Dr. Ing. J. H. (Jo) Walling Consultant Cables Standards Machinery

Size: px
Start display at page:

Download "Dr. Ing. J. H. (Jo) Walling Consultant Cables Standards Machinery"

Transcription

1 The common mode crcut resstance unbalance (CMCU) calculaton based on mn. / max. conductor resstance values and par to par resstance unbalance measurements ncludng loop resstance evsed and extended verson of an orgnal document publshed on May 7, 006 The present s an nformal reply to a problem rased by the lason letter from ISO/IEC JTC/SC5/Wg3 to IEC SC46 on IEC to cables, concernng common mode resstance unbalance (CMCU) between pars n data grade cables, and shall be used as a base for future standardzaton. It s as such forwarded to:.) the secretary of IEC 46.) the secretary of IEC 46C 3.) the char of IEC 46C WG7 4.) the secretary of ISO/IEC JTC/SC5 WG3 5.) the VP of ICEA Communcaton cable secton 6.) the lason offcer of ICEA to the ASTM D9 group 7.) the char of TIA ) the char of the PoEP tas group In fact, n vew of some changes of requrements proposed n the latest versons of IEEE 80.3af and 80.3ar the followng wll have to be consdered for future standardzaton. However, t has to be clearly stressed, that the dervatons gven heren have to be taen not only nto account for all those cables standardzed n the future, but they should serve as well all those cable companes nterested to wor through ther past producton protocols n order to get an overvew on the performance of the nstalled base, to get an overvew of what lmts can be reasonably specfed.. The common mode resstance unbalance (CMCU) based upon the resstance unbalance defntons The followng assessment of the common mode crcut resstance unbalance (CMCU) s based upon the defnton of the par to par resstance unbalance accordng to IEC and smlar results are gven also based on the par to par resstance unbalance accordng to ASTM D In these cases the common mode crcut resstance unbalance (CMCU) s gven n terms of the maxmum and mnmum conductor resstance n each par. Alternatvely the common mode crcut resstance unbalance (CMCU) s expressed also n terms of the loop resstance and the conductor resstance unbalance of each par 43 Church, Beaconsfeld, QC, H9W 39, Canada (54) or (54) Fax: (54)

2 . Calculatons based on the IEC defntons. Calculaton based on the IEC defnton and the mnmum and maxmum conductor resstance of each par a.) Assessment of all resstance unbalance measurements, usng the IEC defnton,.e.: max mn CU () + max mn That means the resstance of each conductor has to be measured, and then the resstance unbalance wll have to be calculated. b.) In the context descrbed above t s mandatory for hgh performance data grade cables to calculate the common mode crcut resstance unbalance. Ths value s calculated for the 6 possble par combnatons usng the followng equaton: CMCU, ( max + mn ) max mn ( max + ) ( + ) + ( + ) max () max mn max mn where the ndces and desgnate the par combnaton under consderaton,.e. these ndces may run from to 4 under the condton: and < (3).3 Calculaton based on the IEC defnton and the loop resstance and the conductor resstance unbalance of each par For the loop resstances L of any par combnaton par we have: + + (4) Hence we get: max mn + CU CU max mn + CU CU (5) 43 Church, Beaconsfeld, QC, H9W 39, Canada (54) or (54) Fax: (54)

3 Hence we get for the common mode crcut resstance unbalance (CMCU), respectng the condton of Eq (3): CMCU, ( CU ) ( CU ) ( CU ) + ( CU ) (6) Obvously the CU values have to be taen nto account as straght values, not n percent. If we assume a maxmum specfed value for the conductor resstance unbalance, then we get: CMCU, ( CU ) Spec L + L Spec ( CU ) C, (7) where CL - s the loop resstance unbalance As a result we see, that the CMCU depends prmarly on the loop resstance unbalance, as the frst term of the rght sde of Eq (7) s approxmately.. Calculaton based on the ASTM defntons. Calculaton based on the ASTM defnton and the mnmum and maxmum conductor resstance of each par a.) The calculaton of the present CU assessment follows the defnton of ASTM D and may be consdered for the North Amercan customers. Ths defnton s as follows, and yelds resstance unbalance values approxmately twce as hgh as the IEC defnton: max mn CU (8) Frst the resstance of each common mode crcut conductor ( CMC ) and (that s the conductors of each par connected n parallel) has to be determned: 3 43 Church, Beaconsfeld, QC, H9W 39, Canada mn b.) To use the ASTM defnton of the resstance unbalance accordng to the ASTM D defnton, s slghtly more awward. The calculaton yelds two results, and the correct one has to be determned as follows: (54) or (54) Fax: (54)

4 CMC max mn max mn CMC (9) + + max mn Then the calculaton of the two possble solutons I and II contnues: For: (0) CMC CMC We have CMCU I ( max + mn ) ( + ) max mn CMCUCMC, () max mn For: () CMC CMC We have CMCU II ( max + mn ) ( + ) max mn CMCUCMC, (3) max mn.3 Calculaton based on the ASTM defnton and the loop resstance and the conductor resstance unbalance of each par For the loop resstances L of any par combnaton par we have as n Eq (4): + + (4) Hence we get: max mn + CU + CU + CU max mn + CU + CU + CU (5) Hence we get for the condton accordng to Eq (0): 4 43 Church, Beaconsfeld, QC, H9W 39, Canada (54) or (54) Fax: (54)

5 CMCU, Dr. Ing. J. H. (Jo) Wallng + CU + CU CU CU (6) + + And for the condton accordng to Eq (): CMCU, + CU + CU CU CU (7) + + The programmng of ths common mode crcut resstance unbalance s defntely more cumbersome and should be mplemented only f there s a real customer demand expected n North Amerca. Agan under maxmum specfed conductor resstance unbalance beween all pars we get CMCU CMCU,, (8) for the condtons accordng to the EQs (0) and (), respectvely. Hence we get two dfferent common mode crcut resstance unbalances, as before, but based upon the Loop resstances of the consdered par combnaton. Note: PoE and PoEP are mplemented by IEEE 80.3af and IEEE 80.3ar respectvely, both beng nternatonal organzatons, and as such followng IEC rules. TIA may follow the ASTM defnton though. The mplementaton of these addtonal calculatons of already mplemented measurements should be done ASAP, n order to assess future cables desgn optons to comply to emergng requrements. Jo Wallng Beaconsfeld, July 4, Church, Beaconsfeld, QC, H9W 39, Canada (54) or (54) Fax: (54)

Chapter Newton s Method

Chapter Newton s Method Chapter 9. Newton s Method After readng ths chapter, you should be able to:. Understand how Newton s method s dfferent from the Golden Secton Search method. Understand how Newton s method works 3. Solve

More information

CHAPTER 13. Exercises. E13.1 The emitter current is given by the Shockley equation:

CHAPTER 13. Exercises. E13.1 The emitter current is given by the Shockley equation: HPT 3 xercses 3. The emtter current s gen by the Shockley equaton: S exp VT For operaton wth, we hae exp >> S >>, and we can wrte VT S exp VT Solng for, we hae 3. 0 6ln 78.4 mv 0 0.784 5 4.86 V VT ln 4

More information

Second Order Analysis

Second Order Analysis Second Order Analyss In the prevous classes we looked at a method that determnes the load correspondng to a state of bfurcaton equlbrum of a perfect frame by egenvalye analyss The system was assumed to

More information

Foundations of Arithmetic

Foundations of Arithmetic Foundatons of Arthmetc Notaton We shall denote the sum and product of numbers n the usual notaton as a 2 + a 2 + a 3 + + a = a, a 1 a 2 a 3 a = a The notaton a b means a dvdes b,.e. ac = b where c s an

More information

Linear Approximation with Regularization and Moving Least Squares

Linear Approximation with Regularization and Moving Least Squares Lnear Approxmaton wth Regularzaton and Movng Least Squares Igor Grešovn May 007 Revson 4.6 (Revson : March 004). 5 4 3 0.5 3 3.5 4 Contents: Lnear Fttng...4. Weghted Least Squares n Functon Approxmaton...

More information

Department of Statistics University of Toronto STA305H1S / 1004 HS Design and Analysis of Experiments Term Test - Winter Solution

Department of Statistics University of Toronto STA305H1S / 1004 HS Design and Analysis of Experiments Term Test - Winter Solution Department of Statstcs Unversty of Toronto STA35HS / HS Desgn and Analyss of Experments Term Test - Wnter - Soluton February, Last Name: Frst Name: Student Number: Instructons: Tme: hours. Ads: a non-programmable

More information

College of Computer & Information Science Fall 2009 Northeastern University 20 October 2009

College of Computer & Information Science Fall 2009 Northeastern University 20 October 2009 College of Computer & Informaton Scence Fall 2009 Northeastern Unversty 20 October 2009 CS7880: Algorthmc Power Tools Scrbe: Jan Wen and Laura Poplawsk Lecture Outlne: Prmal-dual schema Network Desgn:

More information

Some modelling aspects for the Matlab implementation of MMA

Some modelling aspects for the Matlab implementation of MMA Some modellng aspects for the Matlab mplementaton of MMA Krster Svanberg krlle@math.kth.se Optmzaton and Systems Theory Department of Mathematcs KTH, SE 10044 Stockholm September 2004 1. Consdered optmzaton

More information

Lecture 20: Lift and Project, SDP Duality. Today we will study the Lift and Project method. Then we will prove the SDP duality theorem.

Lecture 20: Lift and Project, SDP Duality. Today we will study the Lift and Project method. Then we will prove the SDP duality theorem. prnceton u. sp 02 cos 598B: algorthms and complexty Lecture 20: Lft and Project, SDP Dualty Lecturer: Sanjeev Arora Scrbe:Yury Makarychev Today we wll study the Lft and Project method. Then we wll prove

More information

Calculation of time complexity (3%)

Calculation of time complexity (3%) Problem 1. (30%) Calculaton of tme complexty (3%) Gven n ctes, usng exhaust search to see every result takes O(n!). Calculaton of tme needed to solve the problem (2%) 40 ctes:40! dfferent tours 40 add

More information

Analysis of the Magnetomotive Force of a Three-Phase Winding with Concentrated Coils and Different Symmetry Features

Analysis of the Magnetomotive Force of a Three-Phase Winding with Concentrated Coils and Different Symmetry Features Analyss of the Magnetomotve Force of a Three-Phase Wndng wth Concentrated Cols and Dfferent Symmetry Features Deter Gerlng Unversty of Federal Defense Munch, Neubberg, 85579, Germany Emal: Deter.Gerlng@unbw.de

More information

The optimal delay of the second test is therefore approximately 210 hours earlier than =2.

The optimal delay of the second test is therefore approximately 210 hours earlier than =2. THE IEC 61508 FORMULAS 223 The optmal delay of the second test s therefore approxmately 210 hours earler than =2. 8.4 The IEC 61508 Formulas IEC 61508-6 provdes approxmaton formulas for the PF for smple

More information

Recover plaintext attack to block ciphers

Recover plaintext attack to block ciphers Recover plantext attac to bloc cphers L An-Png Bejng 100085, P.R.Chna apl0001@sna.com Abstract In ths paper, we wll present an estmaton for the upper-bound of the amount of 16-bytes plantexts for Englsh

More information

Solution Thermodynamics

Solution Thermodynamics Soluton hermodynamcs usng Wagner Notaton by Stanley. Howard Department of aterals and etallurgcal Engneerng South Dakota School of nes and echnology Rapd Cty, SD 57701 January 7, 001 Soluton hermodynamcs

More information

Econ107 Applied Econometrics Topic 3: Classical Model (Studenmund, Chapter 4)

Econ107 Applied Econometrics Topic 3: Classical Model (Studenmund, Chapter 4) I. Classcal Assumptons Econ7 Appled Econometrcs Topc 3: Classcal Model (Studenmund, Chapter 4) We have defned OLS and studed some algebrac propertes of OLS. In ths topc we wll study statstcal propertes

More information

Chapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems

Chapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems Numercal Analyss by Dr. Anta Pal Assstant Professor Department of Mathematcs Natonal Insttute of Technology Durgapur Durgapur-713209 emal: anta.bue@gmal.com 1 . Chapter 5 Soluton of System of Lnear Equatons

More information

Transfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system

Transfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng

More information

MMA and GCMMA two methods for nonlinear optimization

MMA and GCMMA two methods for nonlinear optimization MMA and GCMMA two methods for nonlnear optmzaton Krster Svanberg Optmzaton and Systems Theory, KTH, Stockholm, Sweden. krlle@math.kth.se Ths note descrbes the algorthms used n the author s 2007 mplementatons

More information

Difference Equations

Difference Equations Dfference Equatons c Jan Vrbk 1 Bascs Suppose a sequence of numbers, say a 0,a 1,a,a 3,... s defned by a certan general relatonshp between, say, three consecutve values of the sequence, e.g. a + +3a +1

More information

Magnetic Field Around The New 400kV OH Power Transmission Lines In Libya

Magnetic Field Around The New 400kV OH Power Transmission Lines In Libya ECENT ADVANCES n ENEGY & ENVIONMENT Magnetc Feld Around The New kv OH Power Transmsson Lnes In Lbya JAMAL M. EHTAIBA * SAYEH M. ELHABASHI ** Organzaton for Development of Admnstratve Centers, ODAC MISUATA

More information

Simulated Power of the Discrete Cramér-von Mises Goodness-of-Fit Tests

Simulated Power of the Discrete Cramér-von Mises Goodness-of-Fit Tests Smulated of the Cramér-von Mses Goodness-of-Ft Tests Steele, M., Chaselng, J. and 3 Hurst, C. School of Mathematcal and Physcal Scences, James Cook Unversty, Australan School of Envronmental Studes, Grffth

More information

CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE

CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng

More information

Kernel Methods and SVMs Extension

Kernel Methods and SVMs Extension Kernel Methods and SVMs Extenson The purpose of ths document s to revew materal covered n Machne Learnng 1 Supervsed Learnng regardng support vector machnes (SVMs). Ths document also provdes a general

More information

( ) 1/ 2. ( P SO2 )( P O2 ) 1/ 2.

( ) 1/ 2. ( P SO2 )( P O2 ) 1/ 2. Chemstry 360 Dr. Jean M. Standard Problem Set 9 Solutons. The followng chemcal reacton converts sulfur doxde to sulfur troxde. SO ( g) + O ( g) SO 3 ( l). (a.) Wrte the expresson for K eq for ths reacton.

More information

Winter 2008 CS567 Stochastic Linear/Integer Programming Guest Lecturer: Xu, Huan

Winter 2008 CS567 Stochastic Linear/Integer Programming Guest Lecturer: Xu, Huan Wnter 2008 CS567 Stochastc Lnear/Integer Programmng Guest Lecturer: Xu, Huan Class 2: More Modelng Examples 1 Capacty Expanson Capacty expanson models optmal choces of the tmng and levels of nvestments

More information

Lecture 10 Support Vector Machines II

Lecture 10 Support Vector Machines II Lecture 10 Support Vector Machnes II 22 February 2016 Taylor B. Arnold Yale Statstcs STAT 365/665 1/28 Notes: Problem 3 s posted and due ths upcomng Frday There was an early bug n the fake-test data; fxed

More information

Chapter 3 Describing Data Using Numerical Measures

Chapter 3 Describing Data Using Numerical Measures Chapter 3 Student Lecture Notes 3-1 Chapter 3 Descrbng Data Usng Numercal Measures Fall 2006 Fundamentals of Busness Statstcs 1 Chapter Goals To establsh the usefulness of summary measures of data. The

More information

Newton s Method for One - Dimensional Optimization - Theory

Newton s Method for One - Dimensional Optimization - Theory Numercal Methods Newton s Method for One - Dmensonal Optmzaton - Theory For more detals on ths topc Go to Clck on Keyword Clck on Newton s Method for One- Dmensonal Optmzaton You are free to Share to copy,

More information

Report on Image warping

Report on Image warping Report on Image warpng Xuan Ne, Dec. 20, 2004 Ths document summarzed the algorthms of our mage warpng soluton for further study, and there s a detaled descrpton about the mplementaton of these algorthms.

More information

ASSOCIATION POUR LA CERTIFICATION DES MATERIAUX ISOLANTS

ASSOCIATION POUR LA CERTIFICATION DES MATERIAUX ISOLANTS Revson ndex Date of mplementaton C 15/03/017 Techncal Specfcaton E ASSOCIATIO POUR LA CERTIFICATIO DES MATERIAUX ISOLATS 4, avenue du Recteur-Poncaré, 7578 Pars Cedex 16 Tel. 33.(0)1.64.68.84.97 Fax. 33.(0)1.64.68.83.45

More information

CSci 6974 and ECSE 6966 Math. Tech. for Vision, Graphics and Robotics Lecture 21, April 17, 2006 Estimating A Plane Homography

CSci 6974 and ECSE 6966 Math. Tech. for Vision, Graphics and Robotics Lecture 21, April 17, 2006 Estimating A Plane Homography CSc 6974 and ECSE 6966 Math. Tech. for Vson, Graphcs and Robotcs Lecture 21, Aprl 17, 2006 Estmatng A Plane Homography Overvew We contnue wth a dscusson of the major ssues, usng estmaton of plane projectve

More information

Section 8.1 Exercises

Section 8.1 Exercises Secton 8.1 Non-rght Trangles: Law of Snes and Cosnes 519 Secton 8.1 Exercses Solve for the unknown sdes and angles of the trangles shown. 10 70 50 1.. 18 40 110 45 5 6 3. 10 4. 75 15 5 6 90 70 65 5. 6.

More information

Comparison of Regression Lines

Comparison of Regression Lines STATGRAPHICS Rev. 9/13/2013 Comparson of Regresson Lnes Summary... 1 Data Input... 3 Analyss Summary... 4 Plot of Ftted Model... 6 Condtonal Sums of Squares... 6 Analyss Optons... 7 Forecasts... 8 Confdence

More information

Module 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur

Module 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:

More information

Norms, Condition Numbers, Eigenvalues and Eigenvectors

Norms, Condition Numbers, Eigenvalues and Eigenvectors Norms, Condton Numbers, Egenvalues and Egenvectors 1 Norms A norm s a measure of the sze of a matrx or a vector For vectors the common norms are: N a 2 = ( x 2 1/2 the Eucldean Norm (1a b 1 = =1 N x (1b

More information

Time-Varying Systems and Computations Lecture 6

Time-Varying Systems and Computations Lecture 6 Tme-Varyng Systems and Computatons Lecture 6 Klaus Depold 14. Januar 2014 The Kalman Flter The Kalman estmaton flter attempts to estmate the actual state of an unknown dscrete dynamcal system, gven nosy

More information

Physics 114 Exam 2 Fall 2014 Solutions. Name:

Physics 114 Exam 2 Fall 2014 Solutions. Name: Physcs 114 Exam Fall 014 Name: For gradng purposes (do not wrte here): Queston 1. 1... 3. 3. Problem Answer each of the followng questons. Ponts for each queston are ndcated n red. Unless otherwse ndcated,

More information

Color Rendering Uncertainty

Color Rendering Uncertainty Australan Journal of Basc and Appled Scences 4(10): 4601-4608 010 ISSN 1991-8178 Color Renderng Uncertanty 1 A.el Bally M.M. El-Ganany 3 A. Al-amel 1 Physcs Department Photometry department- NIS Abstract:

More information

THE IGNITION PARAMETER - A quantification of the probability of ignition

THE IGNITION PARAMETER - A quantification of the probability of ignition THE IGNITION PARAMETER - A quantfcaton of the probablty of ton INFUB9-2011 Topc: Modellng of fundamental processes Man author Nels Bjarne K. Rasmussen Dansh Gas Technology Centre (DGC) NBR@dgc.dk Co-author

More information

APPENDIX A Some Linear Algebra

APPENDIX A Some Linear Algebra APPENDIX A Some Lnear Algebra The collecton of m, n matrces A.1 Matrces a 1,1,..., a 1,n A = a m,1,..., a m,n wth real elements a,j s denoted by R m,n. If n = 1 then A s called a column vector. Smlarly,

More information

Module 9. Lecture 6. Duality in Assignment Problems

Module 9. Lecture 6. Duality in Assignment Problems Module 9 1 Lecture 6 Dualty n Assgnment Problems In ths lecture we attempt to answer few other mportant questons posed n earler lecture for (AP) and see how some of them can be explaned through the concept

More information

Here is the rationale: If X and y have a strong positive relationship to one another, then ( x x) will tend to be positive when ( y y)

Here is the rationale: If X and y have a strong positive relationship to one another, then ( x x) will tend to be positive when ( y y) Secton 1.5 Correlaton In the prevous sectons, we looked at regresson and the value r was a measurement of how much of the varaton n y can be attrbuted to the lnear relatonshp between y and x. In ths secton,

More information

FE REVIEW OPERATIONAL AMPLIFIERS (OP-AMPS)( ) 8/25/2010

FE REVIEW OPERATIONAL AMPLIFIERS (OP-AMPS)( ) 8/25/2010 FE REVEW OPERATONAL AMPLFERS (OP-AMPS)( ) 1 The Op-amp 2 An op-amp has two nputs and one output. Note the op-amp below. The termnal labeled l wth the (-) sgn s the nvertng nput and the nput labeled wth

More information

FUZZY FINITE ELEMENT METHOD

FUZZY FINITE ELEMENT METHOD FUZZY FINITE ELEMENT METHOD RELIABILITY TRUCTURE ANALYI UING PROBABILITY 3.. Maxmum Normal tress Internal force s the shear force, V has a magntude equal to the load P and bendng moment, M. Bendng moments

More information

Department of Electrical & Electronic Engineeing Imperial College London. E4.20 Digital IC Design. Median Filter Project Specification

Department of Electrical & Electronic Engineeing Imperial College London. E4.20 Digital IC Design. Median Filter Project Specification Desgn Project Specfcaton Medan Flter Department of Electrcal & Electronc Engneeng Imperal College London E4.20 Dgtal IC Desgn Medan Flter Project Specfcaton A medan flter s used to remove nose from a sampled

More information

Complex Numbers, Signals, and Circuits

Complex Numbers, Signals, and Circuits Complex Numbers, Sgnals, and Crcuts 3 August, 009 Complex Numbers: a Revew Suppose we have a complex number z = x jy. To convert to polar form, we need to know the magntude of z and the phase of z. z =

More information

APPENDIX 2 FITTING A STRAIGHT LINE TO OBSERVATIONS

APPENDIX 2 FITTING A STRAIGHT LINE TO OBSERVATIONS Unversty of Oulu Student Laboratory n Physcs Laboratory Exercses n Physcs 1 1 APPEDIX FITTIG A STRAIGHT LIE TO OBSERVATIOS In the physcal measurements we often make a seres of measurements of the dependent

More information

Assignment 4 Solutions

Assignment 4 Solutions Assgnment 4 Solutons Tmothy Vs February 3, 2006 3-3-2 We have n 25, 0.04, P MT 100, and we need to fnd F V. F V P MT (1 + )n 1 100 (1 + 0.04)2 5 1 0.04 4164.59 3-3-6 We have F V 8000, n 30, 0.03, and we

More information

3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X

3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X Statstcs 1: Probablty Theory II 37 3 EPECTATION OF SEVERAL RANDOM VARIABLES As n Probablty Theory I, the nterest n most stuatons les not on the actual dstrbuton of a random vector, but rather on a number

More information

On the correction of the h-index for career length

On the correction of the h-index for career length 1 On the correcton of the h-ndex for career length by L. Egghe Unverstet Hasselt (UHasselt), Campus Depenbeek, Agoralaan, B-3590 Depenbeek, Belgum 1 and Unverstet Antwerpen (UA), IBW, Stadscampus, Venusstraat

More information

Example: (13320, 22140) =? Solution #1: The divisors of are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 41,

Example: (13320, 22140) =? Solution #1: The divisors of are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 41, The greatest common dvsor of two ntegers a and b (not both zero) s the largest nteger whch s a common factor of both a and b. We denote ths number by gcd(a, b), or smply (a, b) when there s no confuson

More information

Temperature. Chapter Heat Engine

Temperature. Chapter Heat Engine Chapter 3 Temperature In prevous chapters of these notes we ntroduced the Prncple of Maxmum ntropy as a technque for estmatng probablty dstrbutons consstent wth constrants. In Chapter 9 we dscussed the

More information

Lecture 12: Discrete Laplacian

Lecture 12: Discrete Laplacian Lecture 12: Dscrete Laplacan Scrbe: Tanye Lu Our goal s to come up wth a dscrete verson of Laplacan operator for trangulated surfaces, so that we can use t n practce to solve related problems We are mostly

More information

Asymptotics of the Solution of a Boundary Value. Problem for One-Characteristic Differential. Equation Degenerating into a Parabolic Equation

Asymptotics of the Solution of a Boundary Value. Problem for One-Characteristic Differential. Equation Degenerating into a Parabolic Equation Nonl. Analyss and Dfferental Equatons, ol., 4, no., 5 - HIKARI Ltd, www.m-har.com http://dx.do.org/.988/nade.4.456 Asymptotcs of the Soluton of a Boundary alue Problem for One-Characterstc Dfferental Equaton

More information

8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS

8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS SECTION 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS 493 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS All the vector spaces you have studed thus far n the text are real vector spaces because the scalars

More information

The Expectation-Maximization Algorithm

The Expectation-Maximization Algorithm The Expectaton-Maxmaton Algorthm Charles Elan elan@cs.ucsd.edu November 16, 2007 Ths chapter explans the EM algorthm at multple levels of generalty. Secton 1 gves the standard hgh-level verson of the algorthm.

More information

Note 10. Modeling and Simulation of Dynamic Systems

Note 10. Modeling and Simulation of Dynamic Systems Lecture Notes of ME 475: Introducton to Mechatroncs Note 0 Modelng and Smulaton of Dynamc Systems Department of Mechancal Engneerng, Unversty Of Saskatchewan, 57 Campus Drve, Saskatoon, SK S7N 5A9, Canada

More information

Compilers. Spring term. Alfonso Ortega: Enrique Alfonseca: Chapter 4: Syntactic analysis

Compilers. Spring term. Alfonso Ortega: Enrique Alfonseca: Chapter 4: Syntactic analysis Complers Sprng term Alfonso Ortega: alfonso.ortega@uam.es nrque Alfonseca: enrque.alfonseca@uam.es Chapter : Syntactc analyss. Introducton. Bottom-up Analyss Syntax Analyser Concepts It analyses the context-ndependent

More information

Physics 4B. A positive value is obtained, so the current is counterclockwise around the circuit.

Physics 4B. A positive value is obtained, so the current is counterclockwise around the circuit. Physcs 4B Solutons to Chapter 7 HW Chapter 7: Questons:, 8, 0 Problems:,,, 45, 48,,, 7, 9 Queston 7- (a) no (b) yes (c) all te Queston 7-8 0 μc Queston 7-0, c;, a;, d; 4, b Problem 7- (a) Let be the current

More information

p 1 c 2 + p 2 c 2 + p 3 c p m c 2

p 1 c 2 + p 2 c 2 + p 3 c p m c 2 Where to put a faclty? Gven locatons p 1,..., p m n R n of m houses, want to choose a locaton c n R n for the fre staton. Want c to be as close as possble to all the house. We know how to measure dstance

More information

Lab 2e Thermal System Response and Effective Heat Transfer Coefficient

Lab 2e Thermal System Response and Effective Heat Transfer Coefficient 58:080 Expermental Engneerng 1 OBJECTIVE Lab 2e Thermal System Response and Effectve Heat Transfer Coeffcent Warnng: though the experment has educatonal objectves (to learn about bolng heat transfer, etc.),

More information

Kinematics in 2-Dimensions. Projectile Motion

Kinematics in 2-Dimensions. Projectile Motion Knematcs n -Dmensons Projectle Moton A medeval trebuchet b Kolderer, c1507 http://members.net.net.au/~rmne/ht/ht0.html#5 Readng Assgnment: Chapter 4, Sectons -6 Introducton: In medeval das, people had

More information

Advanced Circuits Topics - Part 1 by Dr. Colton (Fall 2017)

Advanced Circuits Topics - Part 1 by Dr. Colton (Fall 2017) Advanced rcuts Topcs - Part by Dr. olton (Fall 07) Part : Some thngs you should already know from Physcs 0 and 45 These are all thngs that you should have learned n Physcs 0 and/or 45. Ths secton s organzed

More information

Turing Machines (intro)

Turing Machines (intro) CHAPTER 3 The Church-Turng Thess Contents Turng Machnes defntons, examples, Turng-recognzable and Turng-decdable languages Varants of Turng Machne Multtape Turng machnes, non-determnstc Turng Machnes,

More information

Correlation and Regression. Correlation 9.1. Correlation. Chapter 9

Correlation and Regression. Correlation 9.1. Correlation. Chapter 9 Chapter 9 Correlaton and Regresson 9. Correlaton Correlaton A correlaton s a relatonshp between two varables. The data can be represented b the ordered pars (, ) where s the ndependent (or eplanator) varable,

More information

Lectures - Week 4 Matrix norms, Conditioning, Vector Spaces, Linear Independence, Spanning sets and Basis, Null space and Range of a Matrix

Lectures - Week 4 Matrix norms, Conditioning, Vector Spaces, Linear Independence, Spanning sets and Basis, Null space and Range of a Matrix Lectures - Week 4 Matrx norms, Condtonng, Vector Spaces, Lnear Independence, Spannng sets and Bass, Null space and Range of a Matrx Matrx Norms Now we turn to assocatng a number to each matrx. We could

More information

Appendix for Causal Interaction in Factorial Experiments: Application to Conjoint Analysis

Appendix for Causal Interaction in Factorial Experiments: Application to Conjoint Analysis A Appendx for Causal Interacton n Factoral Experments: Applcaton to Conjont Analyss Mathematcal Appendx: Proofs of Theorems A. Lemmas Below, we descrbe all the lemmas, whch are used to prove the man theorems

More information

G = G 1 + G 2 + G 3 G 2 +G 3 G1 G2 G3. Network (a) Network (b) Network (c) Network (d)

G = G 1 + G 2 + G 3 G 2 +G 3 G1 G2 G3. Network (a) Network (b) Network (c) Network (d) Massachusetts Insttute of Technology Department of Electrcal Engneerng and Computer Scence 6.002 í Electronc Crcuts Homework 2 Soluton Handout F98023 Exercse 21: Determne the conductance of each network

More information

ACTM State Calculus Competition Saturday April 30, 2011

ACTM State Calculus Competition Saturday April 30, 2011 ACTM State Calculus Competton Saturday Aprl 30, 2011 ACTM State Calculus Competton Sprng 2011 Page 1 Instructons: For questons 1 through 25, mark the best answer choce on the answer sheet provde Afterward

More information

Principles of Food and Bioprocess Engineering (FS 231) Solutions to Example Problems on Heat Transfer

Principles of Food and Bioprocess Engineering (FS 231) Solutions to Example Problems on Heat Transfer Prncples of Food and Boprocess Engneerng (FS 31) Solutons to Example Problems on Heat Transfer 1. We start wth Fourer s law of heat conducton: Q = k A ( T/ x) Rearrangng, we get: Q/A = k ( T/ x) Here,

More information

ALGORITHM FOR THE CALCULATION OF THE TWO VARIABLES CUBIC SPLINE FUNCTION

ALGORITHM FOR THE CALCULATION OF THE TWO VARIABLES CUBIC SPLINE FUNCTION ANALELE ŞTIINŢIFICE ALE UNIVERSITĂŢII AL.I. CUZA DIN IAŞI (S.N.) MATEMATICĂ, Tomul LIX, 013, f.1 DOI: 10.478/v10157-01-00-y ALGORITHM FOR THE CALCULATION OF THE TWO VARIABLES CUBIC SPLINE FUNCTION BY ION

More information

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. ME 270 Sprng 2014 Fnal Exam NME (Last, Frst): Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS

More information

DUE: WEDS FEB 21ST 2018

DUE: WEDS FEB 21ST 2018 HOMEWORK # 1: FINITE DIFFERENCES IN ONE DIMENSION DUE: WEDS FEB 21ST 2018 1. Theory Beam bendng s a classcal engneerng analyss. The tradtonal soluton technque makes smplfyng assumptons such as a constant

More information

Dynamic Programming. Preview. Dynamic Programming. Dynamic Programming. Dynamic Programming (Example: Fibonacci Sequence)

Dynamic Programming. Preview. Dynamic Programming. Dynamic Programming. Dynamic Programming (Example: Fibonacci Sequence) /24/27 Prevew Fbonacc Sequence Longest Common Subsequence Dynamc programmng s a method for solvng complex problems by breakng them down nto smpler sub-problems. It s applcable to problems exhbtng the propertes

More information

( ) = ( ) + ( 0) ) ( )

( ) = ( ) + ( 0) ) ( ) EETOMAGNETI OMPATIBIITY HANDBOOK 1 hapter 9: Transent Behavor n the Tme Doman 9.1 Desgn a crcut usng reasonable values for the components that s capable of provdng a tme delay of 100 ms to a dgtal sgnal.

More information

Queens College, CUNY, Department of Computer Science Numerical Methods CSCI 361 / 761 Spring 2018 Instructor: Dr. Sateesh Mane.

Queens College, CUNY, Department of Computer Science Numerical Methods CSCI 361 / 761 Spring 2018 Instructor: Dr. Sateesh Mane. Queens College, CUNY, Department of Computer Scence Numercal Methods CSCI 361 / 761 Sprng 2018 Instructor: Dr. Sateesh Mane c Sateesh R. Mane 2018 16 Lecture 16a May 3, 2018 Numercal soluton of systems

More information

LECTURE 9 CANONICAL CORRELATION ANALYSIS

LECTURE 9 CANONICAL CORRELATION ANALYSIS LECURE 9 CANONICAL CORRELAION ANALYSIS Introducton he concept of canoncal correlaton arses when we want to quantfy the assocatons between two sets of varables. For example, suppose that the frst set of

More information

APPROXIMATE PRICES OF BASKET AND ASIAN OPTIONS DUPONT OLIVIER. Premia 14

APPROXIMATE PRICES OF BASKET AND ASIAN OPTIONS DUPONT OLIVIER. Premia 14 APPROXIMAE PRICES OF BASKE AND ASIAN OPIONS DUPON OLIVIER Prema 14 Contents Introducton 1 1. Framewor 1 1.1. Baset optons 1.. Asan optons. Computng the prce 3. Lower bound 3.1. Closed formula for the prce

More information

Structure and Drive Paul A. Jensen Copyright July 20, 2003

Structure and Drive Paul A. Jensen Copyright July 20, 2003 Structure and Drve Paul A. Jensen Copyrght July 20, 2003 A system s made up of several operatons wth flow passng between them. The structure of the system descrbes the flow paths from nputs to outputs.

More information

= z 20 z n. (k 20) + 4 z k = 4

= z 20 z n. (k 20) + 4 z k = 4 Problem Set #7 solutons 7.2.. (a Fnd the coeffcent of z k n (z + z 5 + z 6 + z 7 + 5, k 20. We use the known seres expanson ( n+l ( z l l z n below: (z + z 5 + z 6 + z 7 + 5 (z 5 ( + z + z 2 + z + 5 5

More information

Formulas for the Determinant

Formulas for the Determinant page 224 224 CHAPTER 3 Determnants e t te t e 2t 38 A = e t 2te t e 2t e t te t 2e 2t 39 If 123 A = 345, 456 compute the matrx product A adj(a) What can you conclude about det(a)? For Problems 40 43, use

More information

Société de Calcul Mathématique SA

Société de Calcul Mathématique SA Socété de Calcul Mathématque SA Outls d'ade à la décson Tools for decson help Probablstc Studes: Normalzng the Hstograms Bernard Beauzamy December, 202 I. General constructon of the hstogram Any probablstc

More information

( ) 2 ( ) ( ) Problem Set 4 Suggested Solutions. Problem 1

( ) 2 ( ) ( ) Problem Set 4 Suggested Solutions. Problem 1 Problem Set 4 Suggested Solutons Problem (A) The market demand functon s the soluton to the followng utlty-maxmzaton roblem (UMP): The Lagrangean: ( x, x, x ) = + max U x, x, x x x x st.. x + x + x y x,

More information

Additional Codes using Finite Difference Method. 1 HJB Equation for Consumption-Saving Problem Without Uncertainty

Additional Codes using Finite Difference Method. 1 HJB Equation for Consumption-Saving Problem Without Uncertainty Addtonal Codes usng Fnte Dfference Method Benamn Moll 1 HJB Equaton for Consumpton-Savng Problem Wthout Uncertanty Before consderng the case wth stochastc ncome n http://www.prnceton.edu/~moll/ HACTproect/HACT_Numercal_Appendx.pdf,

More information

Errors for Linear Systems

Errors for Linear Systems Errors for Lnear Systems When we solve a lnear system Ax b we often do not know A and b exactly, but have only approxmatons  and ˆb avalable. Then the best thng we can do s to solve ˆx ˆb exactly whch

More information

LAB 4: Modulus of elasticity

LAB 4: Modulus of elasticity LAB 4: Modulus of elastcty 1. Preparaton: modulus of elastcty (chapter15, p.79) Hook s law graphcal determnaton of modulus of elastcty (p.8) determnaton of modulus of elastcty n tenson and flexural stress

More information

COMPLEX NUMBERS AND QUADRATIC EQUATIONS

COMPLEX NUMBERS AND QUADRATIC EQUATIONS COMPLEX NUMBERS AND QUADRATIC EQUATIONS INTRODUCTION We know that x 0 for all x R e the square of a real number (whether postve, negatve or ero) s non-negatve Hence the equatons x, x, x + 7 0 etc are not

More information

Lecture 3 Stat102, Spring 2007

Lecture 3 Stat102, Spring 2007 Lecture 3 Stat0, Sprng 007 Chapter 3. 3.: Introducton to regresson analyss Lnear regresson as a descrptve technque The least-squares equatons Chapter 3.3 Samplng dstrbuton of b 0, b. Contnued n net lecture

More information

VARIATION OF CONSTANT SUM CONSTRAINT FOR INTEGER MODEL WITH NON UNIFORM VARIABLES

VARIATION OF CONSTANT SUM CONSTRAINT FOR INTEGER MODEL WITH NON UNIFORM VARIABLES VARIATION OF CONSTANT SUM CONSTRAINT FOR INTEGER MODEL WITH NON UNIFORM VARIABLES BÂRZĂ, Slvu Faculty of Mathematcs-Informatcs Spru Haret Unversty barza_slvu@yahoo.com Abstract Ths paper wants to contnue

More information

THE CHINESE REMAINDER THEOREM. We should thank the Chinese for their wonderful remainder theorem. Glenn Stevens

THE CHINESE REMAINDER THEOREM. We should thank the Chinese for their wonderful remainder theorem. Glenn Stevens THE CHINESE REMAINDER THEOREM KEITH CONRAD We should thank the Chnese for ther wonderful remander theorem. Glenn Stevens 1. Introducton The Chnese remander theorem says we can unquely solve any par of

More information

Games of Threats. Elon Kohlberg Abraham Neyman. Working Paper

Games of Threats. Elon Kohlberg Abraham Neyman. Working Paper Games of Threats Elon Kohlberg Abraham Neyman Workng Paper 18-023 Games of Threats Elon Kohlberg Harvard Busness School Abraham Neyman The Hebrew Unversty of Jerusalem Workng Paper 18-023 Copyrght 2017

More information

CHEM 112 Exam 3 Practice Test Solutions

CHEM 112 Exam 3 Practice Test Solutions CHEM 11 Exam 3 Practce Test Solutons 1A No matter what temperature the reacton takes place, the product of [OH-] x [H+] wll always equal the value of w. Therefore, f you take the square root of the gven

More information

Economic and Social Council

Economic and Social Council Unted Natons Economc and Socal Councl Dstr.: General 26 October 2018 Orgnal: Englsh Economc Commsson for Europe Inland Transport Commttee World Forum for Harmonzaton of ehcle Regulatons Workng Party on

More information

THE VIBRATIONS OF MOLECULES II THE CARBON DIOXIDE MOLECULE Student Instructions

THE VIBRATIONS OF MOLECULES II THE CARBON DIOXIDE MOLECULE Student Instructions THE VIBRATIONS OF MOLECULES II THE CARBON DIOXIDE MOLECULE Student Instructons by George Hardgrove Chemstry Department St. Olaf College Northfeld, MN 55057 hardgrov@lars.acc.stolaf.edu Copyrght George

More information

Appendix B. The Finite Difference Scheme

Appendix B. The Finite Difference Scheme 140 APPENDIXES Appendx B. The Fnte Dfference Scheme In ths appendx we present numercal technques whch are used to approxmate solutons of system 3.1 3.3. A comprehensve treatment of theoretcal and mplementaton

More information

Open Systems: Chemical Potential and Partial Molar Quantities Chemical Potential

Open Systems: Chemical Potential and Partial Molar Quantities Chemical Potential Open Systems: Chemcal Potental and Partal Molar Quanttes Chemcal Potental For closed systems, we have derved the followng relatonshps: du = TdS pdv dh = TdS + Vdp da = SdT pdv dg = VdP SdT For open systems,

More information

Order parameters of crystals in LAMMPS

Order parameters of crystals in LAMMPS Order parameters of crystals n LAMMPS Aula Tegar Wcaksono Department of Materals Engneerng, The Unversty of Brtsh Columba tegar@alumn.ubc.ca Wrtten on: July 19, 015 Abstract To dentfy atoms n a bcrystal

More information

The internal structure of natural numbers and one method for the definition of large prime numbers

The internal structure of natural numbers and one method for the definition of large prime numbers The nternal structure of natural numbers and one method for the defnton of large prme numbers Emmanul Manousos APM Insttute for the Advancement of Physcs and Mathematcs 3 Poulou str. 53 Athens Greece Abstract

More information

Negative Binomial Regression

Negative Binomial Regression STATGRAPHICS Rev. 9/16/2013 Negatve Bnomal Regresson Summary... 1 Data Input... 3 Statstcal Model... 3 Analyss Summary... 4 Analyss Optons... 7 Plot of Ftted Model... 8 Observed Versus Predcted... 10 Predctons...

More information

2.3 Nilpotent endomorphisms

2.3 Nilpotent endomorphisms s a block dagonal matrx, wth A Mat dm U (C) In fact, we can assume that B = B 1 B k, wth B an ordered bass of U, and that A = [f U ] B, where f U : U U s the restrcton of f to U 40 23 Nlpotent endomorphsms

More information