Complex Number Representation in RCBNS Form for Arithmetic Operations and Conversion of the Result into Standard Binary Form

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Complex Number Representation in RCBNS Form for Arithmetic Operations and Conversion of the Result into Standard Binary Form"

Transcription

1 Complex Number epresentaton n CBNS Form for Arthmetc Operatons and Converson of the esult nto Standard Bnary Form Hatm Zan and. G. Deshmukh Florda Insttute of Technology ABSTACT Ths paper ntroduces a novel method for complex number representaton. The proposed edundant Complex Bnary Number System (CBNS) s developed by combnng a edundant Bnary Number and a complex number n base (-. Donald [] and Walter Penny [,3] represented complex numbers usng base j and (- n the classfed algorthmc models. A edundant Complex Bnary Number System conssts of both real and magnary-radx number systems that form a redundant nteger dgt set. Ths system s formed by usng complex radx of (- and a dgt set of α = 3, where α assumes a value of -3, -, -,,,, 3. The arthmetc operatons of complex numbers wth ths system treat the real and magnary parts as one unt. The carry-free addton has the advantage of edundancy n number representaton n the arthmetc operatons. esults of the arthmetc operatons are n the CBNS form. The two methods for converson from the CBNS form to the standard bnary number form have been presented. In ths paper the CBNS reduces the number of steps reured to perform complex number arthmetc operatons, thus enhancng the speed. Keywords: Complex Bnary number, edundant Bnary Number, edundant Complex Bnary Number System, Addton and Subtracton.. INTODUCTION Algorthms n complex orthogonal transformatons, correlatons, and fltratons are nvolved n arthmetc computatons (e.g. geometrc analyss n graphcs or mage processng). These applcatons reure effcent representatons and treatment of complex numbers. In today s computers nvolvng complex numbers, the complex operatons use the real and magnary parts separately and then accumulate ther ndvdual results to obtan the fnal result. For example, the natural way of multplcaton of two complex numbers reures four real multplcatons and one real addton and one real subtracton. To convert complex number n the CBNS form, the real part and the magnary part of the gven number must be treated as one unt. Ths wll ncrease the speed of arthmetc operatons due to a decrease n the number of steps nvolved n these operatons. The complex Bnary Number System (CBNS) method uses a base of (- nstead of a base normally used n the Standard Bnary Number (SBN). There s a unue representaton for each complex number n the new base of (-. The value of an n-bt bnary number n the CBNS form wth the base (- can be wrtten n the form of a power seres as shown below.... a ( a ( a ( j () ) The coeffcents a assume a value of or. The powers of (- are grouped n a row of 4-bt postons as shown n Table. Each row labeled as s generated by multplyng the current row by 4. In other words, the followng expresson can be used to generate a row of 4 bts: ( = = ( j) ( j) ( ) ),,,3,,, j, =, *( 4 where ). For example, multplyng row by -4 generates the st row and multplyng the st row by -4 generates the nd row and so on. In 988, T. T. Dao attempted to defne specfc arthmetc operatons n radces /- 4 by mprovng an algorthm to generate several bts [4]. The focus s on the CBNS form where (- s the mnmum possble radx n the defnton of CBNS. Table shows the weghts of (- n a complex plane and ths s closely related to the radx -4 Sgn Dgt (SD) number system. Therefore, -4 s an element of the set of the CBNS of some power and t s effcent to work wth the edundant Bnary Sgn Dgt numbers. The CBNS s a postonal number system that has a complex radx and uses a dgt set { α to α} that allows for carry free addtons. The combnaton of the two algorthms, the redundant bnary numbers system [4, 5] and the bnary number system for the complex numbers [, ] results n the edundant Complex Bnary Number System (CBNS). 78 SYSTEMICS, CYBENETICS AND INFOMATICS VOLUME - NUMBE 6

2 ( ( j ) = ( -3 6 ( j ) = 9 ( ( j ) = 8 ( 6 4 ( j ) =,3,,, ( j ) = ( j ) = ( j ) = ( j ) =,3,,, - - ow = ow * (-4) ow = ow * (-4) ow = In ths paper the representaton of CBSN s ntroduced for the radx r = (- and a dgt set, D α Table. eal and magnary values wth radx (- D α where α = 3 and has the dgt set of (-3, -, -,,,, 3). Alpha ( α ) s restrcted to [( r ) / ] α ( r ) where r = 4. edundancy provdes carry-free addton n arthmetc operatons. The value of a number, X = ( xn, xn,..., x, x ) n the CBNS of base (- and α =3 can be shown by the followng expresson. X n = = x ( X = { α,..., α} () Fgure shows a block dagram for the complex number converson, followed by the arthmetc operatons (addtons and subtractons only), and then obtanng the results n the CBNS form and fnally convertng the CBNS result nto a regular bnary number. the bnary form for the real and magnary parts and then by usng the followng steps: Step : Check the sgn of both the real and magnary parts. If each s postve or negatve, then for the postve numbers place a n front of each of -bt dgt (e.g. for 9 =, then and ), and smlarly for the negatve numbers place n front of each of -bt dgt (e.g. for 9 = -, then and ). Step : Get 3 bts of each part and combne them together wth the LSB 3-bt of the magnary part catenated to the 3 bts of real part and then put them n the order of. st Complex Number nd Complex Number In the next secton, the basc propertes of the CBNS epresentaton are ntroduced wth ther basc arthmetc operatons.. EDUNDANT COMPLEX BINAY NUMBE SYSTEM EPESENTATION The redundancy n the CBNS representaton usng radx (- allows the converson of any complex number wthout any restrctons. Any complex number s represented by a row of 4 bts n the radx 4. To smplfy the converson from a bnary number to a base 4 CBNS form, a range of -3-j3 through 3j3 has been used for the representaton. A porton of the representaton s shown n Table. 3. COMPLEX NUMBE CONVESION IN THE TEM OF CBNS FOM Conversons of the complex numbers to the CBNS form s acheved by convertng the complex number nto Bnary code to CBNS Converson form st n n n = row s nd CBNS Converson form t Bnary form Fgure. Block dagram for the proposed algorthm s SYSTEMICS, CYBENETICS AND INFOMATICS VOLUME - NUMBE 6 79

3 ( 3 ( Table. Bt representatons for a row n 4 bts ( ( No j - j - j -3 j3 - - j j j j3 - -j3-3-j j j j3 - j3 - j3 - j j j -3 - j - --j - -j -j -j 3-j 3 Step 3: Combne the rght three bts of the magnary part to the rght three bts of the real part. epeat the same for the next three bts to form (see example ). There are four tables for the combnatons of the sgn of the real part and the sgn of the magnary part (/, /-, -/, -/-). Table 3 shows only the postve sgn for both the magnary and real parts. Step 4: Label a group of 4 bts n the frst row as. To generate the successve rows, multply the current row by 4 and so on. Ths results n the change of sgn and magntude from one row to the next. Therefore, even rows have postve and odd rows have negatve sgns as shown below. (...,,,, ) , The example below llustrates the converson of a complex bnary number to the CBNS form. The converson of the complex number, (j7) to the CBNS form s as follow. Step : Express numbers n the bnary form for magnary and real parts. Part () 7 = 7 = Part () = = Step : Get 3 bts of each part and combne them together startng wth LSB as 3 bts of and put them together wth 3 bts of. & Step 3: Fnd the euvalent values for each group of and from Table Step 4: Multply the postve sgn to even rows and the negatve sgn to the odd rows. ---, -- Fnally combne them agan n the followng order....,,,,, Use the term [( ) * ] 5 4 3, for each n the 4-bt row. 3. educton of Converson tables 4 The four tables generated for the four possble combnatons of the sgn of real and magnary parts of complex numbers can be reduced to only two tables. The -/- table can be obtaned by changng the sgn of the 4-bt rows of / table, and vce versa. The same s vald for /- table to -/ table and vce versa. ( ) base CBNS (-,3 j -j -j S -3 S -3 S -3 S -3 Table 3. Table of converson from Bnary form to CBNS form n / case 4. AITHMETIC OPEATION Complex numbers expressed n the CBNS form are used as operands to perform arthmetc operatons. The results of the operaton wll be n the CBNS form. An example of the addton operaton s shown below. In the subtracton operaton the sgn of real and magnary parts 8 SYSTEMICS, CYBENETICS AND INFOMATICS VOLUME - NUMBE 6

4 of the subtrahend are complemented and then added to the mnuend. An example of the addton of two complex numbers, (9 and (35j5) expressed n the CBNS form s llustrated below. *,3 *, *, 3-bt 3-bt 3-bt *,3 *, *, 3-bt 3-bt 3-bt Frst, two complex numbers (9 and (35j5) are converted nto the CBNS form. Then the addton operaton s performed. The complex number (9 s euvalent to (-- -) n the CBNS form, and smlarly the complex number (35j5) s euvalent to ( - -). X Y S In some cases the result may have numbers rangng from -6 to 6; n such cases normalzaton s necessary. The process of normalzaton s as follows: Normalze the ntermedate result to be n the set of {-3, -, -,,,, and 3}. Get the fnal result S = Normalzaton Carry, or S= S, f S n the range of 3 to 3. The above result wll be n the CBNS form. The next secton dscusses the converson of the CBNS result to an euvalent bnary number. 5. CONVESION FOM CBNS FOM TO BINAY FOM The result of the arthmetc operaton that s n the CBNS form should be converted back to the standard bnary number (SBN) form. Two methods are presented for the converson. Both methods produce the fnal result n the s complement form. Method : In ths method splt the real and magnary parts of each group (one row) and forward t to two dedcated regsters. The real number porton s moved nto regster and the magnary number porton s moved nto regster as shown n Fgure (a), (b).,3,,, j -j -j n n (a) 5-bt 5-bt (b) Fgure. Converson dagram from CBNS to SBN The calculaton for a row s gvng by the followng expressons. = ( *,3 ) (*, ) ( *, ) (*, ) = * ) ( * ) (* ) (* ) (,3,,, The maxmum value of the eal part for one row of the CBNS form s between - and ([ 3 *( j)] [ 3*( ] (3*) ), and the maxmum value of the Imagnary part for one row of CBNS form s between 5 and 5 ([ 3*( j )] [ 3*( j)] [3*( ] ). Ths method reures 5 bts for the output n the adder unt. For example, n ths method, convert the CBNS number ( ) ( s used for - and for - for convenence) to SBN form. The result s eual to row ( ) - 4* row ( ) 6* row ( ) = 44j36 where row = [ * * *] j[* * *] and so on for the rest of the rows. Method : In ths method, separate the real and magnary numbers of each dgt n a row to have two parts, one for real and the other for magnary. Ths method modfes each row n the form shown, =,3 =, =,, =, and the entre real number part goes nto regster. For each row, has 5 bts and have 3 bts, and the magnary number part goes nto regster. For each row, has 3 bts and has 5 bts. The values for the real and the magnary parts go nto the output regsters and for each row of,,, and where: =, = =, =, SYSTEMICS, CYBENETICS AND INFOMATICS VOLUME - NUMBE 6 8

5 Fgure 3 shows the block dagram for mplementaton of Method for converson from the CBNS form to the SBN form. An example of ths converson s shown n Fgure CONCLUSION A method to convert complex numbers to ther euvalent CBNS form has been presented. Combnng two algorthms, the redundant bnary numbers system and the bnary number system for complex numbers, results n the edundant Complex Bnary Number System. Operands are receved n the CBNS form as nputs to an adder for the addton (wth the sgn changed to the subtrahend operaton) and the sum results n the CBNS form. Two methods have been presented for the converson of the CBNS result nto the SBN form. The entre process wll ncrease the speed of arthmetc operatons due to a decrease n the number of steps nvolved. A crcut dagram mplementaton of the arthmetc unt based on CBNS form usng FPGA s under progress. Load, 3 5-bt 3-bt -,,, Normalzaton to be n SBN 3-bt 5-bt Fgure 3. Converson dagram from CBNS to SBN,3,,,,3,,,,3,,, = = = = - = = = - = -4 = = 4 = The fnal result s = [6*()-4*(-) 4] j[6*()-4*(-4) (4)] = 44 j36 Fgure 4. Converson of the fnal result back to SBN 7. EFEENCES [] D. E. Knuth, An Imagnary Number System, Communcatons of the ACM, Vol. 3, pp , 96. [] W. Penney, A Number System Wth a Negatve Base, Mathematc Student ournal, Vol., No. 4, pp. -, May 964. [3] W. Penney, A Bnary System For a Complex Numbers, ournal of the ACM, Vol., No., pp , Aprl 965. [4] Y. Oh, T. Aok, and T. Hguch, edundant Complex Number System, 5 th IEEE Int. Symp. on Multple- Valued Logc, pp. 4-9,Bloomngton,IN,USA, May 995. [5] A. Avzens, Sgned Dgt Number epresentatons for Fast Parallel Arthmetc, IE Trans. Electronc Computers, Vol. EC-, pp , September 96. [6] T. aml, N. Holmes, and D. Blest, Towards Implementaton of a Bnary Number System for Complex Numbers, Proceedng of the IEEE SouthEastCon, pp ,. [7] T. aml, The Complex Bnary Number System, Proceedng of the IEEE potentals on, pp [8] T. Aok, K. Hosh and T. Hguch, edundant Complex Arthmetc and Its Applcaton to Complex 8 SYSTEMICS, CYBENETICS AND INFOMATICS VOLUME - NUMBE 6

6 Multpler desgn, 9 th IEEE Int. Symp. on Multple- Valued Logc, pp. -7, Freburg, 999. [9]. Mcllhenny, and M. D. Ercegovac, On-Lne Algorthem for Complex Number Arthmetc, Proceedng of the IEEE 998, 3 nd Aslomar Conference on Sgnals, Systems & Computers, part (of ), Pacfc Grove, CA, USA, pp. 7-76, Nov [] T. T. Dao, Specfc Arthmetc n adces /-4, 8 th IEEE Int. Symp. on Multple-Valued Logc, pp , 988. SYSTEMICS, CYBENETICS AND INFOMATICS VOLUME - NUMBE 6 83

Multiplication Algorithms for Radix-2 RN-Codings and Two s Complement Numbers

Multiplication Algorithms for Radix-2 RN-Codings and Two s Complement Numbers Multplcaton Algorthms for Radx- RN-Codngs and Two s Complement Numbers Jean-Luc Beuchat Projet Arénare, LIP, ENS Lyon 46, Allée d Itale F 69364 Lyon Cedex 07 jean-luc.beuchat@ens-lyon.fr Jean-Mchel Muller

More information

Aryabhata s Root Extraction Methods. Abhishek Parakh Louisiana State University Aug 31 st 2006

Aryabhata s Root Extraction Methods. Abhishek Parakh Louisiana State University Aug 31 st 2006 Aryabhata s Root Extracton Methods Abhshek Parakh Lousana State Unversty Aug 1 st 1 Introducton Ths artcle presents an analyss of the root extracton algorthms of Aryabhata gven n hs book Āryabhatīya [1,

More information

Implementation of Deutsch's Algorithm Using Mathcad

Implementation of Deutsch's Algorithm Using Mathcad Implementaton of Deutsch's Algorthm Usng Mathcad Frank Roux The followng s a Mathcad mplementaton of Davd Deutsch's quantum computer prototype as presented on pages - n "Machnes, Logc and Quantum Physcs"

More information

Chapter 3 Group Theory p. 1 - Remark: This is only a brief summary of most important results of groups theory with respect

Chapter 3 Group Theory p. 1 - Remark: This is only a brief summary of most important results of groups theory with respect Chapter 3 Group Theory p. - 3. Compact Course: Groups Theory emark: Ths s only a bref summary of most mportant results of groups theory wth respect to the applcatons dscussed n the followng chapters. For

More information

An approach to Digital Low-Pass IIR Filter Design

An approach to Digital Low-Pass IIR Filter Design An approach to Dgtal Low-Pass IIR Flter Desgn Bojan Jovanovć, and Mlun Jevtć Abstract The paper descrbes the desgn process of dscrete network dgtal low-pass flter wth Infnte Impulse Response (IIR flter).

More information

Texas Instruments 30X IIS Calculator

Texas Instruments 30X IIS Calculator Texas Instruments 30X IIS Calculator Keystrokes for the TI-30X IIS are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the

More information

Laddered Multilevel DC/AC Inverters used in Solar Panel Energy Systems

Laddered Multilevel DC/AC Inverters used in Solar Panel Energy Systems Proceedngs of the nd Internatonal Conference on Computer Scence and Electroncs Engneerng (ICCSEE 03) Laddered Multlevel DC/AC Inverters used n Solar Panel Energy Systems Fang Ln Luo, Senor Member IEEE

More information

Texas Instruments 30Xa Calculator

Texas Instruments 30Xa Calculator Teas Instruments 30Xa Calculator Keystrokes for the TI-30Xa are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the tet, check

More information

where the coordinates are related to those in the old frame as follows.

where the coordinates are related to those in the old frame as follows. Chapter 2 - Cartesan Vectors and Tensors: Ther Algebra Defnton of a vector Examples of vectors Scalar multplcaton Addton of vectors coplanar vectors Unt vectors A bass of non-coplanar vectors Scalar product

More information

Module 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur

Module 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..

More information

Solution : (a) FALSE. Let C be a binary one-error correcting code of length 9. Then it follows from the Sphere packing bound that.

Solution : (a) FALSE. Let C be a binary one-error correcting code of length 9. Then it follows from the Sphere packing bound that. MATH 29T Exam : Part I Solutons. TRUE/FALSE? Prove your answer! (a) (5 pts) There exsts a bnary one-error correctng code of length 9 wth 52 codewords. (b) (5 pts) There exsts a ternary one-error correctng

More information

What is Candidate Sampling

What is Candidate Sampling What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble

More information

Introduction: Analysis of Electronic Circuits

Introduction: Analysis of Electronic Circuits /30/008 ntroducton / ntroducton: Analyss of Electronc Crcuts Readng Assgnment: KVL and KCL text from EECS Just lke EECS, the majorty of problems (hw and exam) n EECS 3 wll be crcut analyss problems. Thus,

More information

BERNSTEIN POLYNOMIALS

BERNSTEIN POLYNOMIALS On-Lne Geometrc Modelng Notes BERNSTEIN POLYNOMIALS Kenneth I. Joy Vsualzaton and Graphcs Research Group Department of Computer Scence Unversty of Calforna, Davs Overvew Polynomals are ncredbly useful

More information

Level Annuities with Payments Less Frequent than Each Interest Period

Level Annuities with Payments Less Frequent than Each Interest Period Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annuty-mmedate 2 Annuty-due Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annuty-mmedate 2 Annuty-due Symoblc approach

More information

Digital Logic Design: An Embedded Systems Approach Using VHDL. Chapter 3 Numeric Basics

Digital Logic Design: An Embedded Systems Approach Using VHDL. Chapter 3 Numeric Basics Dgtal Logc Desgn. Chapter 3 6 March 7 Dgtal Logc Desgn: An Embedded Systems Approach Usng VHDL Chapter 3 Numerc Bascs Portons of ths work are from the book, Dgtal Logc Desgn: An Embedded Systems Approach

More information

9.1 The Cumulative Sum Control Chart

9.1 The Cumulative Sum Control Chart Learnng Objectves 9.1 The Cumulatve Sum Control Chart 9.1.1 Basc Prncples: Cusum Control Chart for Montorng the Process Mean If s the target for the process mean, then the cumulatve sum control chart s

More information

( ) Homework Solutions Physics 8B Spring 09 Chpt. 32 5,18,25,27,36,42,51,57,61,76

( ) Homework Solutions Physics 8B Spring 09 Chpt. 32 5,18,25,27,36,42,51,57,61,76 Homework Solutons Physcs 8B Sprng 09 Chpt. 32 5,8,25,27,3,42,5,57,,7 32.5. Model: Assume deal connectng wres and an deal battery for whch V bat = E. Please refer to Fgure EX32.5. We wll choose a clockwse

More information

EE201 Circuit Theory I 2015 Spring. Dr. Yılmaz KALKAN

EE201 Circuit Theory I 2015 Spring. Dr. Yılmaz KALKAN EE201 Crcut Theory I 2015 Sprng Dr. Yılmaz KALKAN 1. Basc Concepts (Chapter 1 of Nlsson - 3 Hrs.) Introducton, Current and Voltage, Power and Energy 2. Basc Laws (Chapter 2&3 of Nlsson - 6 Hrs.) Voltage

More information

Section C2: BJT Structure and Operational Modes

Section C2: BJT Structure and Operational Modes Secton 2: JT Structure and Operatonal Modes Recall that the semconductor dode s smply a pn juncton. Dependng on how the juncton s based, current may easly flow between the dode termnals (forward bas, v

More information

Graph Theory and Cayley s Formula

Graph Theory and Cayley s Formula Graph Theory and Cayley s Formula Chad Casarotto August 10, 2006 Contents 1 Introducton 1 2 Bascs and Defntons 1 Cayley s Formula 4 4 Prüfer Encodng A Forest of Trees 7 1 Introducton In ths paper, I wll

More information

Homework Solutions Physics 8B Spring 2012 Chpt. 32 5,18,25,27,36,42,51,57,61,76

Homework Solutions Physics 8B Spring 2012 Chpt. 32 5,18,25,27,36,42,51,57,61,76 Homework Solutons Physcs 8B Sprng 202 Chpt. 32 5,8,25,27,3,42,5,57,,7 32.5. Model: Assume deal connectng wres and an deal battery for whch V bat =. Please refer to Fgure EX32.5. We wll choose a clockwse

More information

Time Value of Money Module

Time Value of Money Module Tme Value of Money Module O BJECTIVES After readng ths Module, you wll be able to: Understand smple nterest and compound nterest. 2 Compute and use the future value of a sngle sum. 3 Compute and use the

More information

Passive Filters. References: Barbow (pp 265-275), Hayes & Horowitz (pp 32-60), Rizzoni (Chap. 6)

Passive Filters. References: Barbow (pp 265-275), Hayes & Horowitz (pp 32-60), Rizzoni (Chap. 6) Passve Flters eferences: Barbow (pp 6575), Hayes & Horowtz (pp 360), zzon (Chap. 6) Frequencyselectve or flter crcuts pass to the output only those nput sgnals that are n a desred range of frequences (called

More information

Logistic Regression. Lecture 4: More classifiers and classes. Logistic regression. Adaboost. Optimization. Multiple class classification

Logistic Regression. Lecture 4: More classifiers and classes. Logistic regression. Adaboost. Optimization. Multiple class classification Lecture 4: More classfers and classes C4B Machne Learnng Hlary 20 A. Zsserman Logstc regresson Loss functons revsted Adaboost Loss functons revsted Optmzaton Multple class classfcaton Logstc Regresson

More information

Quantization Effects in Digital Filters

Quantization Effects in Digital Filters Quantzaton Effects n Dgtal Flters Dstrbuton of Truncaton Errors In two's complement representaton an exact number would have nfntely many bts (n general). When we lmt the number of bts to some fnte value

More information

1. Measuring association using correlation and regression

1. Measuring association using correlation and regression How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a

More information

Using Alpha-Beta Associative Memories to Learn and Recall RGB Images

Using Alpha-Beta Associative Memories to Learn and Recall RGB Images Usng Alpha-Beta Assocatve Memores to Learn and Recall RGB Images Cornelo Yáñez-Márquez, María Elena Cruz-Meza, Flavo Arturo Sánchez-Garfas, and Itzamá López-Yáñez Centro de Investgacón en Computacón, Insttuto

More information

"Research Note" APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES *

Research Note APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES * Iranan Journal of Scence & Technology, Transacton B, Engneerng, ol. 30, No. B6, 789-794 rnted n The Islamc Republc of Iran, 006 Shraz Unversty "Research Note" ALICATION OF CHARGE SIMULATION METHOD TO ELECTRIC

More information

Linear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits

Linear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits Lnear Crcuts Analyss. Superposton, Theenn /Norton Equalent crcuts So far we hae explored tmendependent (resste) elements that are also lnear. A tmendependent elements s one for whch we can plot an / cure.

More information

High-Speed Decoding of the Binary Golay Code

High-Speed Decoding of the Binary Golay Code Hgh-Speed Decodng of the Bnary Golay Code H. P. Lee *1, C. H. Chang 1, S. I. Chu 2 1 Department of Computer Scence and Informaton Engneerng, Fortune Insttute of Technology, Kaohsung 83160, Tawan *hpl@fotech.edu.tw

More information

Lesson 2 Chapter Two Three Phase Uncontrolled Rectifier

Lesson 2 Chapter Two Three Phase Uncontrolled Rectifier Lesson 2 Chapter Two Three Phase Uncontrolled Rectfer. Operatng prncple of three phase half wave uncontrolled rectfer The half wave uncontrolled converter s the smplest of all three phase rectfer topologes.

More information

IMPROVEMENT OF CONVERGENCE CONDITION OF THE SQUARE-ROOT INTERVAL METHOD FOR MULTIPLE ZEROS 1

IMPROVEMENT OF CONVERGENCE CONDITION OF THE SQUARE-ROOT INTERVAL METHOD FOR MULTIPLE ZEROS 1 Nov Sad J. Math. Vol. 36, No. 2, 2006, 0-09 IMPROVEMENT OF CONVERGENCE CONDITION OF THE SQUARE-ROOT INTERVAL METHOD FOR MULTIPLE ZEROS Modrag S. Petkovć 2, Dušan M. Mloševć 3 Abstract. A new theorem concerned

More information

Implementation of Boolean Functions through Multiplexers with the Help of Shannon Expansion Theorem

Implementation of Boolean Functions through Multiplexers with the Help of Shannon Expansion Theorem Internatonal Journal o Computer pplcatons (975 8887) Volume 62 No.6, January 23 Implementaton o Boolean Functons through Multplexers wth the Help o Shannon Expanson Theorem Saurabh Rawat Graphc Era Unversty.

More information

Moment of a force about a point and about an axis

Moment of a force about a point and about an axis 3. STATICS O RIGID BODIES In the precedng chapter t was assumed that each of the bodes consdered could be treated as a sngle partcle. Such a vew, however, s not always possble, and a body, n general, should

More information

ALTERNATIVE ARITHMETIC STRUCTURES USING REDUNDANT NUMBERS AND MULTI-VALUED CIRCUIT TECHNIQUES

ALTERNATIVE ARITHMETIC STRUCTURES USING REDUNDANT NUMBERS AND MULTI-VALUED CIRCUIT TECHNIQUES ALTERNATIVE ARITHMETIC STRUCTURES USING REDUNDANT NUMBERS AND MULTI-VALUED CIRCUIT TECHNIQUES by Uğur Çn B.S., Electroncs and Communcatons Engneerng, Yıldız Techncal Unversty, 1999 M.S., Electrcal and

More information

Power-of-Two Policies for Single- Warehouse Multi-Retailer Inventory Systems with Order Frequency Discounts

Power-of-Two Policies for Single- Warehouse Multi-Retailer Inventory Systems with Order Frequency Discounts Power-of-wo Polces for Sngle- Warehouse Mult-Retaler Inventory Systems wth Order Frequency Dscounts José A. Ventura Pennsylvana State Unversty (USA) Yale. Herer echnon Israel Insttute of echnology (Israel)

More information

9 Arithmetic and Geometric Sequence

9 Arithmetic and Geometric Sequence AAU - Busness Mathematcs I Lecture #5, Aprl 4, 010 9 Arthmetc and Geometrc Sequence Fnte sequence: 1, 5, 9, 13, 17 Fnte seres: 1 + 5 + 9 + 13 +17 Infnte sequence: 1,, 4, 8, 16,... Infnte seres: 1 + + 4

More information

21 Vectors: The Cross Product & Torque

21 Vectors: The Cross Product & Torque 21 Vectors: The Cross Product & Torque Do not use our left hand when applng ether the rght-hand rule for the cross product of two vectors dscussed n ths chapter or the rght-hand rule for somethng curl

More information

A Secure Password-Authenticated Key Agreement Using Smart Cards

A Secure Password-Authenticated Key Agreement Using Smart Cards A Secure Password-Authentcated Key Agreement Usng Smart Cards Ka Chan 1, Wen-Chung Kuo 2 and Jn-Chou Cheng 3 1 Department of Computer and Informaton Scence, R.O.C. Mltary Academy, Kaohsung 83059, Tawan,

More information

IDENTIFICATION AND CONTROL OF A FLEXIBLE TRANSMISSION SYSTEM

IDENTIFICATION AND CONTROL OF A FLEXIBLE TRANSMISSION SYSTEM Abstract IDENTIFICATION AND CONTROL OF A FLEXIBLE TRANSMISSION SYSTEM Alca Esparza Pedro Dept. Sstemas y Automátca, Unversdad Poltécnca de Valenca, Span alespe@sa.upv.es The dentfcaton and control of a

More information

A Crossplatform ECG Compression Library for Mobile HealthCare Services

A Crossplatform ECG Compression Library for Mobile HealthCare Services A Crossplatform ECG Compresson Lbrary for Moble HealthCare Servces Alexander Borodn, Yulya Zavyalova Department of Computer Scence Petrozavodsk State Unversty Petrozavodsk, Russa {aborod, yzavyalo}@cs.petrsu.ru

More information

State function: eigenfunctions of hermitian operators-> normalization, orthogonality completeness

State function: eigenfunctions of hermitian operators-> normalization, orthogonality completeness Schroednger equaton Basc postulates of quantum mechancs. Operators: Hermtan operators, commutators State functon: egenfunctons of hermtan operators-> normalzaton, orthogonalty completeness egenvalues and

More information

1E6 Electrical Engineering AC Circuit Analysis and Power Lecture 12: Parallel Resonant Circuits

1E6 Electrical Engineering AC Circuit Analysis and Power Lecture 12: Parallel Resonant Circuits E6 Electrcal Engneerng A rcut Analyss and Power ecture : Parallel esonant rcuts. Introducton There are equvalent crcuts to the seres combnatons examned whch exst n parallel confguratons. The ssues surroundng

More information

Pre-Algebra. Mix-N-Match. Line-Ups. Inside-Outside Circle. A c t. t i e s & v i

Pre-Algebra. Mix-N-Match. Line-Ups. Inside-Outside Circle. A c t. t i e s & v i IV A c t Pre-Algebra v Mx-N-Match 1. Operatons on Fractons.................15 2. Order of Operatons....................15 3. Exponental Form......................16 4. Scentfc Notaton......................16

More information

Recurrence. 1 Definitions and main statements

Recurrence. 1 Definitions and main statements Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.

More information

8 Algorithm for Binary Searching in Trees

8 Algorithm for Binary Searching in Trees 8 Algorthm for Bnary Searchng n Trees In ths secton we present our algorthm for bnary searchng n trees. A crucal observaton employed by the algorthm s that ths problem can be effcently solved when the

More information

Multicomponent Distillation

Multicomponent Distillation Multcomponent Dstllaton need more than one dstllaton tower, for n components, n-1 fractonators are requred Specfcaton Lmtatons The followng are establshed at the begnnng 1. Temperature, pressure, composton,

More information

Aberration fields of a combination of plane symmetric systems

Aberration fields of a combination of plane symmetric systems Aberraton felds of a combnaton of pne symmetrc systems Lor B. Moore Anastaca M. vsc and Jose Sasan * College of Optcal Scences Unversty of Arzona 630 E. Unversty Boulevard Tucson AZ 857 USA * Correspondng

More information

v a 1 b 1 i, a 2 b 2 i,..., a n b n i.

v a 1 b 1 i, a 2 b 2 i,..., a n b n i. SECTION 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS 455 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS All the vector spaces we have studed thus far n the text are real vector spaces snce the scalars are

More information

8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by

8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by 6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng

More information

U.C. Berkeley CS270: Algorithms Lecture 4 Professor Vazirani and Professor Rao Jan 27,2011 Lecturer: Umesh Vazirani Last revised February 10, 2012

U.C. Berkeley CS270: Algorithms Lecture 4 Professor Vazirani and Professor Rao Jan 27,2011 Lecturer: Umesh Vazirani Last revised February 10, 2012 U.C. Berkeley CS270: Algorthms Lecture 4 Professor Vazran and Professor Rao Jan 27,2011 Lecturer: Umesh Vazran Last revsed February 10, 2012 Lecture 4 1 The multplcatve weghts update method The multplcatve

More information

Section 5.4 Annuities, Present Value, and Amortization

Section 5.4 Annuities, Present Value, and Amortization Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today

More information

Using Series to Analyze Financial Situations: Present Value

Using Series to Analyze Financial Situations: Present Value 2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated

More information

2.4 Bivariate distributions

2.4 Bivariate distributions page 28 2.4 Bvarate dstrbutons 2.4.1 Defntons Let X and Y be dscrete r.v.s defned on the same probablty space (S, F, P). Instead of treatng them separately, t s often necessary to thnk of them actng together

More information

2. Linear Algebraic Equations

2. Linear Algebraic Equations 2. Lnear Algebrac Equatons Many physcal systems yeld smultaneous algebrac equatons when mathematcal functons are requred to satsfy several condtons smultaneously. Each condton results n an equaton that

More information

LETTER IMAGE RECOGNITION

LETTER IMAGE RECOGNITION LETTER IMAGE RECOGNITION 1. Introducton. 1. Introducton. Objectve: desgn classfers for letter mage recognton. consder accuracy and tme n takng the decson. 20,000 samples: Startng set: mages based on 20

More information

A Computer Technique for Solving LP Problems with Bounded Variables

A Computer Technique for Solving LP Problems with Bounded Variables Dhaka Unv. J. Sc. 60(2): 163-168, 2012 (July) A Computer Technque for Solvng LP Problems wth Bounded Varables S. M. Atqur Rahman Chowdhury * and Sanwar Uddn Ahmad Department of Mathematcs; Unversty of

More information

Section B9: Zener Diodes

Section B9: Zener Diodes Secton B9: Zener Dodes When we frst talked about practcal dodes, t was mentoned that a parameter assocated wth the dode n the reverse bas regon was the breakdown voltage, BR, also known as the peak-nverse

More information

Communication Networks II Contents

Communication Networks II Contents 8 / 1 -- Communcaton Networs II (Görg) -- www.comnets.un-bremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP

More information

Project Networks With Mixed-Time Constraints

Project Networks With Mixed-Time Constraints Project Networs Wth Mxed-Tme Constrants L Caccetta and B Wattananon Western Australan Centre of Excellence n Industral Optmsaton (WACEIO) Curtn Unversty of Technology GPO Box U1987 Perth Western Australa

More information

PLANAR GRAPHS. Plane graph (or embedded graph) A graph that is drawn on the plane without edge crossing, is called a Plane graph

PLANAR GRAPHS. Plane graph (or embedded graph) A graph that is drawn on the plane without edge crossing, is called a Plane graph PLANAR GRAPHS Basc defntons Isomorphc graphs Two graphs G(V,E) and G2(V2,E2) are somorphc f there s a one-to-one correspondence F of ther vertces such that the followng holds: - u,v V, uv E, => F(u)F(v)

More information

A) 3.1 B) 3.3 C) 3.5 D) 3.7 E) 3.9 Solution.

A) 3.1 B) 3.3 C) 3.5 D) 3.7 E) 3.9 Solution. ACTS 408 Instructor: Natala A. Humphreys SOLUTION TO HOMEWOR 4 Secton 7: Annutes whose payments follow a geometrc progresson. Secton 8: Annutes whose payments follow an arthmetc progresson. Problem Suppose

More information

QUANTUM MECHANICS, BRAS AND KETS

QUANTUM MECHANICS, BRAS AND KETS PH575 SPRING QUANTUM MECHANICS, BRAS AND KETS The followng summares the man relatons and defntons from quantum mechancs that we wll be usng. State of a phscal sstem: The state of a phscal sstem s represented

More information

SIGNIFICANT FIGURES (4SF) (4SF) (5SF) (3 SF) 62.4 (3 SF) x 10 4 (5 SF) Figure 0

SIGNIFICANT FIGURES (4SF) (4SF) (5SF) (3 SF) 62.4 (3 SF) x 10 4 (5 SF) Figure 0 SIGIFICAT FIGURES Wth any calbrated nstrument, there s a lmt to the number of fgures that can be relably kept n the answer. For dgtal nstruments, the lmtaton s the number of fgures appearng n the dsplay.

More information

1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP)

1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP) 6.3 / -- Communcaton Networks II (Görg) SS20 -- www.comnets.un-bremen.de Communcaton Networks II Contents. Fundamentals of probablty theory 2. Emergence of communcaton traffc 3. Stochastc & Markovan Processes

More information

A Performance Analysis of View Maintenance Techniques for Data Warehouses

A Performance Analysis of View Maintenance Techniques for Data Warehouses A Performance Analyss of Vew Mantenance Technques for Data Warehouses Xng Wang Dell Computer Corporaton Round Roc, Texas Le Gruenwald The nversty of Olahoma School of Computer Scence orman, OK 739 Guangtao

More information

NPAR TESTS. One-Sample Chi-Square Test. Cell Specification. Observed Frequencies 1O i 6. Expected Frequencies 1EXP i 6

NPAR TESTS. One-Sample Chi-Square Test. Cell Specification. Observed Frequencies 1O i 6. Expected Frequencies 1EXP i 6 PAR TESTS If a WEIGHT varable s specfed, t s used to replcate a case as many tmes as ndcated by the weght value rounded to the nearest nteger. If the workspace requrements are exceeded and samplng has

More information

The k-binomial Transforms and the Hankel Transform

The k-binomial Transforms and the Hankel Transform 1 2 3 47 6 23 11 Journal of Integer Sequences, Vol. 9 (2006, Artcle 06.1.1 The k-bnomal Transforms and the Hankel Transform Mchael Z. Spvey Department of Mathematcs and Computer Scence Unversty of Puget

More information

PERRON FROBENIUS THEOREM

PERRON FROBENIUS THEOREM PERRON FROBENIUS THEOREM R. CLARK ROBINSON Defnton. A n n matrx M wth real entres m, s called a stochastc matrx provded () all the entres m satsfy 0 m, () each of the columns sum to one, m = for all, ()

More information

SCALAR A physical quantity that is completely characterized by a real number (or by its numerical value) is called a scalar. In other words, a scalar

SCALAR A physical quantity that is completely characterized by a real number (or by its numerical value) is called a scalar. In other words, a scalar SCALAR A phscal quantt that s completel charactered b a real number (or b ts numercal value) s called a scalar. In other words, a scalar possesses onl a magntude. Mass, denst, volume, temperature, tme,

More information

Fuzzy TOPSIS Method in the Selection of Investment Boards by Incorporating Operational Risks

Fuzzy TOPSIS Method in the Selection of Investment Boards by Incorporating Operational Risks , July 6-8, 2011, London, U.K. Fuzzy TOPSIS Method n the Selecton of Investment Boards by Incorporatng Operatonal Rsks Elssa Nada Mad, and Abu Osman Md Tap Abstract Mult Crtera Decson Makng (MCDM) nvolves

More information

ASIC Implementation Of Reed Solomon Codec For Burst Error Detection And Correction

ASIC Implementation Of Reed Solomon Codec For Burst Error Detection And Correction Vol. 2 Issue 4, Aprl - 2013 ASIC Implementaton Of Reed Solomon Codec For Burst Error etecton And Correcton Sangeeta Sngh Assocate Professor ept. of ECE Vardhaman College of Engneerng Hyderabad (A.P) S.

More information

Conversion between the vector and raster data structures using Fuzzy Geographical Entities

Conversion between the vector and raster data structures using Fuzzy Geographical Entities Converson between the vector and raster data structures usng Fuzzy Geographcal Enttes Cdála Fonte Department of Mathematcs Faculty of Scences and Technology Unversty of Combra, Apartado 38, 3 454 Combra,

More information

A Perfect QoS Routing Algorithm for Finding the Best Path for Dynamic Networks

A Perfect QoS Routing Algorithm for Finding the Best Path for Dynamic Networks A Perfect QoS Routng Algorthm for Fndng the Best Path for Dynamc Networks Hazem M. El-Bakry Faculty of Computer Scence & Informaton Systems, Mansoura Unversty, EGYPT helbakry20@yahoo.com Nkos Mastoraks

More information

How Sets of Coherent Probabilities May Serve as Models for Degrees of Incoherence

How Sets of Coherent Probabilities May Serve as Models for Degrees of Incoherence 1 st Internatonal Symposum on Imprecse Probabltes and Ther Applcatons, Ghent, Belgum, 29 June 2 July 1999 How Sets of Coherent Probabltes May Serve as Models for Degrees of Incoherence Mar J. Schervsh

More information

Traffic State Estimation in the Traffic Management Center of Berlin

Traffic State Estimation in the Traffic Management Center of Berlin Traffc State Estmaton n the Traffc Management Center of Berln Authors: Peter Vortsch, PTV AG, Stumpfstrasse, D-763 Karlsruhe, Germany phone ++49/72/965/35, emal peter.vortsch@ptv.de Peter Möhl, PTV AG,

More information

A linear recurrence sequence of composite numbers

A linear recurrence sequence of composite numbers LMS J Comput Math 15 (2012) 360 373 C 2012 Author do:101112/s1461157012001143 A lnear recurrence sequence of composte numbers Jonas Šurys Abstract We prove that for each postve nteger k n the range 2 k

More information

Gibbs Free Energy and Chemical Equilibrium (or how to predict chemical reactions without doing experiments)

Gibbs Free Energy and Chemical Equilibrium (or how to predict chemical reactions without doing experiments) Gbbs Free Energy and Chemcal Equlbrum (or how to predct chemcal reactons wthout dong experments) OCN 623 Chemcal Oceanography Readng: Frst half of Chapter 3, Snoeynk and Jenkns (1980) Introducton We want

More information

Optical Signal-to-Noise Ratio and the Q-Factor in Fiber-Optic Communication Systems

Optical Signal-to-Noise Ratio and the Q-Factor in Fiber-Optic Communication Systems Applcaton ote: FA-9.0. Re.; 04/08 Optcal Sgnal-to-ose Rato and the Q-Factor n Fber-Optc Communcaton Systems Functonal Dagrams Pn Confguratons appear at end of data sheet. Functonal Dagrams contnued at

More information

2. Introduction and Chapter Objectives

2. Introduction and Chapter Objectives eal Analog Crcuts Chapter : Crcut educton. Introducton and Chapter Objectes In Chapter, we presented Krchoff s laws (whch goern the nteractons between crcut elements) and Ohm s law (whch goerns the oltagecurrent

More information

On-Board Satellite Implementation of Wavelet-Based Predictive Coding of Hyperspectral Images

On-Board Satellite Implementation of Wavelet-Based Predictive Coding of Hyperspectral Images On-oard Satellte Implementaton of -ased Predctve Codng of Hyperspectral Images Agneszka C. Mguel*, Alexander Chang #, Rchard E. Ladner #, Scott Hauck*, Eve A. Rskn* * Department of Electrcal Engneerng,

More information

Fast degree elevation and knot insertion for B-spline curves

Fast degree elevation and knot insertion for B-spline curves Computer Aded Geometrc Desgn 22 (2005) 183 197 www.elsever.com/locate/cagd Fast degree elevaton and knot nserton for B-splne curves Q-Xng Huang a,sh-mnhu a,, Ralph R. Martn b a Department of Computer Scence

More information

Online Learning from Experts: Minimax Regret

Online Learning from Experts: Minimax Regret E0 370 tatstcal Learnng Theory Lecture 2 Nov 24, 20) Onlne Learnng from Experts: Mn Regret Lecturer: hvan garwal crbe: Nkhl Vdhan Introducton In the last three lectures we have been dscussng the onlne

More information

THE APPLICATION OF DATA MINING TECHNIQUES AND MULTIPLE CLASSIFIERS TO MARKETING DECISION

THE APPLICATION OF DATA MINING TECHNIQUES AND MULTIPLE CLASSIFIERS TO MARKETING DECISION Internatonal Journal of Electronc Busness Management, Vol. 3, No. 4, pp. 30-30 (2005) 30 THE APPLICATION OF DATA MINING TECHNIQUES AND MULTIPLE CLASSIFIERS TO MARKETING DECISION Yu-Mn Chang *, Yu-Cheh

More information

A Fault Tree Analysis Strategy Using Binary Decision Diagrams.

A Fault Tree Analysis Strategy Using Binary Decision Diagrams. A Fault Tree Analyss Strategy Usng Bnary Decson Dagrams. Karen A. Reay and John D. Andrews Loughborough Unversty, Loughborough, Lecestershre, LE 3TU. Abstract The use of Bnary Decson Dagrams (BDDs) n fault

More information

Support Vector Machines

Support Vector Machines Support Vector Machnes Max Wellng Department of Computer Scence Unversty of Toronto 10 Kng s College Road Toronto, M5S 3G5 Canada wellng@cs.toronto.edu Abstract Ths s a note to explan support vector machnes.

More information

Lossless Data Compression

Lossless Data Compression Lossless Data Compresson Lecture : Unquely Decodable and Instantaneous Codes Sam Rowes September 5, 005 Let s focus on the lossless data compresson problem for now, and not worry about nosy channel codng

More information

greatest common divisor

greatest common divisor 4. GCD 1 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

More information

Extending Probabilistic Dynamic Epistemic Logic

Extending Probabilistic Dynamic Epistemic Logic Extendng Probablstc Dynamc Epstemc Logc Joshua Sack May 29, 2008 Probablty Space Defnton A probablty space s a tuple (S, A, µ), where 1 S s a set called the sample space. 2 A P(S) s a σ-algebra: a set

More information

R-HASH: HASH FUNCTION USING RANDOM QUADRATIC POLYNOMIALS OVER GF(2)

R-HASH: HASH FUNCTION USING RANDOM QUADRATIC POLYNOMIALS OVER GF(2) R-AS: AS FUNCTION USING RANDO QUADRATIC POLYNOIALS OVER GF() Dhananoy Dey 1, Noopur Shrotrya 1, Indranath Sengupta 1 SAG, etcalfe ouse, Delh-11 54, INDIA. {dhananoydey, noopurshrotrya}@sag.drdo.n Department

More information

IAJIT First Online Publication

IAJIT First Online Publication Lossless Data Hdng Based on Hstogram Modfcaton Rajkumar Ramaswamy and Vasuk Arumugam 2 Research Scholar, Department of Electroncs and Communcaton Engneerng Kumaraguru College of Technology, Inda 2 Assstant

More information

Halliday/Resnick/Walker 7e Chapter 25 Capacitance

Halliday/Resnick/Walker 7e Chapter 25 Capacitance HRW 7e hapter 5 Page o 0 Hallday/Resnck/Walker 7e hapter 5 apactance. (a) The capactance o the system s q 70 p 35. pf. 0 (b) The capactance s ndependent o q; t s stll 3.5 pf. (c) The potental derence becomes

More information

Causal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting

Causal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting Causal, Explanatory Forecastng Assumes cause-and-effect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of

More information

Statistical Approach for Offline Handwritten Signature Verification

Statistical Approach for Offline Handwritten Signature Verification Journal of Computer Scence 4 (3): 181-185, 2008 ISSN 1549-3636 2008 Scence Publcatons Statstcal Approach for Offlne Handwrtten Sgnature Verfcaton 2 Debnath Bhattacharyya, 1 Samr Kumar Bandyopadhyay, 2

More information

A. P. Sakis Meliopoulos Power System Modeling, Analysis and Control. Appendix B 1 Linear Programming 1

A. P. Sakis Meliopoulos Power System Modeling, Analysis and Control. Appendix B 1 Linear Programming 1 able of Contents from A. P. Sas Melopoulos Power Sstem Modelng, Analss and Control Append 1 Lnear Programmng 1.1 Introducton 1.2 Forms of Lnear Programmng Problems 1.3 Converson of Optmzaton Problems nto

More information

(6)(2) (-6)(-4) (-4)(6) + (-2)(-3) + (4)(3) + (2)(-3) = -12-24 + 24 + 6 + 12 6 = 0

(6)(2) (-6)(-4) (-4)(6) + (-2)(-3) + (4)(3) + (2)(-3) = -12-24 + 24 + 6 + 12 6 = 0 Chapter 3 Homework Soluton P3.-, 4, 6, 0, 3, 7, P3.3-, 4, 6, P3.4-, 3, 6, 9, P3.5- P3.6-, 4, 9, 4,, 3, 40 ---------------------------------------------------- P 3.- Determne the alues of, 4,, 3, and 6

More information

II. PROBABILITY OF AN EVENT

II. PROBABILITY OF AN EVENT II. PROBABILITY OF AN EVENT As ndcated above, probablty s a quantfcaton, or a mathematcal model, of a random experment. Ths quantfcaton s a measure of the lkelhood that a gven event wll occur when the

More information

An MILP model for planning of batch plants operating in a campaign-mode

An MILP model for planning of batch plants operating in a campaign-mode An MILP model for plannng of batch plants operatng n a campagn-mode Yanna Fumero Insttuto de Desarrollo y Dseño CONICET UTN yfumero@santafe-concet.gov.ar Gabrela Corsano Insttuto de Desarrollo y Dseño

More information

Loop Parallelization

Loop Parallelization - - Loop Parallelzaton C-52 Complaton steps: nested loops operatng on arrays, sequentell executon of teraton space DECLARE B[..,..+] FOR I :=.. FOR J :=.. I B[I,J] := B[I-,J]+B[I-,J-] ED FOR ED FOR analyze

More information