QJ) Zz LI Zz. Dd Jj. Jj Ww J' J Ww. Jj Ww. Jj I\~~ SOUN,DS AND LETTERS

Size: px
Start display at page:

Download "QJ) Zz LI Zz. Dd Jj. Jj Ww J' J Ww. Jj Ww. Jj I\~~ SOUN,DS AND LETTERS"

Transcription

1 SOUN,DS AND LETTERS.--< Say the name of each picture.llsten to the first sound. Then circle the letters with that"sound..-.. Dd QJ) Jj Ww J' J Ww Zz LI Zz Dd Jj Ww Dd Jj Zz Jj LI Ww Jj LI Ww Jj Ww Zz Dd Jj I\ Ww Skills: Auditory and visual discrimination; Recognition of sounds and their symbols 92

2 SOUNDS AND LETTERS ':.', ",' Say the name of each picture. Listen to the first sound.;:,, - Then circle the ietters with that sound. '@ Pp 'Yy Cc Hh Pp Hh Pp Yy Cc Hh Yy Cc 0> Mm fr11i1i/f\-_ Yy Cc Mm -; Pp Hh Hh Mm Mm Pp Pp - Yy Yy Yy _. "' =-:s::. ::"5, Cc Mm Yy Cc Mm =;::::::::=": I Pp Hh Pp Yy Skills: Auditory and visual discrimination; Recognition of sounds and their symbols 91

3 BEGINNING PI-IONICS Say the name of each picture. Listen to the first sound. Then circle the letters with that sound.,.,. Bb \ \ \ Mm \ Zz Ff Bb Qq Mm Gg Hh Jj Pp Vv S8 Yy Nn.. Cc Qq Ww Hh Skills: Auditory and visual disc imination; Recognition of sounds and their symbols 139

4 BEGINNING PHONICS r-' Say the name of each picture, Listen to the first sound. Then circle the letters with that sound. Hh Mm Kk,.,,. Rr Nn Cc.- -". LI Pp Hh Ss Mm Nn Kk Rr LI Dd,.Yy Vv Bb Ww Ff! t I. f I! Skills: Auditory and visual dislrimination; Recognition of sounds and their symbols I t

5 BEGINNING PHONICS Say the name of each picture. Listen to the first sound. Then circle the letters with that sound. Kk Mm Hh Ff Dd Ww Rr Gg Ff Ss Tt Vv Jj Pp Dd Hh Ss Nn Cc Rr Nn Ss LI Ww Qq Ww...-/'- Tt,. Skills: Auditory and visual discrimination; Recognition of sounds and their symbols 140

6 I Know Beginning Sounds, ;1 ;. Vi.!..<

7 Name _ Add one letter to name the picture. _an _an _an _en _en _en

8 " P, r I k ca_ c mo_ sn_ I=========doo soc_ -- q;;:j# s -, ',. J I, ', ",,', :' I,I' In_ - shee ----!- la m ---- bea DIRECTIONS: Say each pict I re name. Write the missing final consonant.

9 .Say the name of each picture and read the letter that ends the e _ 0 _ '.,. '.!' 'I L = 1. Name the picture. Write the letter that ends the word : \. :. 11 /

10 1,.j -.,:1 '. TRY IT AGAIN. j. a j lj-----t-- --f-----b C- -- Write the letter that starts the word. /

11 Look at each picture. Say its nome.', Read the letter it beg ins with.,.--"':.\!-- Name the picture. Write the letter that starts the word.....,.., y,,,,",,,, 'N. " _",,. "-."" "v...w......,""' J' _.,--_._---!

12 ".. Name the picture. Write the letter that starts the,word. "!" ",. {: f " j \ ',',,', , /

13 r 9 I p b n 5 d m ALPHABET SOUP Find the right letter to make a word. Write the letter on the line. --. ird Ion,'-- _obbit othing on,y _octor even -- icture -- iroffe ogon School Zone Publishing Company 63

14 GET SET...Matching Sounds and Letters Say the name of each picture. How does each start? Circle the letter that stands for the beginning sound. k CD X r s. f b t e d (,.: I 0 q 9 c k r p b b n' s m u r 9. t. Z J Y ty &if / , ITillill 0..t!J f!}!jj.::/:l:' I U CDDe) 21

15 Name _ Write the Missing Letter ----an an an _Ig _en -----en -en -- abcdefghijklmnopqrstuvwxyz

16 "".r;'/(",!;i. Directions: Say the name for each 'Picture below. Fill in the bot56h3 beside the letter that makes the beginning sound in each word Ok Oc Of Ot Of \ Or Oz Od Od 7. Om 8. OP Oq 9.'. o c 10. o f 11. o q 12. Oc Op o d::.', 01 to '. \ '. ( '; S t _ 'Ị.'. \... :,: "..- Of O b 15..I1_. O v 16. Og Or Oz Ow Teacher Created Resources, Inc. 7 #3016 Phonics: Book 2

17 .' I I c J c J c J I h f h f h f P P P J J J <Ii E t1l c: III - :l ti "a. s: 0<II '0 '" " c :l 0 III Cl c: "c e "0,.0 h I J: ;." h I h I "u.!!l "a. :;J 0- Q 90 Lesson 58: Review: Letter-Sound Correspondences....E Sl ]1

18 Draw a line to match each picture with its beginning sound. 6 Qoo()O Hh Jj Kk LI Mm Carson-Dellosa Pub!. CD

19 ) ) ) e o 0> en o :::J 6 6' (J> OJ -u c Q: o m(x) -' o ::J CD.... o 3 ao zr '. (Jl (J) N N -< '< >< >< < < -i,... CD P> o zr "'0 ọ.... c... CD :E.... (J) 0- CD co ::J ::J ::J (Q

20 Draw a line to match each picture with its beginning sound. Nn Pp Qq Rr Ss

21 Draw a line to match each picture with its beginning sound. Bb ii. '1:_' { '?) /4 Eli!!)». \ ) 1:-r. ll\,jj t( "-'f;:j i J.' \','J, I/I',', -, \ ',: j"',! / '. \. \ ;. " I I I f f / '. ', : 1/,/,. \\I,:!II"'/'// '. \' " 'j / \\\\\:;/:'1/ //// " -, \ II i 11" : /'/ ). '\\\\\1' /'/ "<".\\\\\\\'i!,::'<1;: '.\ J'_-'.lf:;-/ Cc Dd Ff Gg Carson-Dellosa Pub!. CD """"'\

22 l- Name Skill: Beginning consonant c f h j. Circle the beginning letter for each picture.. J h h f f c. J h c f h. J f Frank Schaffer Publications, Inc. 5 FS-3058 Phonics

23 r, j, f, g, h, d, w, v, I Ion ----oat iol in obot». c "- o '- orse indow ----oot elly ::: r. tf. -= '::: :!- S'= u< 2 DIRECTIONS: Say each picture name. Write the missing initial consonant.

24 Name _ -, Consonants: l. k. s Circus Pony Circle the beginning letter. <J))c:=:::»)) Color. k s J S k s k J k s J s The Education Center, Inc. Teacher's He/per Kindergarten April/May/June

25 '1itS?F!:::;:>-. / ( 'n+.'-/ r"""'o', 'b n k b n k b n k b n k b n k a) E ell C (J). :::l ts '0..c oell '0 "0 c:::l o (J) Ol E c '0,.0 :5 E 2 ]i b n k b nk b n k :5 b n k b n k '0 III '0. :::l o, Lesson 12: Review: Initial b. k, n 21

26 'b n k b n k b n k b n k b n k ai E t1l c.rj) ::J ti 00..c ot1l 0> 0 n "0 c ::J 0 rj) ell c c.s ell <ll.c <ll -5.E... 2 ]i <ll -5 <ll u... u!!2 00. ::J C- O> s: r- b k b n k b n k b n k b n k b n k Lesson 17: Unit 2 Conclusion: Decoding: b, n, k 27

27 II I dsg dsg I - /\ d s 9 dsg <Ii E ca c. '" :> U '0..s::: o ca '0 "0 c: :> o sn Ol c: Ol.0 d s 9.;:;.2 '- 2 ]i.;:; I dsg d s 9 dsg \.i! r Lesson 29: Unit 3 Conclusion: Decoding: d. s, 9 45 ""l dsg ' r \ -::-,'::/"--' " - ''. -.:... dsg '1:(,\

28 h p r h p r h p r h p r r <Ii E '"c rn - ::J U '0..J:: o '" '0 "0 c: ::J 0 rn Cl c 'c c: '61.0 a> -E h h h P r P r P r i '-u" I.E L- a> ; '0!!1 '0. :J Co.J:: I- h h h i=-;ju p r r p r II Lesson 41: Unit 4 Conclusion: Decoding: n, p, r 63

29 n[1 f I j f I j F23 f I j f I j oj E «l C III - 2 o "a.i::. o «l "0 "0 C::s 0 III 01 C "c c "5>..a.;;.$2 f I j f I j f I j.;; '\ "13 "0. ::s 0- m.i::. I- I j f I j f I j f Lesson 53: Unit 5 Conclusion: Decoding: t, I, j 81

30 )9'!.:.?",.'./.);;J,Ct?. \ Qoq?. '. f I d r f d r f d r f cd E <1l c III -.;1o 00. s: o<1l b b b s 9 s 9 s 9 [23 f d f d f d s s s 88 Lesson 58: Review: Letter-Sound Correspondences (5 c ::::l 0 III Cl C c c 00, ]i -... (3 u 05. :J a. s: l-

31 ""\ \ mjk m j k mjk cd E <tl C.1Il :s u "0. s: o<tl '0 "0 C:::l P t n P t n P t n o III 0> C "c C "0, E Q; ; "0 III "0. :::l a. J n p J n p * J n p Lesson 58: Heview: Letter-Sound Correspondences 89

32 Name '--- Skill: Beginning consona Circle the pictures in each row that start like the first picture Schaffer Publications, Inc. 2 FS-3058 Phonics

33 Name Skill: Beginning consonant d k Circle the beginning letter for each picture. w 9 \\lill,'i...,..." II,.II. IIIJ' 9 w ' k w 9 d d g 9 w k k d w k Frank Schaffer Publications, Inc. 15 FS-3058 Phonics

34 Name <: Skill:Review beginning consonants mbsl Circle the pictures in each row that start like the first Schaffer Publications, Inc. 10 FS-3058 Phonics

35 Name Skill: Beginning consonant q <, Circle the picture in each row that starts like the first SChaffer Publications, Inc. 21 FS-3058 Phonics

36 Say the name of the letter in each row. Circle the picture in that row that begins with that sound. Qq Rr Ss Tt Carson-Dellosa Pub!. CD

37 Say the name of the letter in each row. Circle the picture in that row that begins with that sound. Vv Ww Xx Yy Zz Carson-Dellosa Pub!. CO

38 Say the name of the letter in each row. Circle the picture in that row that begins with that sound. Bb Cc Dd Ff Carson-Dellosa Publ. CD

39 INITIAL CONSONANT SOUNDS / A

Terms of Use. Copyright Embark on the Journey

Terms of Use. Copyright Embark on the Journey Terms of Use All rights reserved. No part of this packet may be reproduced, stored in a retrieval system, or transmitted in any form by any means - electronic, mechanical, photo-copies, recording, or otherwise

More information

" = Y(#,$) % R(r) = 1 4& % " = Y(#,$) % R(r) = Recitation Problems: Week 4. a. 5 B, b. 6. , Ne Mg + 15 P 2+ c. 23 V,

 = Y(#,$) % R(r) = 1 4& %  = Y(#,$) % R(r) = Recitation Problems: Week 4. a. 5 B, b. 6. , Ne Mg + 15 P 2+ c. 23 V, Recitation Problems: Week 4 1. Which of the following combinations of quantum numbers are allowed for an electron in a one-electron atom: n l m l m s 2 2 1! 3 1 0 -! 5 1 2! 4-1 0! 3 2 1 0 2 0 0 -! 7 2-2!

More information

children's illustrator

children's illustrator th, The summer before kindergarten is so exciting. This packet was designed to give you insight in to the different activities you can do with your child. After completing a worksheet, you have an idea

More information

Worksheets for GCSE Mathematics. Quadratics. mr-mathematics.com Maths Resources for Teachers. Algebra

Worksheets for GCSE Mathematics. Quadratics. mr-mathematics.com Maths Resources for Teachers. Algebra Worksheets for GCSE Mathematics Quadratics mr-mathematics.com Maths Resources for Teachers Algebra Quadratics Worksheets Contents Differentiated Independent Learning Worksheets Solving x + bx + c by factorisation

More information

Work, Energy, and Power. Chapter 6 of Essential University Physics, Richard Wolfson, 3 rd Edition

Work, Energy, and Power. Chapter 6 of Essential University Physics, Richard Wolfson, 3 rd Edition Work, Energy, and Power Chapter 6 of Essential University Physics, Richard Wolfson, 3 rd Edition 1 With the knowledge we got so far, we can handle the situation on the left but not the one on the right.

More information

Lesson 24: True and False Number Sentences

Lesson 24: True and False Number Sentences NYS COMMON CE MATHEMATICS CURRICULUM Lesson 24 6 4 Student Outcomes Students identify values for the variables in equations and inequalities that result in true number sentences. Students identify values

More information

Worksheets for GCSE Mathematics. Algebraic Expressions. Mr Black 's Maths Resources for Teachers GCSE 1-9. Algebra

Worksheets for GCSE Mathematics. Algebraic Expressions. Mr Black 's Maths Resources for Teachers GCSE 1-9. Algebra Worksheets for GCSE Mathematics Algebraic Expressions Mr Black 's Maths Resources for Teachers GCSE 1-9 Algebra Algebraic Expressions Worksheets Contents Differentiated Independent Learning Worksheets

More information

necessita d'interrogare il cielo

necessita d'interrogare il cielo gigi nei necessia d'inegae i cie cic pe sax span s inuie a dispiegaa fma dea uce < affeandi ves i cen dea uce isnane " sienzi dei padi sie veic dei' anima 5 J i f H 5 f AL J) i ) L '3 J J "' U J J ö'

More information

i;\-'i frz q > R>? >tr E*+ [S I z> N g> F 'x sa :r> >,9 T F >= = = I Y E H H>tr iir- g-i I * s I!,i --' - = a trx - H tnz rqx o >.F g< s Ire tr () -s

i;\-'i frz q > R>? >tr E*+ [S I z> N g> F 'x sa :r> >,9 T F >= = = I Y E H H>tr iir- g-i I * s I!,i --' - = a trx - H tnz rqx o >.F g< s Ire tr () -s 5 C /? >9 T > ; '. ; J ' ' J. \ ;\' \.> ). L; c\ u ( (J ) \ 1 ) : C ) (... >\ > 9 e!) T C). '1!\ /_ \ '\ ' > 9 C > 9.' \( T Z > 9 > 5 P + 9 9 ) :> : + (. \ z : ) z cf C : u 9 ( :!z! Z c (! $ f 1 :.1 f.

More information

1. The graph of a function f is given above. Answer the question: a. Find the value(s) of x where f is not differentiable. Ans: x = 4, x = 3, x = 2,

1. The graph of a function f is given above. Answer the question: a. Find the value(s) of x where f is not differentiable. Ans: x = 4, x = 3, x = 2, 1. The graph of a function f is given above. Answer the question: a. Find the value(s) of x where f is not differentiable. x = 4, x = 3, x = 2, x = 1, x = 1, x = 2, x = 3, x = 4, x = 5 b. Find the value(s)

More information

6 Lowercase Letter a Number Puzzles

6 Lowercase Letter a Number Puzzles 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 70 80 90 100 6 Lowercase Letter a Nuber Puzzles 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1 10 20 30 40 50 60 70 80 90 100 1 2 3 4 5 6 7 8 9 10 10 9 8 7 6 5 4 3 2 1

More information

A A A A A A A A A A A A. a a a a a a a a a a a a a a a. Apples taste amazingly good.

A A A A A A A A A A A A. a a a a a a a a a a a a a a a. Apples taste amazingly good. Victorian Handwriting Sheet Aa A A A A A A A A A A A A Aa Aa Aa Aa Aa Aa Aa a a a a a a a a a a a a a a a Apples taste amazingly good. Apples taste amazingly good. Now make up a sentence of your own using

More information

Secondary 3H Unit = 1 = 7. Lesson 3.3 Worksheet. Simplify: Lesson 3.6 Worksheet

Secondary 3H Unit = 1 = 7. Lesson 3.3 Worksheet. Simplify: Lesson 3.6 Worksheet Secondary H Unit Lesson Worksheet Simplify: mm + 2 mm 2 4 mm+6 mm + 2 mm 2 mm 20 mm+4 5 2 9+20 2 0+25 4 +2 2 + 2 8 2 6 5. 2 yy 2 + yy 6. +2 + 5 2 2 2 0 Lesson 6 Worksheet List all asymptotes, holes and

More information

Systems of Linear Equations

Systems of Linear Equations Systems of Linear Equations As stated in Section G, Definition., a linear equation in two variables is an equation of the form AAAA + BBBB = CC, where AA and BB are not both zero. Such an equation has

More information

Section 5: Quadratic Equations and Functions Part 1

Section 5: Quadratic Equations and Functions Part 1 Section 5: Quadratic Equations and Functions Part 1 Topic 1: Real-World Examples of Quadratic Functions... 121 Topic 2: Factoring Quadratic Expressions... 125 Topic 3: Solving Quadratic Equations by Factoring...

More information

176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s

176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps

More information

Aa Bb Cc Dd. Ee Ff Gg Hh

Aa Bb Cc Dd. Ee Ff Gg Hh Aa Bb Cc Dd ------------------------------------------------------------------------------------------------------------------------------------------------------- Ee Ff Gg Hh -------------------------------------------------------------------------------------------------------------------------------------------------------

More information

Section 2: Equations and Inequalities

Section 2: Equations and Inequalities Topic 1: Equations: True or False?... 29 Topic 2: Identifying Properties When Solving Equations... 31 Topic 3: Solving Equations... 34 Topic 4: Solving Equations Using the Zero Product Property... 36 Topic

More information

APPH 4200 Physics of Fluids

APPH 4200 Physics of Fluids APPH 42 Physics of Fluids Problem Solving and Vorticity (Ch. 5) 1.!! Quick Review 2.! Vorticity 3.! Kelvin s Theorem 4.! Examples 1 How to solve fluid problems? (Like those in textbook) Ç"Tt=l I $T1P#(

More information

10.4 The Cross Product

10.4 The Cross Product Math 172 Chapter 10B notes Page 1 of 9 10.4 The Cross Product The cross product, or vector product, is defined in 3 dimensions only. Let aa = aa 1, aa 2, aa 3 bb = bb 1, bb 2, bb 3 then aa bb = aa 2 bb

More information

Eureka Lessons for 6th Grade Unit FIVE ~ Equations & Inequalities

Eureka Lessons for 6th Grade Unit FIVE ~ Equations & Inequalities Eureka Lessons for 6th Grade Unit FIVE ~ Equations & Inequalities These 2 lessons can easily be taught in 2 class periods. If you like these lessons, please consider using other Eureka lessons as well.

More information

ME5286 Robotics Spring 2017 Quiz 2

ME5286 Robotics Spring 2017 Quiz 2 Page 1 of 5 ME5286 Robotics Spring 2017 Quiz 2 Total Points: 30 You are responsible for following these instructions. Please take a minute and read them completely. 1. Put your name on this page, any other

More information

SECTION 7: STEADY-STATE ERROR. ESE 499 Feedback Control Systems

SECTION 7: STEADY-STATE ERROR. ESE 499 Feedback Control Systems SECTION 7: STEADY-STATE ERROR ESE 499 Feedback Control Systems 2 Introduction Steady-State Error Introduction 3 Consider a simple unity-feedback system The error is the difference between the reference

More information

General Strong Polarization

General Strong Polarization General Strong Polarization Madhu Sudan Harvard University Joint work with Jaroslaw Blasiok (Harvard), Venkatesan Gurswami (CMU), Preetum Nakkiran (Harvard) and Atri Rudra (Buffalo) December 4, 2017 IAS:

More information

Chapter y. 8. n cd (x y) 14. (2a b) 15. (a) 3(x 2y) = 3x 3(2y) = 3x 6y. 16. (a)

Chapter y. 8. n cd (x y) 14. (2a b) 15. (a) 3(x 2y) = 3x 3(2y) = 3x 6y. 16. (a) Chapter 6 Chapter 6 opener A. B. C. D. 6 E. 5 F. 8 G. H. I. J.. 7. 8 5. 6 6. 7. y 8. n 9. w z. 5cd.. xy z 5r s t. (x y). (a b) 5. (a) (x y) = x (y) = x 6y x 6y = x (y) = (x y) 6. (a) a (5 a+ b) = a (5

More information

P.3 Division of Polynomials

P.3 Division of Polynomials 00 section P3 P.3 Division of Polynomials In this section we will discuss dividing polynomials. The result of division of polynomials is not always a polynomial. For example, xx + 1 divided by xx becomes

More information

KENNESAW STATE UNIVERSITY ATHLETICS VISUAL IDENTITY

KENNESAW STATE UNIVERSITY ATHLETICS VISUAL IDENTITY KENNESAW STATE UNIVERSITY ATHLETICS VISUAL IDENTITY KENNESAW STATE DEPARTMENT OF ATHLETICS VISUAL IDENTITY GENERAL University Athletics Brand History...3 Referencing the Institution...3 Referencing the

More information

Future Self-Guides. E,.?, :0-..-.,0 Q., 5...q ',D5', 4,] 1-}., d-'.4.., _. ZoltAn Dbrnyei Introduction. u u rt 5,4) ,-,4, a. a aci,, u 4.

Future Self-Guides. E,.?, :0-..-.,0 Q., 5...q ',D5', 4,] 1-}., d-'.4.., _. ZoltAn Dbrnyei Introduction. u u rt 5,4) ,-,4, a. a aci,, u 4. te SelfGi ZltAn Dbnyei Intdtin ; ) Q) 4 t? ) t _ 4 73 y S _ E _ p p 4 t t 4) 1_ ::_ J 1 `i () L VI O I4 " " 1 D 4 L e Q) 1 k) QJ 7 j ZS _Le t 1 ej!2 i1 L 77 7 G (4) 4 6 t (1 ;7 bb F) t f; n (i M Q) 7S

More information

Lesson 15: Rearranging Formulas

Lesson 15: Rearranging Formulas Exploratory Challenge Rearranging Familiar Formulas 1. The area AA of a rectangle is 25 in 2. The formula for area is AA = llll. A. If the width ll is 10 inches, what is the length ll? AA = 25 in 2 ll

More information

Chapter 22 : Electric potential

Chapter 22 : Electric potential Chapter 22 : Electric potential What is electric potential? How does it relate to potential energy? How does it relate to electric field? Some simple applications What does it mean when it says 1.5 Volts

More information

Number Representations

Number Representations Computer Arithmetic Algorithms Prof. Dae Hyun Kim School of Electrical Engineering and Computer Science Washington State University Number Representations Information Textbook Israel Koren, Computer Arithmetic

More information

TSOKOS READING ACTIVITY Section 7-2: The Greenhouse Effect and Global Warming (8 points)

TSOKOS READING ACTIVITY Section 7-2: The Greenhouse Effect and Global Warming (8 points) IB PHYSICS Name: Period: Date: DEVIL PHYSICS BADDEST CLASS ON CAMPUS TSOKOS READING ACTIVITY Section 7-2: The Greenhouse Effect and Global Warming (8 points) 1. IB Assessment Statements for Topic 8.5.

More information

Support Vector Machines. CSE 4309 Machine Learning Vassilis Athitsos Computer Science and Engineering Department University of Texas at Arlington

Support Vector Machines. CSE 4309 Machine Learning Vassilis Athitsos Computer Science and Engineering Department University of Texas at Arlington Support Vector Machines CSE 4309 Machine Learning Vassilis Athitsos Computer Science and Engineering Department University of Texas at Arlington 1 A Linearly Separable Problem Consider the binary classification

More information

Citation for published version (APA): Harinck, S. (2001). Conflict issues matter : how conflict issues influence negotiation

Citation for published version (APA): Harinck, S. (2001). Conflict issues matter : how conflict issues influence negotiation UvA-DARE (Digital Academic Repository) Conflict issues matter : how conflict issues influence negotiation Harinck, S. Link to publication Citation for published version (APA): Harinck, S. (2001). Conflict

More information

Uncertain Compression & Graph Coloring. Madhu Sudan Harvard

Uncertain Compression & Graph Coloring. Madhu Sudan Harvard Uncertain Compression & Graph Coloring Madhu Sudan Harvard Based on joint works with: (1) Adam Kalai (MSR), Sanjeev Khanna (U.Penn), Brendan Juba (WUStL) (2) Elad Haramaty (Harvard) (3) Badih Ghazi (MIT),

More information

Pg #11-13, 15, 17, 18, AND Pg # 3-5, 12-15, 19, 20, 25, 27

Pg #11-13, 15, 17, 18, AND Pg # 3-5, 12-15, 19, 20, 25, 27 Pg 506-507 #11-13, 15, 17, 18, 21-24 AND Pg 512-513 # 3-5, 12-15, 19, 20, 25, 27 Pg 518-519 #6-12, 27 AND Pg 520-521 #1-17 Name ~~y~~-0 Date m:t.]iifu;fj - Area of Polygons, Find the area of each polygon.

More information

Big Bang Planck Era. This theory: cosmological model of the universe that is best supported by several aspects of scientific evidence and observation

Big Bang Planck Era. This theory: cosmological model of the universe that is best supported by several aspects of scientific evidence and observation Big Bang Planck Era Source: http://www.crystalinks.com/bigbang.html Source: http://www.odec.ca/index.htm This theory: cosmological model of the universe that is best supported by several aspects of scientific

More information

Lesson 24: Using the Quadratic Formula,

Lesson 24: Using the Quadratic Formula, , b ± b 4ac x = a Opening Exercise 1. Examine the two equation below and discuss what is the most efficient way to solve each one. A. 4xx + 5xx + 3 = xx 3xx B. cc 14 = 5cc. Solve each equation with the

More information

Teacher Road Map for Lesson 10: True and False Equations

Teacher Road Map for Lesson 10: True and False Equations Teacher Road Map for Objective in Student Friendly Language: Today I am: sorting equation cards So that I can: determine when an equation is true or false. I ll know I have it when I can: write my own

More information

CH 61 USING THE GCF IN EQUATIONS AND FORMULAS

CH 61 USING THE GCF IN EQUATIONS AND FORMULAS CH 61 USING THE GCF IN EQUATIONS AND FORMULAS Introduction A while back we studied the Quadratic Formula and used it to solve quadratic equations such as x 5x + 6 = 0; we were also able to solve rectangle

More information

Agenda Rationale for ETG S eek ing I d eas ETG fram ew ork and res u lts 2

Agenda Rationale for ETG S eek ing I d eas ETG fram ew ork and res u lts 2 Internal Innovation @ C is c o 2 0 0 6 C i s c o S y s t e m s, I n c. A l l r i g h t s r e s e r v e d. C i s c o C o n f i d e n t i a l 1 Agenda Rationale for ETG S eek ing I d eas ETG fram ew ork

More information

Winsome Winsome W Wins e ins e WUin ser some s Guide

Winsome Winsome W Wins e ins e WUin ser some s Guide Winsome Winsome Wins e Wins e U ser s Guide Winsome font faq HOW TO INSTALL YOUR FONT You will receive your files as a zipped folder. For instructions on how to unzip your folder, visit LauraWorthingtonType.com/faqs/.

More information

Aa Bb Cc Dd. Ee Ff Gg Hh

Aa Bb Cc Dd. Ee Ff Gg Hh Aa Bb Cc Dd ------------------------------------------------------------------------------------------------------------------------------------------------------- Ee Ff Gg Hh -------------------------------------------------------------------------------------------------------------------------------------------------------

More information

Polynomials and Polynomial Functions

Polynomials and Polynomial Functions 1 Polynomials and Polynomial Functions One of the simplest types of algebraic expressions are polynomials. They are formed only by addition and multiplication of variables and constants. Since both addition

More information

A/P Warrants. June 15, To Approve. To Ratify. Authorize the City Manager to approve such expenditures as are legally due and

A/P Warrants. June 15, To Approve. To Ratify. Authorize the City Manager to approve such expenditures as are legally due and T. 7 TY LS ALATS A/P rrnts June 5, 5 Pges: To Approve - 5 89, 54.3 A/P rrnts 6/ 5/ 5 Subtotl $ 89, 54. 3 To Rtify Pges: 6-, 34. 98 Advnce rrnts 5/ 6/ 5-4 3, 659. 94 Advnce rrnts 6/ / 5 4, 7. 69 June Retirees

More information

Using the Rational Root Theorem to Find Real and Imaginary Roots Real roots can be one of two types: ra...-\; 0 or - l (- - ONLl --

Using the Rational Root Theorem to Find Real and Imaginary Roots Real roots can be one of two types: ra...-\; 0 or - l (- - ONLl -- Using the Rational Root Theorem to Find Real and Imaginary Roots Real roots can be one of two types: ra...-\; 0 or - l (- - ONLl -- Consider the function h(x) =IJ\ 4-8x 3-12x 2 + 24x {?\whose graph is

More information

Patterns of soiling in the Old Library Trinity College Dublin. Allyson Smith, Robbie Goodhue, Susie Bioletti

Patterns of soiling in the Old Library Trinity College Dublin. Allyson Smith, Robbie Goodhue, Susie Bioletti Patterns of soiling in the Old Library Trinity College Dublin Allyson Smith, Robbie Goodhue, Susie Bioletti Trinity College aerial view Old Library E N S W Old Library main (south) elevation Gallery Fagel

More information

o C *$ go ! b», S AT? g (i * ^ fc fa fa U - S 8 += C fl o.2h 2 fl 'fl O ' 0> fl l-h cvo *, &! 5 a o3 a; O g 02 QJ 01 fls g! r«'-fl O fl s- ccco

o C *$ go ! b», S AT? g (i * ^ fc fa fa U - S 8 += C fl o.2h 2 fl 'fl O ' 0> fl l-h cvo *, &! 5 a o3 a; O g 02 QJ 01 fls g! r«'-fl O fl s- ccco > p >>>> ft^. 2 Tble f Generl rdnes. t^-t - +«0 -P k*ph? -- i t t i S i-h l -H i-h -d. *- e Stf H2 t s - ^ d - 'Ct? "fi p= + V t r & ^ C d Si d n. M. s - W ^ m» H ft ^.2. S'Sll-pl e Cl h /~v S s, -P s'l

More information

Worksheets for GCSE Mathematics. Solving Equations. Mr Black's Maths Resources for Teachers GCSE 1-9. Algebra

Worksheets for GCSE Mathematics. Solving Equations. Mr Black's Maths Resources for Teachers GCSE 1-9. Algebra Worksheets for GCSE Mathematics Solving Equations Mr Black's Maths Resources for Teachers GCSE 1-9 Algebra Equations Worksheets Contents Differentiated Independent Learning Worksheets Solving Equations

More information

3.2 A2 - Just Like Derivatives but Backwards

3.2 A2 - Just Like Derivatives but Backwards 3. A - Just Like Derivatives but Backwards The Definite Integral In the previous lesson, you saw that as the number of rectangles got larger and larger, the values of Ln, Mn, and Rn all grew closer and

More information

Charge carrier density in metals and semiconductors

Charge carrier density in metals and semiconductors Charge carrier density in metals and semiconductors 1. Introduction The Hall Effect Particles must overlap for the permutation symmetry to be relevant. We saw examples of this in the exchange energy in

More information

ALPHABET. 0Letter Practice

ALPHABET. 0Letter Practice ALPHABET 0Ltt Pat Ltt Pat - Aa A A A A a a a Cl A s A a a A A Cl a s A a k Aa a Cut ut th ltt s a glu thm th ght st. Catal A Las a 2014 Lau Thms.msthmsstasus.m a a A a A A Ltt Pat - B B B B B Cl B s m

More information

F.3 Special Factoring and a General Strategy of Factoring

F.3 Special Factoring and a General Strategy of Factoring F.3 Special Factoring and a General Strategy of Factoring Difference of Squares section F4 233 Recall that in Section P2, we considered formulas that provide a shortcut for finding special products, such

More information

English 1 Name:

English 1 Name: English 1 Name: 2A 2014-2015 English 1 Name: 2B 2014-2015 Alphabet Aa (ei) Bb (bi) Cc (si) Dd (di) Ee (i) Ff (ef) Gg (lli) Hh (eich) Ii (ai) Jj (llei) Kk (quei) Ll (el) Mm (em) Nn (en) Oo (Ou) Pp (pi)

More information

General Strong Polarization

General Strong Polarization General Strong Polarization Madhu Sudan Harvard University Joint work with Jaroslaw Blasiok (Harvard), Venkatesan Gurswami (CMU), Preetum Nakkiran (Harvard) and Atri Rudra (Buffalo) May 1, 018 G.Tech:

More information

Tausend Und Eine Nacht

Tausend Und Eine Nacht Connecticut College Digital Commons @ Connecticut College Historic Sheet Music Collection Greer Music Library 87 Tausend Und Eine Nacht Johann Strauss Follow this and additional works at: https:digitalcommonsconncolledusheetmusic

More information

Harlean. User s Guide

Harlean. User s Guide Harlean User s Guide font faq HOW TO INSTALL YOUR FONT You will receive your files as a zipped folder. For instructions on how to unzip your folder, visit LauraWorthingtonType.com/faqs/. Your font is available

More information

Module 7 (Lecture 25) RETAINING WALLS

Module 7 (Lecture 25) RETAINING WALLS Module 7 (Lecture 25) RETAINING WALLS Topics Check for Bearing Capacity Failure Example Factor of Safety Against Overturning Factor of Safety Against Sliding Factor of Safety Against Bearing Capacity Failure

More information

Lesson 7: Algebraic Expressions The Commutative and Associative Properties

Lesson 7: Algebraic Expressions The Commutative and Associative Properties Algebraic Expressions The Commutative and Associative Properties Classwork Exercise 1 Suzy draws the following picture to represent the sum 3 + 4: Ben looks at this picture from the opposite side of the

More information

SPIRITUALISM. forces. of Spirit, A n stiy a e d f r o m a C o m m o n rhey. n o d and H en so S ta n d p o in t. Lea d s i 1 T U A L I.S M.

SPIRITUALISM. forces. of Spirit, A n stiy a e d f r o m a C o m m o n rhey. n o d and H en so S ta n d p o in t. Lea d s i 1 T U A L I.S M. ~ 3 : K G V 7 G GG 2 3 9 3» < V ; j z_! V 9 7 ' ; > : ; _ < - «-] 88 _ K _ [ -] ZZ - - _ [ ) G K < ' - - ( - '! j () - -] < : : < :?! q z ; [ > # : - 2 - - j ; :!_ - ] ' z ; : j G - j j - [ _ j! { q -

More information

Exhibit 2-9/30/15 Invoice Filing Page 1841 of Page 3660 Docket No

Exhibit 2-9/30/15 Invoice Filing Page 1841 of Page 3660 Docket No xhibit 2-9/3/15 Invie Filing Pge 1841 f Pge 366 Dket. 44498 F u v 7? u ' 1 L ffi s xs L. s 91 S'.e q ; t w W yn S. s t = p '1 F? 5! 4 ` p V -', {} f6 3 j v > ; gl. li -. " F LL tfi = g us J 3 y 4 @" V)

More information

F.4 Solving Polynomial Equations and Applications of Factoring

F.4 Solving Polynomial Equations and Applications of Factoring section F4 243 F.4 Zero-Product Property Many application problems involve solving polynomial equations. In Chapter L, we studied methods for solving linear, or first-degree, equations. Solving higher

More information

Lecture10: Plasma Physics 1. APPH E6101x Columbia University

Lecture10: Plasma Physics 1. APPH E6101x Columbia University Lecture10: Plasma Physics 1 APPH E6101x Columbia University Last Lecture - Conservation principles in magnetized plasma frozen-in and conservation of particles/flux tubes) - Alfvén waves without plasma

More information

Rational Expressions and Functions

Rational Expressions and Functions Rational Expressions and Functions In the previous two chapters we discussed algebraic expressions, equations, and functions related to polynomials. In this chapter, we will examine a broader category

More information

Module 7 (Lecture 27) RETAINING WALLS

Module 7 (Lecture 27) RETAINING WALLS Module 7 (Lecture 27) RETAINING WALLS Topics 1.1 RETAINING WALLS WITH METALLIC STRIP REINFORCEMENT Calculation of Active Horizontal and vertical Pressure Tie Force Factor of Safety Against Tie Failure

More information

Locality in Coding Theory

Locality in Coding Theory Locality in Coding Theory Madhu Sudan Harvard April 9, 2016 Skoltech: Locality in Coding Theory 1 Error-Correcting Codes (Linear) Code CC FF qq nn. FF qq : Finite field with qq elements. nn block length

More information

Grover s algorithm. We want to find aa. Search in an unordered database. QC oracle (as usual) Usual trick

Grover s algorithm. We want to find aa. Search in an unordered database. QC oracle (as usual) Usual trick Grover s algorithm Search in an unordered database Example: phonebook, need to find a person from a phone number Actually, something else, like hard (e.g., NP-complete) problem 0, xx aa Black box ff xx

More information

Mathematics Ext 2. HSC 2014 Solutions. Suite 403, 410 Elizabeth St, Surry Hills NSW 2010 keystoneeducation.com.

Mathematics Ext 2. HSC 2014 Solutions. Suite 403, 410 Elizabeth St, Surry Hills NSW 2010 keystoneeducation.com. Mathematics Ext HSC 4 Solutions Suite 43, 4 Elizabeth St, Surry Hills NSW info@keystoneeducation.com.au keystoneeducation.com.au Mathematics Extension : HSC 4 Solutions Contents Multiple Choice... 3 Question...

More information

Lecture 11. Kernel Methods

Lecture 11. Kernel Methods Lecture 11. Kernel Methods COMP90051 Statistical Machine Learning Semester 2, 2017 Lecturer: Andrey Kan Copyright: University of Melbourne This lecture The kernel trick Efficient computation of a dot product

More information

LOWELL WEEKLY JOURNAL. ^Jberxy and (Jmott Oao M d Ccmsparftble. %m >ai ruv GEEAT INDUSTRIES

LOWELL WEEKLY JOURNAL. ^Jberxy and (Jmott Oao M d Ccmsparftble. %m >ai ruv GEEAT INDUSTRIES ? (») /»» 9 F ( ) / ) /»F»»»»»# F??»»» Q ( ( »»» < 3»» /» > > } > Q ( Q > Z F 5

More information

Lesson 10: Solving Inequalities

Lesson 10: Solving Inequalities Opening Exercise 1. Find the solution set to each inequality. Express the solution graphically on the number line and give the solution in interval notation. A. xx + 4 7 B. mm 3 + 8 > 9 C. 8yy + 4 < 7yy

More information

CS Lecture 8 & 9. Lagrange Multipliers & Varitional Bounds

CS Lecture 8 & 9. Lagrange Multipliers & Varitional Bounds CS 6347 Lecture 8 & 9 Lagrange Multipliers & Varitional Bounds General Optimization subject to: min ff 0() R nn ff ii 0, h ii = 0, ii = 1,, mm ii = 1,, pp 2 General Optimization subject to: min ff 0()

More information

Classification of Components

Classification of Components Classification of Components Classification of SMD LEDs TLM.31../TLM.32../TLM.33../ + 3... series, Mini LEDs TLM.21... / TLM.23.. / TLM.2.. and 63 LEDs TLM.11../TLM1.. Light Intensity / Color Devices are

More information

". :'=: "t',.4 :; :::-':7'- --,r. "c:"" --; : I :. \ 1 :;,'I ~,:-._._'.:.:1... ~~ \..,i ... ~.. ~--~ ( L ;...3L-. ' f.':... I. -.1;':'.

. :'=: t',.4 :; :::-':7'- --,r. c: --; : I :. \ 1 :;,'I ~,:-._._'.:.:1... ~~ \..,i ... ~.. ~--~ ( L ;...3L-. ' f.':... I. -.1;':'. = 47 \ \ L 3L f \ / \ L \ \ j \ \ 6! \ j \ / w j / \ \ 4 / N L5 Dm94 O6zq 9 qmn j!!! j 3DLLE N f 3LLE Of ADL!N RALROAD ORAL OR AL AOAON N 5 5 D D 9 94 4 E ROL 2LL RLLAY RL AY 3 ER OLLL 832 876 8 76 L A

More information

MATH 1080: Calculus of One Variable II Fall 2018 Textbook: Single Variable Calculus: Early Transcendentals, 7e, by James Stewart.

MATH 1080: Calculus of One Variable II Fall 2018 Textbook: Single Variable Calculus: Early Transcendentals, 7e, by James Stewart. MATH 1080: Calculus of One Variable II Fall 2018 Textbook: Single Variable Calculus: Early Transcendentals, 7e, by James Stewart Unit 2 Skill Set Important: Students should expect test questions that require

More information

TABLES OF DISTRIBUTIONS OF QUADRATIC FORMS IN CENTRAL NORMAL VARIABLES II. Institute of Statistics Mimeo Series No. 557.

TABLES OF DISTRIBUTIONS OF QUADRATIC FORMS IN CENTRAL NORMAL VARIABLES II. Institute of Statistics Mimeo Series No. 557. TABLES OF DISTRIBUTIONS OF QUADRATIC FORMS IN CENTRAL NORMAL VARIABLES II N. L. Johnson* and Samuel Kotz** University of North Carolina Chapel Hill, N. C. Temple University Philadelphia, Pa. Institute

More information

SOUTHWESTERN ELECTRIC POWER COMPANY SCHEDULE H-6.1b NUCLEAR UNIT OUTAGE DATA. For the Test Year Ended March 31, 2009

SOUTHWESTERN ELECTRIC POWER COMPANY SCHEDULE H-6.1b NUCLEAR UNIT OUTAGE DATA. For the Test Year Ended March 31, 2009 Schedule H-6.lb SOUTHWSTRN LCTRIC POWR COMPANY SCHDUL H-6.1b NUCLAR UNIT OUTAG DATA For the Test Year nded March 31, 29 This schedule is not applicable to SVvPCO. 5 Schedule H-6.1 c SOUTHWSTRN LCTRIC POWR

More information

Chapter 6 Reed-Solomon Codes. 6.1 Finite Field Algebra 6.2 Reed-Solomon Codes 6.3 Syndrome Based Decoding 6.4 Curve-Fitting Based Decoding

Chapter 6 Reed-Solomon Codes. 6.1 Finite Field Algebra 6.2 Reed-Solomon Codes 6.3 Syndrome Based Decoding 6.4 Curve-Fitting Based Decoding Chapter 6 Reed-Solomon Codes 6. Finite Field Algebra 6. Reed-Solomon Codes 6.3 Syndrome Based Decoding 6.4 Curve-Fitting Based Decoding 6. Finite Field Algebra Nonbinary codes: message and codeword symbols

More information

Lesson 13: More Factoring Strategies for Quadratic Equations & Expressions

Lesson 13: More Factoring Strategies for Quadratic Equations & Expressions : More Factoring Strategies for Quadratic Equations & Expressions Opening Exploration Looking for Signs In the last lesson, we focused on quadratic equations where all the terms were positive. Juan s examples

More information

Variations. ECE 6540, Lecture 02 Multivariate Random Variables & Linear Algebra

Variations. ECE 6540, Lecture 02 Multivariate Random Variables & Linear Algebra Variations ECE 6540, Lecture 02 Multivariate Random Variables & Linear Algebra Last Time Probability Density Functions Normal Distribution Expectation / Expectation of a function Independence Uncorrelated

More information

P a g e 5 1 of R e p o r t P B 4 / 0 9

P a g e 5 1 of R e p o r t P B 4 / 0 9 P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e

More information

OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9

OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9 OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at

More information

Chem 263 Winter 2018 Problem Set #2 Due: February 16

Chem 263 Winter 2018 Problem Set #2 Due: February 16 Chem 263 Winter 2018 Problem Set #2 Due: February 16 1. Use size considerations to predict the crystal structures of PbF2, CoF2, and BeF2. Do your predictions agree with the actual structures of these

More information

= The algebraic expression is 3x 2 x The algebraic expression is x 2 + x. 3. The algebraic expression is x 2 2x.

= The algebraic expression is 3x 2 x The algebraic expression is x 2 + x. 3. The algebraic expression is x 2 2x. Chapter 7 Maintaining Mathematical Proficiency (p. 335) 1. 3x 7 x = 3x x 7 = (3 )x 7 = 5x 7. 4r 6 9r 1 = 4r 9r 6 1 = (4 9)r 6 1 = 5r 5 3. 5t 3 t 4 8t = 5t t 8t 3 4 = ( 5 1 8)t 3 4 = ()t ( 1) = t 1 4. 3(s

More information

Citation for published version (APA): Hartman, C. A. (2000). Changing concepts of child psychopathology. Amsterdam: TT-Publicaties.

Citation for published version (APA): Hartman, C. A. (2000). Changing concepts of child psychopathology. Amsterdam: TT-Publicaties. UvA-DARE (Digital Aademi Repsitry) Changing nepts f hild psyhpathlgy Hartman, C.A. Link t publiatin Citatin fr published versin (APA): Hartman, C. A. (2000). Changing nepts f hild psyhpathlgy. Amsterdam:

More information

PanHomc'r I'rui;* :".>r '.a'' W"»' I'fltolt. 'j'l :. r... Jnfii<on. Kslaiaaac. <.T i.. %.. 1 >

PanHomc'r I'rui;* :.>r '.a'' W»' I'fltolt. 'j'l :. r... Jnfii<on. Kslaiaaac. <.T i.. %.. 1 > 5 28 (x / &» )»(»»» Q ( 3 Q» (» ( (3 5» ( q 2 5 q 2 5 5 8) 5 2 2 ) ~ ( / x {» /»»»»» (»»» ( 3 ) / & Q ) X ] Q & X X X x» 8 ( &» 2 & % X ) 8 x & X ( #»»q 3 ( ) & X 3 / Q X»»» %» ( z 22 (»» 2» }» / & 2 X

More information

Ğ ğ ğ Ğ ğ Öğ ç ğ ö öğ ğ ŞÇ ğ ğ

Ğ ğ ğ Ğ ğ Öğ ç ğ ö öğ ğ ŞÇ ğ ğ Ğ Ü Ü Ü ğ ğ ğ Öğ ş öğ ş ğ öğ ö ö ş ğ ğ ö ğ Ğ ğ ğ Ğ ğ Öğ ç ğ ö öğ ğ ŞÇ ğ ğ l _.j l L., c :, c Ll Ll, c :r. l., }, l : ö,, Lc L.. c l Ll Lr. 0 c (} >,! l LA l l r r l rl c c.r; (Y ; c cy c r! r! \. L : Ll.,

More information

Quantitative Screening of 46 Illicit Drugs in Urine using Exactive Ultrahigh Resolution and Accurate Mass system

Quantitative Screening of 46 Illicit Drugs in Urine using Exactive Ultrahigh Resolution and Accurate Mass system Quantitative Screening of 46 Illicit Drugs in Urine using Exactive Ultrahigh Resolution and Accurate Mass system Kevin Mchale Thermo Fisher Scientific, San Jose CA Presentation Overview Anabolic androgenic

More information

Lesson 7: Linear Transformations Applied to Cubes

Lesson 7: Linear Transformations Applied to Cubes Classwork Opening Exercise Consider the following matrices: AA = 1 2 0 2, BB = 2, and CC = 2 2 4 0 0 2 2 a. Compute the following determinants. i. det(aa) ii. det(bb) iii. det(cc) b. Sketch the image of

More information

10.1 Three Dimensional Space

10.1 Three Dimensional Space Math 172 Chapter 10A notes Page 1 of 12 10.1 Three Dimensional Space 2D space 0 xx.. xx-, 0 yy yy-, PP(xx, yy) [Fig. 1] Point PP represented by (xx, yy), an ordered pair of real nos. Set of all ordered

More information

Lesson 1: Successive Differences in Polynomials

Lesson 1: Successive Differences in Polynomials Lesson 1 Lesson 1: Successive Differences in Polynomials Classwork Opening Exercise John noticed patterns in the arrangement of numbers in the table below. 2.4 3.4 4.4 5.4 6.4 5.76 11.56 19.36 29.16 40.96

More information

General Strong Polarization

General Strong Polarization General Strong Polarization Madhu Sudan Harvard University Joint work with Jaroslaw Blasiok (Harvard), Venkatesan Guruswami (CMU), Preetum Nakkiran (Harvard) and Atri Rudra (Buffalo) Oct. 5, 018 Stanford:

More information

Name: Discussion Section:

Name: Discussion Section: CBE 141: Chemical Engineering Thermodynamics, Spring 2018, UC Berkeley Midterm 2 March 22, 2018 Time: 80 minutes, closed-book and closed-notes, one-sided 8 ½ x 11 equation sheet allowed Please show all

More information

Thermodynamic Cycles

Thermodynamic Cycles Thermodynamic Cycles Content Thermodynamic Cycles Carnot Cycle Otto Cycle Rankine Cycle Refrigeration Cycle Thermodynamic Cycles Carnot Cycle Derivation of the Carnot Cycle Efficiency Otto Cycle Otto Cycle

More information

SECTION 8: ROOT-LOCUS ANALYSIS. ESE 499 Feedback Control Systems

SECTION 8: ROOT-LOCUS ANALYSIS. ESE 499 Feedback Control Systems SECTION 8: ROOT-LOCUS ANALYSIS ESE 499 Feedback Control Systems 2 Introduction Introduction 3 Consider a general feedback system: Closed-loop transfer function is KKKK ss TT ss = 1 + KKKK ss HH ss GG ss

More information

7.3 The Jacobi and Gauss-Seidel Iterative Methods

7.3 The Jacobi and Gauss-Seidel Iterative Methods 7.3 The Jacobi and Gauss-Seidel Iterative Methods 1 The Jacobi Method Two assumptions made on Jacobi Method: 1.The system given by aa 11 xx 1 + aa 12 xx 2 + aa 1nn xx nn = bb 1 aa 21 xx 1 + aa 22 xx 2

More information

l [ L&U DOK. SENTER Denne rapport tilhører Returneres etter bruk Dokument: Arkiv: Arkivstykke/Ref: ARKAS OO.S Merknad: CP0205V Plassering:

l [ L&U DOK. SENTER Denne rapport tilhører Returneres etter bruk Dokument: Arkiv: Arkivstykke/Ref: ARKAS OO.S Merknad: CP0205V Plassering: I Denne rapport thører L&U DOK. SENTER Returneres etter bruk UTLÅN FRA FJERNARKIVET. UTLÅN ID: 02-0752 MASKINVN 4, FORUS - ADRESSE ST-MA LANETAKER ER ANSVARLIG FOR RETUR AV DETTE DOKUMENTET. VENNLIGST

More information

General Strong Polarization

General Strong Polarization General Strong Polarization Madhu Sudan Harvard University Joint work with Jaroslaw Blasiok (Harvard), Venkatesan Guruswami (CMU), Preetum Nakkiran (Harvard) and Atri Rudra (Buffalo) Oct. 8, 018 Berkeley:

More information