METHODS CLASSES WEEK SEVEN QUANTITATIVE METHODS CLASSES WEEK SEVEN Th rgrssion modls studid in prvious classs assum that th rspons variabl is quantitativ. Oftn, howvr, w wish to study social procsss that lad to two diffrnt outcoms.

More information

5 2 index. e e. Prime numbers. Prime factors and factor trees. Powers. worked example 10. base. power

5 2 index. e e. Prime numbers. Prime factors and factor trees. Powers. worked example 10. base. power Prim numbrs W giv spcial nams to numbrs dpnding on how many factors thy hav. A prim numbr has xactly two factors: itslf and 1. A composit numbr has mor than two factors. 1 is a spcial numbr nithr prim

More information

Adverse Selection and Moral Hazard in a Model With 2 States of the World

Adverse Selection and Moral Hazard in a Model With 2 States of the World Advrs Slction and Moral Hazard in a Modl With 2 Stats of th World A modl of a risky situation with two discrt stats of th world has th advantag that it can b natly rprsntd using indiffrnc curv diagrams,

More information

What is a robot? Lecture 2: Robot Basics. Remember the Amigobot? Describing the Amigobot. The Unicycle Model. Modeling Robot Interaction.

What is a robot? Lecture 2: Robot Basics. Remember the Amigobot? Describing the Amigobot. The Unicycle Model. Modeling Robot Interaction. What is a robot? Lectre 2: Basics CS 344R/393R: ics Benjamin Kipers A robot is an intelligent sstem that interacts with the phsical environment throgh sensors and effectors. Toda we discss: Abstraction

More information

Cloud and Big Data Summer School, Stockholm, Aug., 2015 Jeffrey D. Ullman

Cloud and Big Data Summer School, Stockholm, Aug., 2015 Jeffrey D. Ullman Cloud and Big Data Summr Scool, Stockolm, Aug., 2015 Jffry D. Ullman Givn a st of points, wit a notion of distanc btwn points, group t points into som numbr of clustrs, so tat mmbrs of a clustr ar clos

More information

SIMULATION OF THE PERFECT COMPETITION AND MONOPOLY MARKET STRUCTURE IN THE COMPANY THEORY

SIMULATION OF THE PERFECT COMPETITION AND MONOPOLY MARKET STRUCTURE IN THE COMPANY THEORY 1 SIMULATION OF THE PERFECT COMPETITION AND MONOPOLY MARKET STRUCTURE IN THE COMPANY THEORY ALEXA Vasil ABSTRACT Th prsnt papr has as targt to crat a programm in th Matlab ara, in ordr to solv, didactically

More information

Mathematics. Mathematics 3. hsn.uk.net. Higher HSN23000

Mathematics. Mathematics 3. hsn.uk.net. Higher HSN23000 hsn uknt Highr Mathmatics UNIT Mathmatics HSN000 This documnt was producd spcially for th HSNuknt wbsit, and w rquir that any copis or drivativ works attribut th work to Highr Still Nots For mor dtails

More information

The ACES Mission Testing Fundamental Physics with Clocks in Space. L. Cacciapuoti European Space Agency

The ACES Mission Testing Fundamental Physics with Clocks in Space. L. Cacciapuoti European Space Agency Th ACES Mission Tsting Fundamntal Physics with Clocks in Spac L. Cacciapuoti Europan Spac Agncy Atomic Clock Ensmbl in Spac La Thuil 21-28 March 2015 Rncontrs d Moriond - Gravitation 2 Th Columbus modul

More information

Topic # Step Up To Fourth Grade Lesson #3. Lesson Focus: Using an Expanded Algorithm

Topic # Step Up To Fourth Grade Lesson #3. Lesson Focus: Using an Expanded Algorithm Lsson Plans: Wk of 5 11 15 Morning Rot/Basic Facts/Caln Math Writing Workshop M o n Bindrs: /Math; complt on own, thn chck togthr opic # Stp Up o Forth Grad Lsson #3 Lsson Focs: Using an Expandd Algorithm

More information

Incomplete 2-Port Vector Network Analyzer Calibration Methods

Incomplete 2-Port Vector Network Analyzer Calibration Methods Incomplt -Port Vctor Ntwork nalyzr Calibration Mthods. Hnz, N. Tmpon, G. Monastrios, H. ilva 4 RF Mtrology Laboratory Instituto Nacional d Tcnología Industrial (INTI) Bunos irs, rgntina ahnz@inti.gov.ar

More information

AN OPTIMAL MARKETING AND ENGINEERING DESIGN MODEL FOR PRODUCT DEVELOPMENT USING ANALYTICAL TARGET CASCADING

AN OPTIMAL MARKETING AND ENGINEERING DESIGN MODEL FOR PRODUCT DEVELOPMENT USING ANALYTICAL TARGET CASCADING Tools and Mthods of Comptiti Enginring, Editd by Horáth and Xirouchakis 2004 Millprss, Rottrdam, ISBN AN OPTIMAL MARKETING AND ENGINEERING DESIGN MODEL FOR PRODUCT DEVELOPMENT USING ANALYTICAL TARGET CASCADING

More information

Feedback Control of a Nonholonomic Car-like Robot

Feedback Control of a Nonholonomic Car-like Robot Feedback Control of a Nonholonomic Car-like Robot A. De Luca G. Oriolo C. Samson This is the fourth chapter of the book: Robot Motion Planning and Control Jean-Paul Laumond (Editor) Laboratoire d Analye

More information

Testing the gravitational properties of the quantum vacuum within the Solar System

Testing the gravitational properties of the quantum vacuum within the Solar System Tsting th gravitational proprtis of th quantum vacuum within th Solar Systm Dragan Hajdukovic To cit this vrsion: Dragan Hajdukovic. Tsting th gravitational proprtis of th quantum vacuum within th Solar

More information

EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS

EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS 25 Vol. 3 () January-March, pp.37-5/tripathi EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS *Shilpa Tripathi Dpartmnt of Chmical Enginring, Indor Institut

More information

Optics Communications

Optics Communications Optics Communications 84 () 43 436 Contnts lists availabl at ScincDirct Optics Communications journal hompag: www.lsvir.com/locat/optcom Scattring forcs in th focal volum of high numrical aprtur microscop

More information

Monetary Policy Shocks and Stock Returns: Evidence from the British Market

Monetary Policy Shocks and Stock Returns: Evidence from the British Market Montary Policy Shocks and Stock Rtrns: Evidnc from th British Markt A. Grgorio a, A. Kontonikas b*, R. MacDonald b, A. Montagnoli c a Norwich Bsinss School, Univrsity of East Anglia b Dpartmnt of Economics,

More information

SOLUTIONS TO CONCEPTS CHAPTER 19

SOLUTIONS TO CONCEPTS CHAPTER 19 SOLUTIONS TO CONCEPTS CHAPTER 9. Th isal angls mad by th tr with th ys can b calclatd b blow. Hight o th tr AB 2 = A.4 Distanc rom th y OB 5 similarly, B = 2.5 / 8 =.25 C =.8 / 7 =.257 D = 2.8 / =.28 Sinc,

More information

STATEMENT OF INSOLVENCY PRACTICE 3.2

STATEMENT OF INSOLVENCY PRACTICE 3.2 STATEMENT OF INSOLVENCY PRACTICE 3.2 COMPANY VOLUNTARY ARRANGEMENTS INTRODUCTION 1 A Company Voluntary Arrangmnt (CVA) is a statutory contract twn a company and its crditors undr which an insolvncy practitionr

More information

Far Field Estimations and Simulation Model Creation from Cable Bundle Scans

Far Field Estimations and Simulation Model Creation from Cable Bundle Scans Far Fild Estimations and Simulation Modl Cration from Cabl Bundl Scans D. Rinas, S. Nidzwidz, S. Fri Dortmund Univrsity of Tchnology Dortmund, Grmany dnis.rinas@tu-dortmund.d stphan.fri@tu-dortmund.d Abstract

More information

An Adaptive Clustering MAP Algorithm to Filter Speckle in Multilook SAR Images

An Adaptive Clustering MAP Algorithm to Filter Speckle in Multilook SAR Images An Adaptiv Clustring MAP Algorithm to Filtr Spckl in Multilook SAR Imags FÁTIMA N. S. MEDEIROS 1,3 NELSON D. A. MASCARENHAS LUCIANO DA F. COSTA 1 1 Cybrntic Vision Group IFSC -Univrsity of São Paulo Caia

More information

A Path Tracking Algorithm Using Future Prediction Control with Spike Detection for an Autonomous Vehicle Robot

A Path Tracking Algorithm Using Future Prediction Control with Spike Detection for an Autonomous Vehicle Robot Intrnational Journal o Avanc Robotic Systms ARTICLE A Path Tracking Algorithm Using Futur Priction Control with Spik Dtction or an Autonomous Vhicl Robot Rgular Papr Muhamma Aizzat Zakaria, Hairi Zamzuri,*,

More information

Using GPU to Compute Options and Derivatives

Using GPU to Compute Options and Derivatives Introdction Algorithmic Trading has created an increasing demand for high performance compting soltions within financial organizations. The actors of portfolio management and ris assessment have the obligation

More information

Statistical Process Control Based Supervisory Generalized Predictive Control of Thin Film Deposition Processes

Statistical Process Control Based Supervisory Generalized Predictive Control of Thin Film Deposition Processes Jiongha Jin 1 Dpartmnt o Indstrial and Oprations Enginring, Th Univrsity o Michigan, Ann Arbor, MI 48109-2117 -mail: jhjin@mich.d Hairi Go Dpartmnt o Systms and Indstrial Enginring, Th Univrsity o Arizona,

More information

ICES REPORT 15-01. January 2015. The Institute for Computational Engineering and Sciences The University of Texas at Austin Austin, Texas 78712

ICES REPORT 15-01. January 2015. The Institute for Computational Engineering and Sciences The University of Texas at Austin Austin, Texas 78712 ICES REPORT 15-01 January 2015 A locking-fr modl for Rissnr-Mindlin plats: Analysis and isogomtric implmntation via NURBS and triangular NURPS by L. Birao da Viga, T.J.R. Hughs, J. Kindl, C. Lovadina,

More information

Examples. Epipoles. Epipolar geometry and the fundamental matrix

Examples. Epipoles. Epipolar geometry and the fundamental matrix Epipoar gomtry and th fundamnta matrix Epipoar ins Lt b a point in P 3. Lt x and x b its mapping in two imags through th camra cntrs C and C. Th point, th camra cntrs C and C and th (3D points corrspon

More information

GAME THEORY SOLUTIONS USING NEURAL NETWORKS FOR MISSILE GUIDANCE

GAME THEORY SOLUTIONS USING NEURAL NETWORKS FOR MISSILE GUIDANCE GAME THEORY SOLUTIONS USING NEURAL NETWORKS FOR MISSILE GUIDANCE Vnkat Durbha * and S.N. Balakrishnan ** vdkc7@umr.du, bala@umr.du Dartmnt of Mchanical and Arosac Enginring Univrsity of Missouri-Rolla,

More information

An International Journal of the Polish Statistical Association

An International Journal of the Polish Statistical Association STATISTICS IN TRANSITION nw sris An Intrnational Journal of th Polish Statistical Association CONTENTS From th Editor... Submission information for authors... 5 Sampling mthods and stimation CIEPIELA P.,

More information

Architecture of the proposed standard

Architecture of the proposed standard Architctur of th proposd standard Introduction Th goal of th nw standardisation projct is th dvlopmnt of a standard dscribing building srvics (.g.hvac) product catalogus basd on th xprincs mad with th

More information

FEEDBACK CONTROL OF A NONHOLONOMIC CAR-LIKE ROBOT

FEEDBACK CONTROL OF A NONHOLONOMIC CAR-LIKE ROBOT FEEDBACK CONTROL OF A NONHOLONOMIC CAR-LIKE ROBOT Alessandro De Luca Giuseppe Oriolo Dipartimento di Informatica e Sistemistica Università di Roma La Sapienza Via Eudossiana 8, 84 Rome, Italy {deluca,oriolo}@labrob.ing.uniroma.it

More information

METHODS FOR HANDLING TIED EVENTS IN THE COX PROPORTIONAL HAZARD MODEL

METHODS FOR HANDLING TIED EVENTS IN THE COX PROPORTIONAL HAZARD MODEL STUDIA OECONOMICA POSNANIENSIA 204, vol. 2, no. 2 (263 Jadwiga Borucka Warsaw School of Economics, Institut of Statistics and Dmography, Evnt History and Multilvl Analysis Unit jadwiga.borucka@gmail.com

More information

Surface wave accelerator based on silicon carbide (SWABSiC)

Surface wave accelerator based on silicon carbide (SWABSiC) Surfac wav acclrator basd on silicon carbid (SWABSiC) V. Khudi, S. Trndafilov, Kamil B. Alici P.I. Gnnady Shvts Th Univrsity of Txas at Austin V. Yaimno, M. Babzin, M. Fdurin, K. Kusch BNL/ATF Lasr Bam

More information

SUBATOMIC PARTICLES AND ANTIPARTICLES AS DIFFERENT STATES OF THE SAME MICROCOSM OBJECT. Eduard N. Klenov* Rostov-on-Don. Russia

SUBATOMIC PARTICLES AND ANTIPARTICLES AS DIFFERENT STATES OF THE SAME MICROCOSM OBJECT. Eduard N. Klenov* Rostov-on-Don. Russia SUBATOMIC PARTICLES AND ANTIPARTICLES AS DIFFERENT STATES OF THE SAME MICROCOSM OBJECT Eduard N. Klnov* Rostov-on-Don. Russia Th distribution law for th valus of pairs of th consrvd additiv quantum numbrs

More information

Performance Evaluation

Performance Evaluation Prformanc Evaluation ( ) Contnts lists availabl at ScincDirct Prformanc Evaluation journal hompag: www.lsvir.com/locat/pva Modling Bay-lik rputation systms: Analysis, charactrization and insuranc mchanism

More information

Journal of Engineering and Natural Sciences Mühendislik ve Fen Bilimleri Dergisi

Journal of Engineering and Natural Sciences Mühendislik ve Fen Bilimleri Dergisi Journal of Enginring and Natural Scincs Mühndisli v Fn Bilimlri Drgisi Sigma 4/ Invitd Rviw Par OPTIMAL DESIGN OF NONLINEAR MAGNETIC SYSTEMS USING FINITE ELEMENTS Lvnt OVACIK * Istanbul Tchnical Univrsity,

More information

Upper Bounding the Price of Anarchy in Atomic Splittable Selfish Routing

Upper Bounding the Price of Anarchy in Atomic Splittable Selfish Routing Uppr Bounding th Pric of Anarchy in Atomic Splittabl Slfish Routing Kamyar Khodamoradi 1, Mhrdad Mahdavi, and Mohammad Ghodsi 3 1 Sharif Univrsity of Tchnology, Thran, Iran, khodamoradi@c.sharif.du Sharif

More information

Meccanica e scienze avanzate dell ingegneria

Meccanica e scienze avanzate dell ingegneria Alma Mater Stdiorm Università di Bologna DOTTORATO DI RICERCA IN Meccanica e scienze avanzate dell ingegneria Ciclo XIII Settore/i scientifico-disciplinare/i di afferenza: ING-IND/3 Meccanica del volo

More information

A Note on Approximating. the Normal Distribution Function

A Note on Approximating. the Normal Distribution Function Applid Mathmatical Scincs, Vol, 00, no 9, 45-49 A Not on Approimating th Normal Distribution Function K M Aludaat and M T Alodat Dpartmnt of Statistics Yarmouk Univrsity, Jordan Aludaatkm@hotmailcom and

More information

Introduction to Physical Systems Modelling with Bond Graphs

Introduction to Physical Systems Modelling with Bond Graphs Introction to Physical Systms Molling with Bon Graphs Jan F. Bronink Univrsity o Twnt, pt EE, Control aboratory PO Box, N-5 AE Ensch Nthrlans -mail: J.F.Bronink@l.twnt.nl Introction Bon graphs ar a omain-inpnnt

More information

Proceedings of the 6th WSEAS International Conference on Simulation, Modelling and Optimization, Lisbon, Portugal, September 22-24, 2006 246

Proceedings of the 6th WSEAS International Conference on Simulation, Modelling and Optimization, Lisbon, Portugal, September 22-24, 2006 246 Procdings of th 6th WSEAS Intrnational Confrnc on Simulation, Modlling and Optimization, Lisbon, Portugal, Sptmbr 22-24, 2006 246 Larg dformation modling in soil-tillag tool intraction using advancd 3D

More information

est with berkeley / uc berkeley exte xtension / be your best with berkel

est with berkeley / uc berkeley exte xtension / be your best with berkel c rkley xtnsion yor st rkly c rkley xtnsion st with rkly c rkley xt Post-Baccalarat yor st Program with for rkly c rk xtnsion yor st with rkl c rkley xtnsion yor st rkly Consling c rkley and xtnsion st

More information

Adaptive Neural-Network Control for Redundant Nonholonomic Mobile Modular Manipulators

Adaptive Neural-Network Control for Redundant Nonholonomic Mobile Modular Manipulators Adaptive Neral-Network Control for Redndant Nonholonomic obile odlar aniplators Yangmin Li, Ygang Li, and Shaoze Yan Faclty of Science and Technology, University of aca, Av. Padre Tomas Pereira S.J., Taipa,

More information

The international Internet site of the geoviticulture MCC system Le site Internet international du système CCM géoviticole

The international Internet site of the geoviticulture MCC system Le site Internet international du système CCM géoviticole Th intrnational Intrnt sit of th goviticultur MCC systm L sit Intrnt intrnational du systèm CCM géoviticol Flávio BELLO FIALHO 1 and Jorg TONIETTO 1 1 Rsarchr, Embrapa Uva Vinho, Caixa Postal 130, 95700-000

More information

L 2 : x = s + 1, y = s, z = 4s + 4. 3. Suppose that C has coordinates (x, y, z). Then from the vector equality AC = BD, one has

L 2 : x = s + 1, y = s, z = 4s + 4. 3. Suppose that C has coordinates (x, y, z). Then from the vector equality AC = BD, one has The line L through the points A and B is parallel to the vector AB = 3, 2, and has parametric equations x = 3t + 2, y = 2t +, z = t Therefore, the intersection point of the line with the plane should satisfy:

More information

Stability of Linear Control System

Stability of Linear Control System Stabilit of Linear Control Sstem Concept of Stabilit Closed-loop feedback sstem is either stable or nstable. This tpe of characterization is referred to as absolte stabilit. Given that the sstem is stable,

More information

AP Calculus Multiple-Choice Question Collection 1969 1998. connect to college success www.collegeboard.com

AP Calculus Multiple-Choice Question Collection 1969 1998. connect to college success www.collegeboard.com AP Calculus Multipl-Choic Qustion Collction 969 998 connct to collg succss www.collgboard.com Th Collg Board: Conncting Studnts to Collg Succss Th Collg Board is a not-for-profit mmbrship association whos

More information

MOBILE ROBOT TRACKING OF PRE-PLANNED PATHS. Department of Computer Science, York University, Heslington, York, Y010 5DD, UK (email:nep@cs.york.ac.

MOBILE ROBOT TRACKING OF PRE-PLANNED PATHS. Department of Computer Science, York University, Heslington, York, Y010 5DD, UK (email:nep@cs.york.ac. MOBILE ROBOT TRACKING OF PRE-PLANNED PATHS N. E. Pears Department of Computer Science, York University, Heslington, York, Y010 5DD, UK (email:nep@cs.york.ac.uk) 1 Abstract A method of mobile robot steering

More information

CHAPTER ONE VECTOR GEOMETRY

CHAPTER ONE VECTOR GEOMETRY CHAPTER ONE VECTOR GEOMETRY. INTRODUCTION In this chapter ectors are first introdced as geometric objects, namely as directed line segments, or arrows. The operations of addition, sbtraction, and mltiplication

More information

Lecture 20: Emitter Follower and Differential Amplifiers

Lecture 20: Emitter Follower and Differential Amplifiers Whits, EE 3 Lctur 0 Pag of 8 Lctur 0: Emittr Followr and Diffrntial Amplifirs Th nxt two amplifir circuits w will discuss ar ry important to lctrical nginring in gnral, and to th NorCal 40A spcifically.

More information

Category 7: Employee Commuting

Category 7: Employee Commuting 7 Catgory 7: Employ Commuting Catgory dscription This catgory includs missions from th transportation of mploys 4 btwn thir homs and thir worksits. Emissions from mploy commuting may aris from: Automobil

More information

IMES DISCUSSION PAPER SERIES

IMES DISCUSSION PAPER SERIES IMES DISCUSSIN PAPER SERIES Th Choic of Invoic Currncy in Intrnational Trad: Implications for th Intrnationalization of th Yn Hiroyuki I, Akira TANI, and Toyoichirou SHIRTA Discussion Papr No. 003-E-13

More information

NUMERICAL COMPUTATION OF THE EFFECTIVENESS-NUMBER OF TRANSFER UNITS FOR SEVERAL CROSS-FLOW HEAT EXCHANGERS WITH DIFFERENT FLOW ARRANGEMENTS

NUMERICAL COMPUTATION OF THE EFFECTIVENESS-NUMBER OF TRANSFER UNITS FOR SEVERAL CROSS-FLOW HEAT EXCHANGERS WITH DIFFERENT FLOW ARRANGEMENTS Prodings of COBEM 2009 20th Intrnational Congrss of Mhanial Enginring Novmbr 15-20, 2009, Gramado, RS, Brazil NUMERICAL COMPUTATION OF THE EFFECTIVENESS-NUMBER OF TRANSFER UNITS FOR SEVERAL CROSS-FLOW

More information

3. Fluid Dynamics. 3.1 Uniform Flow, Steady Flow

3. Fluid Dynamics. 3.1 Uniform Flow, Steady Flow 3. Flid Dynamics Objectives Introdce concepts necessary to analyse flids in motion Identify differences between Steady/nsteady niform/non-niform compressible/incompressible flow Demonstrate streamlines

More information

PRACTICAL ADVANTAGES OF USING THE MECHANICS OF CONTINUUM TO ANALYSE DEFORMATIONS OBTAINED FROM GEODETIC SURVEY

PRACTICAL ADVANTAGES OF USING THE MECHANICS OF CONTINUUM TO ANALYSE DEFORMATIONS OBTAINED FROM GEODETIC SURVEY PRACTICAL ADVANTAGES OF USING THE MECHANICS OF CONTINUUM TO ANALYSE DEFORMATIONS OBTAINED FROM GEODETIC SURVEY Mlan TALICH Rsarch Insttut of Godsy, Topography and Cartography, Zdby 98, CZ-5 66, Czch Rpublc

More information

Gold versus stock investment: An econometric analysis

Gold versus stock investment: An econometric analysis Intrnational Journal of Dvlopmnt and Sustainability Onlin ISSN: 268-8662 www.isdsnt.com/ijds Volum Numbr, Jun 202, Pag -7 ISDS Articl ID: IJDS20300 Gold vrsus stock invstmnt: An conomtric analysis Martin

More information

Modeling Motorcycle Accident on Rural Highway

Modeling Motorcycle Accident on Rural Highway Modling Motorcycl Accidnt on Rural Highway A.K.Sharma, V.S. Landg, and N.V.Dshpand Abstract Motorcyclists ar th most crash-pron road-usr group in many Asian countris including India. Statistics of accidnt

More information

A Project Management framework for Software Implementation Planning and Management

A Project Management framework for Software Implementation Planning and Management PPM02 A Projct Managmnt framwork for Softwar Implmntation Planning and Managmnt Kith Lancastr Lancastr Stratgis Kith.Lancastr@LancastrStratgis.com Th goal of introducing nw tchnologis into your company

More information

Modeling Roughness Effects in Open Channel Flows D.T. Souders and C.W. Hirt Flow Science, Inc.

Modeling Roughness Effects in Open Channel Flows D.T. Souders and C.W. Hirt Flow Science, Inc. FSI-2-TN6 Modeling Roghness Effects in Open Channel Flows D.T. Soders and C.W. Hirt Flow Science, Inc. Overview Flows along rivers, throgh pipes and irrigation channels enconter resistance that is proportional

More information

SPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM

SPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM RESEARCH PAPERS IN MANAGEMENT STUDIES SPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM M.A.H. Dmpstr & S.S.G. Hong WP 26/2000 Th Judg Institut of Managmnt Trumpington Strt Cambridg CB2 1AG Ths paprs

More information

Abstract. Introduction. Statistical Approach for Analyzing Cell Phone Handoff Behavior. Volume 3, Issue 1, 2009

Abstract. Introduction. Statistical Approach for Analyzing Cell Phone Handoff Behavior. Volume 3, Issue 1, 2009 Volum 3, Issu 1, 29 Statistical Approach for Analyzing Cll Phon Handoff Bhavior Shalini Saxna, Florida Atlantic Univrsity, Boca Raton, FL, shalinisaxna1@gmail.com Sad A. Rajput, Farquhar Collg of Arts

More information

Candidate: Suzanne Maxwell. Date: 09/19/2012

Candidate: Suzanne Maxwell. Date: 09/19/2012 Medical Coder / Billing Clerk Assessment Report Szanne Maxwell 09/19/2012 www.resorceassociates.com Szanne Maxwell 09/19/2012 Prepared For: NAME Prepared by: John Lonsbry, Ph.D. & Lcy Gibson, Ph.D., Licensed

More information

On the moments of the aggregate discounted claims with dependence introduced by a FGM copula

On the moments of the aggregate discounted claims with dependence introduced by a FGM copula On th momnts of th aggrgat discountd claims with dpndnc introducd by a FGM copula - Mathiu BARGES Univrsité Lyon, Laboratoir SAF, Univrsité Laval - Hélèn COSSETTE Ecol Actuariat, Univrsité Laval, Québc,

More information

Bonds with Embedded Options and Options on Bonds

Bonds with Embedded Options and Options on Bonds FIXED-INCOME SECURITIES Chapter 14 Bonds with Embedded Options and Options on Bonds Callable and Ptable Bonds Instittional Aspects Valation Convertible Bonds Instittional Aspects Valation Options on Bonds

More information

Exam 1 Sample Question SOLUTIONS. y = 2x

Exam 1 Sample Question SOLUTIONS. y = 2x Exam Sample Question SOLUTIONS. Eliminate the parameter to find a Cartesian equation for the curve: x e t, y e t. SOLUTION: You might look at the coordinates and notice that If you don t see it, we can

More information

Asset set Liability Management for

Asset set Liability Management for KSD -larning and rfrnc products for th global financ profssional Highlights Library of 29 Courss Availabl Products Upcoming Products Rply Form Asst st Liability Managmnt for Insuranc Companis A comprhnsiv

More information

http://www.wwnorton.com/chemistry/tutorials/ch14.htm Repulsive Force

http://www.wwnorton.com/chemistry/tutorials/ch14.htm Repulsive Force ctivation nrgis http://www.wwnorton.com/chmistry/tutorials/ch14.htm (back to collision thory...) Potntial and Kintic nrgy during a collision + + ngativly chargd lctron cloud Rpulsiv Forc ngativly chargd

More information

Natural Gas & Electricity Prices

Natural Gas & Electricity Prices Click to dit Mastr titl styl Click to dit Mastr txt styls Scond lvl Third lvl Natural Gas & Elctricity Prics Fourth lvl» Fifth lvl Glnn S. Pool Manufacturing Support Mgr. Enrgy April 4, 2013 Click Vrso

More information

INTERNATIONAL JOURNAL OF RESEARCH SCIENCE & MANAGEMENT

INTERNATIONAL JOURNAL OF RESEARCH SCIENCE & MANAGEMENT [Lavana t al. (9): Stmbr ] ISSN: 9-9 Imact Factor (PIF):. MHD FLOW OVER N INFINIE VERIL OSILING POROS PLE WIH RDIION HEMIL REION ND DFOR EFFE B Lavana * P.Srivni P. Ramirdd * Dartmnt of Mathmatics Priadarshini

More information

Ra atoms and ions: production and spectroscopy Testing the Standard Model in Heavy Nuclei H.W. Wilschut

Ra atoms and ions: production and spectroscopy Testing the Standard Model in Heavy Nuclei H.W. Wilschut atoms and ions: production and spctroscopy Tsting th Standard Modl in Havy Nucli H.W. Wilschut TRIµP group TRIµP =Trappd dioactiv Isotops, µ-laboratoris for fundamntal Physics KVI - Univrsity of Groningn

More information

Continuity Cloud Virtual Firewall Guide

Continuity Cloud Virtual Firewall Guide Cloud Virtual Firwall Guid uh6 Vrsion 1.0 Octobr 2015 Foldr BDR Guid for Vam Pag 1 of 36 Cloud Virtual Firwall Guid CONTENTS INTRODUCTION... 3 ACCESSING THE VIRTUAL FIREWALL... 4 HYPER-V/VIRTUALBOX CONTINUITY

More information

Many quantities are transduced in a displacement and then in an electric signal (pressure, temperature, acceleration). Prof. B.

Many quantities are transduced in a displacement and then in an electric signal (pressure, temperature, acceleration). Prof. B. Displacmn snsors Many quaniis ar ransducd in a displacmn and hn in an lcric signal (prssur, mpraur, acclraion). Poniomrs Poniomrs i p p i o i p A poniomr is basd on a sliding conac moving on a rsisor.

More information

Research Progress in Acoustical Application to Petroleum Logging and Seismic Exploration

Research Progress in Acoustical Application to Petroleum Logging and Seismic Exploration Snd Ordrs of Rprints at rprints@bnthamscinc.nt Th Opn Acoustics Journal 23 6 - Opn Accss Rsarch Progrss in Acoustical Application to Ptrolum Logging and Sismic Exploration Lin Fa * Li Wang Yuan Zhao 2

More information

Vector Network Analyzer

Vector Network Analyzer Cours on Microwav Masurmnts Vctor Ntwork Analyzr Prof. Luca Prrgrini Dpt. of Elctrical, Computr and Biomdical Enginring Univrsity of Pavia -mail: luca.prrgrini@unipv.it wb: microwav.unipv.it Microwav Masurmnts

More information

Version Issue Date Reason / Description of Change Author Draft February, N/A 2009

Version Issue Date Reason / Description of Change Author Draft February, N/A 2009 Appndix A: CNS Managmnt Procss: OTRS POC Documnt Control Titl : CNS Managmnt Procss Documnt : (Location of Documnt and Documnt numbr) Author : Ettin Vrmuln (EV) Ownr : ICT Stratgic Srvics Vrsion : Draft

More information