Development of Vision Calibration Technology for a Visual Inspection System of Printed Circuit Boards (II)

Size: px
Start display at page:

Download "Development of Vision Calibration Technology for a Visual Inspection System of Printed Circuit Boards (II)"

Transcription

1 ž n m ± Development of Vision Calibration Technolog for a Visual Inspection Sstem of Printed Circuit Boards (II) ƒf 6,''!!! " '& ' '' & " ~ m o ± m ƒ u w i k i m Abstract This report uses the visual inspection technique to measure the dimensions of obects on a PCB. First, we will take a brief review for PCB visual inspection techniques. Then introduce how to built a reference data compared with test data, and the algorithm we use in our inspection sstem, called "Dimensional Verification". At last, we domostrate the whole inspection flow b taking a real eample on PCB.! m ± g u u k µ z i i -3/ -3/ u m i m k -3/ m -3/ k º i i i i «ƒ ƒ º m ƒ i i k ƒ m " m ± u u! " u #! $ % & '

2 "! u " # $ z n % & ƒ '!!!! Ÿ n g { ¼ { z t k # 7EIBJEF A D «ƒ ƒ º m i ƒ # ƒ ƒ!# ƒ u ƒ m p ƒ ƒ m u ƒ ƒ ƒ ƒ u ƒ ƒ ƒ u ƒ!" h # d ƒ v A CCBIB + k k δ, k = tan tan + k k! δ, k «v K> DB K v JLGGFIK D B DKE «, «δ ƒ ƒ h k #! d

3 k ξ, k = tan k! ξ, k ƒ ƒ ƒ ƒ d ƒ i # " ƒ ƒ ξ, k ξ, k ƒ O ƒ ξ, k ƒ O $ m h h i m -3/ -3/ *!, 5, "$ $ #$-!&!#$ - &&! $-#"$! $ *#, 5, &/ $ #$ *$, 5,!!$/#"$! $ > k «ƒ ƒ? m m!> z v ä å 7EIBJEF A D!? «ƒ «!@ ««ƒ «v δ δ ƒ "? ƒ "@ z g g «δ ƒ "A ƒ ξ ƒ ƒ ξ ƒ ξ ƒ "> ƒ ξ ƒ ƒ m ƒ ~ v ƒ ƒ ƒ v ƒ ~! " %

4 ± m w m m w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

5 : (a) (b) () ƒ 35 None None ƒ 2 35 None None ƒ 3 35 None None None (95,45) 70 2 None (435,295) 225 2: (a) (b) 7 %(c)«ƒ "' 3: (a)o ƒ (b)ab K> ƒ (c) (d) (2) ƒ 33 None None ƒ 2 35 None None ƒ 3 36 None None None (97,43) 69 2 None (435,296) 224 (3) ƒ -2 None None ƒ 2 0 None None ƒ 3 + None None None (+2,-2) - 2 None (0,+) - (piel)

ATLANTA, GEORGIA, DECEMBER 12, No. 13. D r. M. L. B r i t t a i n T e l l s S t u d e n t s C o n t r a c t I s B r o k e n

ATLANTA, GEORGIA, DECEMBER 12, No. 13. D r. M. L. B r i t t a i n T e l l s S t u d e n t s C o n t r a c t I s B r o k e n Z-V. XX,, D 141.. 13 ' ' b v k ; D... k x 1 1 7 v f b k f f ' b,, b J 7 11:30 D... D. b " vv f, bv." x v..., bk, b v ff., b b Jk,., f ' v v z. b f. f f b v 123. k,., - f x 123. ' b 140-41, f " f" b - 141-42

More information

Parts Manual. EPIC II Critical Care Bed REF 2031

Parts Manual. EPIC II Critical Care Bed REF 2031 EPIC II Critical Care Bed REF 2031 Parts Manual For parts or technical assistance call: USA: 1-800-327-0770 2013/05 B.0 2031-109-006 REV B www.stryker.com Table of Contents English Product Labels... 4

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

Chapter 30 Design and Analysis of

Chapter 30 Design and Analysis of Chapter 30 Design and Analysis of 2 k DOEs Introduction This chapter describes design alternatives and analysis techniques for conducting a DOE. Tables M1 to M5 in Appendix E can be used to create test

More information

page 1 Total ( )

page 1 Total ( ) A B C D E F Costs budget of [Claimant / Defendant] dated [ ] Estimated page 1 Work done / to be done Pre-action Disbs ( ) Time ( ) Disbs ( ) Time ( ) Total ( ) 1 Issue /statements of case 0.00 0.00 CMC

More information

NVLAP Proficiency Test Round 14 Results. Rolf Bergman CORM 16 May 2016

NVLAP Proficiency Test Round 14 Results. Rolf Bergman CORM 16 May 2016 NVLAP Proficiency Test Round 14 Results Rolf Bergman CORM 16 May 2016 Outline PT 14 Structure Lamp Types Lab Participation Format for results PT 14 Analysis Average values of labs Average values of lamps

More information

ScienceDirect. ScienceDirec

ScienceDirect. ScienceDirec CRX_ / CR X_ / Q Q Q Q : R J : / // / J : / / N K * Jk k G U U U U N k U NC U : R k R J R H k - - - - - H - K: R - H - - V V V R - V V V - - L L H H - - C L H j q C L H j q k k k X k R k k X L k k k -

More information

Junior Soldiers Unit 13 : Lesson 1

Junior Soldiers Unit 13 : Lesson 1 J S U 1 : L 1 R Bb PURPOSE: T v c pp xp pc f Bb f fm B Pc. Ev bf m, G v c C b f. Ep 1: NLT) C Pp R: Ep 1:-10 NLT) 1 C 8:6 CEV) Ep :-5 CEV) T Bb c b cf m, pc fc m p f. T v c B Pc m f Bb. W vc f G W, p v

More information

,,,,..,,., {. (, ),, {,.,.,..,,.,.,,....... {.. : N {, Z {, Q {, Q p { p{ {. 3, R {, C {. : ord p {. 8, (k) {.42,!() { {. 24, () { {. 24, () { {. 25,., () { {. 26,. 9, () { {. 27,. 23, '() { ( ) {. 28,

More information

TRAN S F O R M E R S TRA N SMI S S I O N. SECTION AB Issue 2, March, March,1958, by American Telephone and Telegraph Company

TRAN S F O R M E R S TRA N SMI S S I O N. SECTION AB Issue 2, March, March,1958, by American Telephone and Telegraph Company B B, ch, 9 B h f h c h l f f Bll lh, c chcl l l k l, h, h ch f h f ll ll l f h lh h c ll k f Bll lh, c ck ll ch,9, c lh lh B B c x l l f f f 9 B l f c l f f l 9 f B c, h f c x ch 9 B B h f f fc Bll c f

More information

WEAR A COLLAR RAISE A DOLLAR THIS

WEAR A COLLAR RAISE A DOLLAR THIS WEAR A COLLAR RAISE A DOLLAR THIS f Ac D A Wc Thk f k f Db. Db h f h f Ac D A b h Ocb., h W h f, b D. c h A D c f A Ab Ac D A T Rx A Ib T Ac D A Lb G R h h hc b. O, f h k, k k h b ffc, f b, f hch k k ch

More information

Unit 3. Digital encoding

Unit 3. Digital encoding Unit 3. Digital encoding Digital Electronic Circuits (Circuitos Electrónicos Digitales) E.T.S.I. Informática Universidad de Sevilla 9/2012 Jorge Juan 2010, 2011, 2012 You are free to

More information

W I T H M i A. L I O E T O W A R D ISTOlNrE ^ I S T D C H A. n i T Y F O R - A L L. "

W I T H M i A. L I O E T O W A R D ISTOlNrE ^ I S T D C H A. n i T Y F O R - A L L. J/ H L D N D H Y F L L L N LLL KN NY H Y 2 95 HL N NG F L G NG F LNDD H H J F NH D K GN L _ L L :? H F K b H Y L DD Y N? N L L LD H LL LLL LNNG LL J K N 3 ND DL6 N Lb L F KF FH D LD3 D ND ND F ND LKKN

More information

THE TRANSLATION PLANES OF ORDER 49 AND THEIR AUTOMORPHISM GROUPS

THE TRANSLATION PLANES OF ORDER 49 AND THEIR AUTOMORPHISM GROUPS MATHEMATICS OF COMPUTATION Volume 67, Number 223, July 1998, Pages 1207 1224 S 0025-5718(98)00961-2 THE TRANSLATION PLANES OF ORDER 49 AND THEIR AUTOMORPHISM GROUPS C. CHARNES AND U. DEMPWOLFF Abstract.

More information

THE UNIVERSITY OF TORONTO UNDERGRADUATE MATHEMATICS COMPETITION March, 2005

THE UNIVERSITY OF TORONTO UNDERGRADUATE MATHEMATICS COMPETITION March, 2005 THE UNIVERSITY OF TORONTO UNDERGRADUATE MATHEMATICS COMPETITION March, 5 Time: 3 1 hours No aids or calculators permitted. It is not necessary to do all the problems. Complete solutions to fewer problems

More information

W I T H M A L I C E T O W A R D N O N E A N D C H A R I T Y F O R A L L. " A LOWELL MM. Sent to Jackson for 30 Years for Attempt

W I T H M A L I C E T O W A R D N O N E A N D C H A R I T Y F O R A L L.  A LOWELL MM. Sent to Jackson for 30 Years for Attempt D N N N D Y F 6 KN NY G 2 89 N NG NK!? B! ( Y FB Y N @ N6 F NDD / B F N 8DBK GN B B ) F K Y Y N? x N B D B NNG = ZK N F D BBB ZN F NF? K8 D BND ND ND F ND N DNG FXBN NDNG DD BX N NG ND B K DN G8 > B K

More information

G P P (A G ) (A G ) P (A G )

G P P (A G ) (A G ) P (A G ) 1 1 1 G P P (A G ) A G G (A G ) P (A G ) P (A G ) (A G ) (A G ) A G P (A G ) (A G ) (A G ) A G G A G i, j A G i j C = {0, 1,..., k} i j c > 0 c v k k + 1 k = 4 k = 5 5 5 R(4, 3, 3) 30 n {1,..., n} true

More information

$%! & (, -3 / 0 4, 5 6/ 6 +7, 6 8 9/ 5 :/ 5 A BDC EF G H I EJ KL N G H I. ] ^ _ ` _ ^ a b=c o e f p a q i h f i a j k e i l _ ^ m=c n ^

$%! & (, -3 / 0 4, 5 6/ 6 +7, 6 8 9/ 5 :/ 5 A BDC EF G H I EJ KL N G H I. ] ^ _ ` _ ^ a b=c o e f p a q i h f i a j k e i l _ ^ m=c n ^ ! #" $%! & ' ( ) ) (, -. / ( 0 1#2 ' ( ) ) (, -3 / 0 4, 5 6/ 6 7, 6 8 9/ 5 :/ 5 ;=? @ A BDC EF G H I EJ KL M @C N G H I OPQ ;=R F L EI E G H A S T U S V@C N G H IDW G Q G XYU Z A [ H R C \ G ] ^ _ `

More information

FREE. BJ McNALLY Ltd. Helen Lynch. Remembering Helen. Made in Ireland. memorial cards since 19. Helen Lynch. McNally Family Printers.

FREE. BJ McNALLY Ltd. Helen Lynch. Remembering Helen. Made in Ireland. memorial cards since 19. Helen Lynch. McNally Family Printers. Bkmk W C - 185mm x 60mm - 88mm x 55mm Ackgm C BJ McNALLY L 108mm x 85mm * Rmmbig H T fmi f v H i Lm H Lc ic f i k m f mp i ki xpi bvm. m i i c I vig mm f Sm McDm i 12 J 2033 g 00. f M T H Scific ii. b

More information

DIFFERENTIAL GEOMETRY HW 7

DIFFERENTIAL GEOMETRY HW 7 DIFFERENTIAL GEOMETRY HW 7 CLAY SHONKWILER 1 Show that within a local coordinate system x 1,..., x n ) on M with coordinate vector fields X 1 / x 1,..., X n / x n, if we pick n 3 smooth real-valued functions

More information

Made-to-measure malaria vector control strategies: rational design based on insecticide properties and coverage of blood resources for mosquitoes

Made-to-measure malaria vector control strategies: rational design based on insecticide properties and coverage of blood resources for mosquitoes J v DF. Fy f DF f x (HL) v w b vb. -- v g: g b vg f b f q J 2014, 13:146 :10.1186/1475-2875-13-146 Gy F K (gk@..z) k y (k@y.) J Gg (zg@.gv) Jf C v (jy.v@.g) C J Dky (.ky@..k) k C (k.@b.) 1475-2875 y vw

More information

A B CDE F B FD D A C AF DC A F

A B CDE F B FD D A C AF DC A F International Journal of Arts & Sciences, CD-ROM. ISSN: 1944-6934 :: 4(20):121 131 (2011) Copyright c 2011 by InternationalJournal.org A B CDE F B FD D A C A BC D EF C CE C A D ABC DEF B B C A E E C A

More information

λ(t)f c (t s, s) ds, 0 t < c,

λ(t)f c (t s, s) ds, 0 t < c, L = λw d L k = λ k j Fk j,j, c k = 0, 1,..., d 1, d L k k λ k k Fk,j c j 0 k j k + md m 0 λ k Fk, c L k k L(t) = c 0 λ(t)f c (t s, s) ds, 0 t < c, c d d d 25 number of patients 0 10 20 30 40 50 60 Estimated

More information

Semester University of Sheffield. School of Mathematics and Statistics

Semester University of Sheffield. School of Mathematics and Statistics University of Sheffield School of Mathematics and Statistics MAS140: Mathematics (Chemical) MAS152: Civil Engineering Mathematics MAS152: Essential Mathematical Skills & Techniques MAS156: Mathematics

More information

Atlantic County Properties

Atlantic County Properties () li i () li i () li i V li i li i ii ib ii ii ii i &. ii ii l ii iii bf i - bf i - bf i - bf i - bf i - bf i - bf i - bf i - bf i - bf i - bf i - bf i - bf i - bf i - - bf i - bf i - bf i - bf i - bf

More information

TUCBOR. is feaiherinp hit nest. The day before Thanks, as to reflect great discredit upon that paper. Clocks and Jewelry repaired and warranted.

TUCBOR. is feaiherinp hit nest. The day before Thanks, as to reflect great discredit upon that paper. Clocks and Jewelry repaired and warranted. W B J G Bk 85 X W G WY B 7 B 4 & B k F G? * Bk P j?) G j B k k 4 P & B J B PB Y B * k W Y) WY G G B B Wk J W P W k k J J P -B- W J W J W J k G j F W Wk P j W 8 B Bk B J B P k F BP - W F j $ W & B P & P

More information

CHAPTER 10 VECTORS POINTS TO REMEMBER

CHAPTER 10 VECTORS POINTS TO REMEMBER For more important questions visit : www4onocom CHAPTER 10 VECTORS POINTS TO REMEMBER A quantity that has magnitude as well as direction is called a vector It is denoted by a directed line segment Two

More information

Foundations of tensor algebra and analysis (composed by Dr.-Ing. Olaf Kintzel, September 2007, reviewed June 2011.) Web-site:

Foundations of tensor algebra and analysis (composed by Dr.-Ing. Olaf Kintzel, September 2007, reviewed June 2011.) Web-site: Foundations of tensor algebra and analysis (composed by Dr.-Ing. Olaf Kintzel, September 2007, reviewed June 2011.) Web-site: http://www.kintzel.net 1 Tensor algebra Indices: Kronecker delta: δ i = δ i

More information

CAT. NO /irtl,417~ S- ~ I ';, A RIDER PUBLICATION BY H. A. MIDDLETON

CAT. NO /irtl,417~ S- ~ I ';, A RIDER PUBLICATION BY H. A. MIDDLETON CAT. NO. 139-3 THIRD SUPPLEMENT I /irtl,417~ S- ~ I ';,... 0 f? BY H. A. MIDDLETON.. A RIDER PUBLICATION B36 B65 B152 B309 B319 B329 B719 D63 D77 D152 DA90 DAC32 DAF96 DC70 DC80 DCC90 DD6 DD7 DF62 DF91

More information

Years. Marketing without a plan is like navigating a maze; the solution is unclear.

Years. Marketing without a plan is like navigating a maze; the solution is unclear. F Q 2018 E Mk l lk z; l l Mk El M C C 1995 O Y O S P R j lk q D C Dl Off P W H S P W Sl M Y Pl Cl El M Cl FIRST QUARTER 2018 E El M & D I C/O Jff P RGD S C D M Sl 57 G S Alx ON K0C 1A0 C Tl: 6134821159

More information

In this chapter trusses, frames and machines will be examines as engineering structures.

In this chapter trusses, frames and machines will be examines as engineering structures. In the previous chapter we have employed the equations of equilibrium in order to determine the support / joint reactions acting on a single rigid body or a system of connected members treated as a single

More information

h : sh +i F J a n W i m +i F D eh, 1 ; 5 i A cl m i n i sh» si N «q a : 1? ek ser P t r \. e a & im a n alaa p ( M Scanned by CamScanner

h : sh +i F J a n W i m +i F D eh, 1 ; 5 i A cl m i n i sh» si N «q a : 1? ek ser P t r \. e a & im a n alaa p ( M Scanned by CamScanner m m i s t r * j i ega>x I Bi 5 n ì r s w «s m I L nk r n A F o n n l 5 o 5 i n l D eh 1 ; 5 i A cl m i n i sh» si N «q a : 1? { D v i H R o s c q \ l o o m ( t 9 8 6) im a n alaa p ( M n h k Em l A ma

More information

CCE PR Revised & Un-Revised

CCE PR Revised & Un-Revised D CCE PR Revised & Un-Revised 560 00 KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE 560 00 08 S.S.L.C. EXAMINATION, JUNE, 08 :. 06. 08 ] MODEL ANSWERS : 8-K Date :. 06. 08 ] CODE

More information

ceducate. SCIENCE

ceducate. SCIENCE d f K K K v G v G W f f d v K G G G W f G W f d K v d K k b d d K v G G G f W b d dw f v d K d K v G v G G W G f b W d w d f d d v f d M M d k b d G f - 2016 2015 v bb w.. f d. www.kwb. d f Pd, M 1 Pd,

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

Mundaneum #reopening

Mundaneum #reopening # 1895-2015 k T N, 76 - B-7000 - : P, 15 - B-7000 T : +32 (0)65 31.53.43 - F : +32 (0)65 39.54.86 -.. : E T - P @.@.b T : +32 (0)65 39.54.95 - +32(0)498 48.44.31 [] b B?... 2 T b k : T... 3 : k... 6 Q...

More information

Procedure for Measuring Swing Bearing Movement on 300 A Series Hydraulic Excavators {7063}

Procedure for Measuring Swing Bearing Movement on 300 A Series Hydraulic Excavators {7063} Page 1 of 7 Procedure for Measuring Swing Bearing Movement on 300 A Series Hydraulic Excavators {7063} Excavator: 307 (S/N: 2PM1-UP; 2WM1-UP) 311 (S/N: 9LJ1-UP; 5PK1-UP; 2KM1-UP) 312 (S/N: 6GK1-UP; 7DK1-UP;

More information

1. Determine the Zero-Force Members in the plane truss.

1. Determine the Zero-Force Members in the plane truss. 1. Determine the Zero-orce Members in the plane truss. 1 . Determine the force in each member of the loaded truss. Use the Method of Joints. 3. Determine the force in member GM by the Method of Section.

More information

Parts List, Wiring Diagrams

Parts List, Wiring Diagrams Parts List, Wiring Diagrams PAE180-300 SERIES PACKAGE AIR CONDITIONER UNITS TABLE OF CONTENTS PARTS LIST----------- 2-11 PARTS DRAWING----- 12-34 WIRING DIAGRAMS--- 35-48 Printed in U.S.A. 7/28/08 KEY

More information

Chapter 3 Trusses. Member CO Free-Body Diagram. The force in CO can be obtained by using section bb. Equations of Equilibrium.

Chapter 3 Trusses. Member CO Free-Body Diagram. The force in CO can be obtained by using section bb. Equations of Equilibrium. Chapter 3 Trusses Procedure for analysis 1 Free body diagram: make a decision as to how to cut or section the truss through the members where forces are to be determined. 2 Equation of equilibrium: apply

More information

Planning for Reactive Behaviors in Hide and Seek

Planning for Reactive Behaviors in Hide and Seek University of Pennsylvania ScholarlyCommons Center for Human Modeling and Simulation Department of Computer & Information Science May 1995 Planning for Reactive Behaviors in Hide and Seek Michael B. Moore

More information

Inside! Your Impact...p 5 How You Raised Awareness...p 9 The Bigger Picture...p 14

Inside! Your Impact...p 5 How You Raised Awareness...p 9 The Bigger Picture...p 14 Ii! Y I... 5 H Y Ri A... 9 T Bi Pi... 14 W W v B, W W Gi f b i T. i fii) Fi F v (211 iq M, f i D F fii i i i. i, xii W. b 7 201 i f k ik f xiv f i T v 2017 i i i i i, i i i x ff fi fi-v i fi x M Fi W.

More information

CUTTING EDGE RESOURCES ON LIFE BEFORE BIRTH FOR SECOND-LEVEL STUDENTS

CUTTING EDGE RESOURCES ON LIFE BEFORE BIRTH FOR SECOND-LEVEL STUDENTS CUTTING EDGE RESOURCES ON LIFE BEFORE BIRTH FOR SECOND-LEVEL J F Rf f f i vill jf COMPRE YOUR FINGERPRINTS CRD Y : F : Mk f f j i f i vl v k v f f il 2 Pl x l ll f i f il 3 Lif ff fl k 4 Iif i l f f C

More information

MTH 411 Lecture Notes Based on Hungerford, Abstract Algebra

MTH 411 Lecture Notes Based on Hungerford, Abstract Algebra MTH 411 Lecture Notes Based on Hungerford, Abstract Algebra Ulrich Meierfrankenfeld Department of Mathematics Michigan State University East Lansing MI 48824 meier@math.msu.edu August 28, 2014 2 Contents

More information

A Cluster-based Approach for Biological Hypothesis Testing and its Application

A Cluster-based Approach for Biological Hypothesis Testing and its Application -b B J k, J S Y, M D S, D B I Uv- Uv, F W, I, US {kj,j,@} b v b, v N, O, F b v, v, vv b W z, β-,, b b v q W,, b b b v b : b v b β-, b b b I,,,, b-,, I INRODUION qk b v [] O G Lk,,, k, v, b vv b [] v v

More information

O C E A N G R t» y E ; N :, f T K l O A Y, j A l W A R Y r 1 4, g W / r / FOUR CENTS

O C E A N G R t» y E ; N :, f T K l O A Y, j A l W A R Y r 1 4, g W / r / FOUR CENTS W f& f W f b F W b f W /fx Wbf FU KW UK 2 W U k» F f Wk 7 x W f f " b b f 3 k f x b b f b f k 20 k f f f " f f b 2 x b / f K b b q F ff x k b f f f» f? Wf f / W W f 5 7 0 W b f 4 f / f b k b k b f z

More information

Read & Understan. Understand NEW EDITIO od u. o i. d b. u b. l r. t to. , Grade 3. Correlated Standards WITH LEVELED TEXTS

Read & Understan. Understand NEW EDITIO od u. o i. d b. u b. l r. t to. , Grade 3. Correlated Standards WITH LEVELED TEXTS G 3 EMC 3443 R & U WITH LEVELED TEXTS y l b c V Wi c i Cp bl ici i xpli k Lxil lvl 480 710 Cpi vcbly civii Spp vi i bilii Cv f i kill NEW EDITIO N! A T D k H y M N? I M. W D i i x S Cl S A T D k My H y

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

`G 12 */" T A5&2/, ]&>b ; A%/=W, 62 S 35&.1?& S + ( A; 2 ]/0 ; 5 ; L) ( >>S.

`G 12 */ T A5&2/, ]&>b ; A%/=W, 62 S 35&.1?& S + ( A; 2 ]/0 ; 5 ; L) ( >>S. 01(( +,-. ()*) $%&' "#! : : % $& - "#$ :, (!" -&. #0 12 + 34 2567 () *+ '!" #$%& ; 2 "1? + @)&2 A5&2 () 25& 89:2 *2 72, B97I J$K

More information

ers The Extraordinary Boogie and Swing Festival MUNICH GERMANY 9

ers The Extraordinary Boogie and Swing Festival MUNICH GERMANY 9 W!!! C, E p, C J 95 RT H v D L T BI 10 N P f B 70 5 z V D AY b T Ex B Fv 28.02. - 04.03. MUNICH 1 GERMANY 9 R O C KT H AT W I N G. C O M WING ENT F O LD DLY PRE R WO PROU 14 5 DAY HT G I N UIC M E LIV

More information

Supplementary Information

Supplementary Information If f - - x R f z (F ) w () () f F >, f E jj E, V G >, G >, E G,, f ff f FILY f jj ff LO_ N_ j:rer_ N_ Y_ fg LO_; LO_ N_; N_ j:rer_; j:rer_ N_ Y_ f LO_ N_ j:rer_; j:rer_; N_ j:rer_ Y_ fn LO_ N_ - N_ Y_

More information

Cedar Millwork Products

Cedar Millwork Products 1 BUILD SOME CHARACTER Edmund Allen s Cedar millwork products will set your design apart by adding the beauty, warmth, elegance of design, and functionality only natural Western Red Cedar can provide.

More information

CBT-90 LEDs. CBT-90 Binning and Labeling. Table of Contents. Introduction:

CBT-90 LEDs. CBT-90 Binning and Labeling. Table of Contents. Introduction: CBT-90 LEDs Table of Contents Table of Products.... 2 Shipping and Labeling Nomenclature... 3 Bin Kit Ordering Nomenclature... 4 White Flux Binning Structure... 5 White Chromaticity Binning Structure....

More information

Fundamentals of Engineering Analysis (650163)

Fundamentals of Engineering Analysis (650163) Philadelphia University Faculty of Engineering Communications and Electronics Engineering Fundamentals of Engineering Analysis (6563) Part Dr. Omar R Daoud Matrices: Introduction DEFINITION A matrix is

More information

Computational Intelligence Seminar (8 November, 2005, Waseda University, Tokyo, Japan) Statistical Physics Approaches to Genetic Algorithms Joe Suzuki

Computational Intelligence Seminar (8 November, 2005, Waseda University, Tokyo, Japan) Statistical Physics Approaches to Genetic Algorithms Joe Suzuki Computational Intelligence Seminar (8 November, 2005, Waseda University, Tokyo, Japan) Statistical Physics Approaches to Genetic Algorithms Joe Suzuki 1 560-0043 1-1 Abstract We address genetic algorithms

More information

!"#$%-&'%'()*(+!$,- +.!*/"(!%0'##1- *#,0'(!,%'%!" #$"%"& $'()#*+* ).2.%,# /3,%(,-!'(+''0,4

!#$%-&'%'()*(+!$,- +.!*/(!%0'##1- *#,0'(!,%'%! #$%& $'()#*+* ).2.%,# /3,%(,-!'(+''0,4 "#$%-&'%'()*(+$,- +.*/"(%0'##1- *#,0'(,%'% " #$"%"& $'()#*+* ).2.%,# /3,%(,- '(+''0,4 #*$2'.5,26#.' &(,.'/,#'#,' "3,/.$,3.0 $ #,%(,2"3, "$%,0,(.0"##13 &2"%,#.- /7889:;," +)*+(",*- './,)0 +1-#-,* (",2*2"1"

More information

NACC Uniform Data Set (UDS) FTLD Module

NACC Uniform Data Set (UDS) FTLD Module NACC Uniform Data Set (UDS) FTLD Module Data Template For FOLLOW-UP Visit Packet Version 2.0, January 2012 Copyright 2013 University of Washington Created and published by the FTLD work group of the ADC

More information

Phoiie or',wniu today!.. '-''. ; inmtment Securities. \.! do f hank youl. (^obstruction Bids

Phoiie or',wniu today!.. '-''. ; inmtment Securities. \.! do f hank youl. (^obstruction Bids v 963 b Y K f B B k v v pp f k v f v k bf k q b f b J J? f k p " f " f v p " f k " b p f p b p k b " k " f b k p pp b f b f b f k q p k pp v p v ff p pb p Y k k f k b f k b ; v f b p p f f b v f v bp ff:

More information

and Union One end Inseparable." LOWELL. MICHIGAN. WEDNESDAY. JUNE HUMPHBHT'S HOMEOPATHIC SPECIFICS

and Union One end Inseparable. LOWELL. MICHIGAN. WEDNESDAY. JUNE HUMPHBHT'S HOMEOPATHIC SPECIFICS Y J B B BD Y DDY 8 B F B F x F D > q q j 8 8 J 4 8 8 24 B j 88 4 4 4 8 q 8 bb B 6 B q B b b b B 4 B D J B B b B

More information

1 Multiply Eq. E i by λ 0: (λe i ) (E i ) 2 Multiply Eq. E j by λ and add to Eq. E i : (E i + λe j ) (E i )

1 Multiply Eq. E i by λ 0: (λe i ) (E i ) 2 Multiply Eq. E j by λ and add to Eq. E i : (E i + λe j ) (E i ) Direct Methods for Linear Systems Chapter Direct Methods for Solving Linear Systems Per-Olof Persson persson@berkeleyedu Department of Mathematics University of California, Berkeley Math 18A Numerical

More information

Daily Register Q7 w r\ i i n i i /"\ HTT /"\I AIM MPmf>riAnpn ^ ^ oikiar <mn ^^^*»^^*^^ _.. *-.,..,» * * w ^.. i nr\r\

Daily Register Q7 w r\ i i n i i /\ HTT /\I AIM MPmf>riAnpn ^ ^ oikiar <mn ^^^*»^^*^^ _.. *-.,..,» * * w ^.. i nr\r\ $ 000 w G K G y' F: w w w y' w-y k Yk w k ' V 0 8 y Q w \ /"\ /"\ > ^ ^ k < ^^^*»^^*^^ _*-» * * w ^ \\ Y 88 Y Y 8 G b k =-- K w' K y J KKY G - - v v -y- K -y- x- y bb K' w k y k y K y y w b v w y F y w

More information

RENEWABLE IDEA LESSON PLANS

RENEWABLE IDEA LESSON PLANS RENEWABLE IDEA LESSON PLANS LESSON PLANS ESSON PLANS CONTENT LESSON PLAN 1 Mv: W k b? W? P E N T 4 R T m vm. T, m. C 3R m. U 4 R, b, b, b. T b mk k m mm m. AIM T b b 4R. OBJECTIVES T k b b. T 3R b v b.

More information

(tnaiaun uaejna) o il?smitfl?^ni7wwuiinuvitgviisyiititvi2a-a a imaviitjivi5a^ qw^ww^i fiaa!i-j?s'u'uil?g'ijimqwuwiijami.wti. a nmj 1,965,333.

(tnaiaun uaejna) o il?smitfl?^ni7wwuiinuvitgviisyiititvi2a-a a imaviitjivi5a^ qw^ww^i fiaa!i-j?s'u'uil?g'ijimqwuwiijami.wti. a nmj 1,965,333. 0 fltu77jjiimviu«7mi^ gi^"ijhm?'ijjw?flfi^ V m 1 /14 il?mitfl?^i7wwuiinuvitgviiyiititvi2- imviitvi^ qw^ww^i fi!i-j?'u'uil?g'iqwuwiijmi.wti twwrlf^ imii2^

More information

The fact there s no hard evidence to back up the claims of psychics doesn t always matter to women

The fact there s no hard evidence to back up the claims of psychics doesn t always matter to women T R N A E M S EV O D E L S? B Y C H EN H M YC S O P g,? p? S c g, g c k g p f R KE f AL X AL k D AN f LY L E R g g p OM A O R D S : N F . g T. cc b p p b k j g f g b P b f S S c c c c 07 p 0 2 TV cc 2

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

Studio Scientiarum Mathematicarum Hungarica 22 (1987), SOME REMARKS ON INFINITE SERIES P. ERDŐS, I. JOÓ and L. A. SZÉKELY Dedicated to Profes

Studio Scientiarum Mathematicarum Hungarica 22 (1987), SOME REMARKS ON INFINITE SERIES P. ERDŐS, I. JOÓ and L. A. SZÉKELY Dedicated to Profes Studio Scientiarum Mathematicarum Hungarica 22 (1987), 3 95-400 SOME REMARKS ON INFINITE SERIES P. ERDŐS, I. JOÓ and L. A. SZÉKELY Dedicated to Professor K. Tandori on the occasion of his 60th birthday

More information

CITY OF LAS CRUCES INFRASTRUCTURE/CIP POLICY REVIEW COMMITTEE

CITY OF LAS CRUCES INFRASTRUCTURE/CIP POLICY REVIEW COMMITTEE 1 5 6 7 8 9 11 1 1 1 15 16 17 18 19 0 1 6 7 8 9 0 1 5 6 7 8 9 0 1 ITY OF L U IFTUTU/I OLIY VI OITT T fwg f g f f L - If/I w f b 17, 018 :0.., f L,, bg (f 007-), 700, L, w x. B T: Gg,, G g, / T, 5 J, g,

More information

a 11 x 1 + a 12 x a 1n x n = b 1 a 21 x 1 + a 22 x a 2n x n = b 2.

a 11 x 1 + a 12 x a 1n x n = b 1 a 21 x 1 + a 22 x a 2n x n = b 2. Chapter 1 LINEAR EQUATIONS 11 Introduction to linear equations A linear equation in n unknowns x 1, x,, x n is an equation of the form a 1 x 1 + a x + + a n x n = b, where a 1, a,, a n, b are given real

More information

( ) JournalofChang anuniversity(socialscienceedition) Vol.20 No.4 Jul.2018 F Z $ [\]D ^_` 7a 1,2,3, 1,2, 1,2 (1.! -Z; 3O,O N ;2.O\]

( ) JournalofChang anuniversity(socialscienceedition) Vol.20 No.4 Jul.2018 F Z $ [\]D ^_` 7a 1,2,3, 1,2, 1,2 (1.! -Z; 3O,O N ;2.O\] 20 4 2018 7 ( ) JournalofChang anuniversity(socialscienceedition) Vol.20 No.4 Jul.2018 F Z $ [\]D ^_` 7a 1,2,3, 1,2, 1,2 (1.! -Z; 3O,O N 430079;2.O\] > I /! N,O N 430079; 3. HI, CB21SB) :./ \],./ ) HI

More information

Boolean Inner-Product Spaces and Boolean Matrices

Boolean Inner-Product Spaces and Boolean Matrices Boolean Inner-Product Spaces and Boolean Matrices Stan Gudder Department of Mathematics, University of Denver, Denver CO 80208 Frédéric Latrémolière Department of Mathematics, University of Denver, Denver

More information

Week 15-16: Combinatorial Design

Week 15-16: Combinatorial Design Week 15-16: Combinatorial Design May 8, 2017 A combinatorial design, or simply a design, is an arrangement of the objects of a set into subsets satisfying certain prescribed properties. The area of combinatorial

More information

Certain matrices related to Fibonacci sequence having recursive entries

Certain matrices related to Fibonacci sequence having recursive entries Electronic Journal of Linear Algebra Volume 17 Volume 17 (2008) Article 40 2008 Certain matrices related to Fibonacci sequence having recursive entries Ali Reza Moghaddamfar moghadam@mail.ipm.ir S. Navid

More information

A matrix over a field F is a rectangular array of elements from F. The symbol

A matrix over a field F is a rectangular array of elements from F. The symbol Chapter MATRICES Matrix arithmetic A matrix over a field F is a rectangular array of elements from F The symbol M m n (F ) denotes the collection of all m n matrices over F Matrices will usually be denoted

More information

100Z-1 100Z-1 51 HA 50. Cushion ring Cushion ring. Type. Standard type. Switch Set

100Z-1 100Z-1 51 HA 50. Cushion ring Cushion ring. Type. Standard type. Switch Set 0Z-1 0Z-1 51 Type Nominal pressure Maximum allowable pressure Proof test pressure Minimum operating pressure Working speed range Working temperature range (ambient/fluid temperature) Structure of cushioning

More information

35H MPa Hydraulic Cylinder 3.5 MPa Hydraulic Cylinder 35H-3

35H MPa Hydraulic Cylinder 3.5 MPa Hydraulic Cylinder 35H-3 - - - - ff ff - - - - - - B B BB f f f f f f f 6 96 f f f f f f f 6 f LF LZ f 6 MM f 9 P D RR DD M6 M6 M6 M. M. M. M. M. SL. E 6 6 9 ZB Z EE RC/ RC/ RC/ RC/ RC/ ZM 6 F FP 6 K KK M. M. M. M. M M M M f f

More information

ECS 178 Course Notes QUATERNIONS

ECS 178 Course Notes QUATERNIONS ECS 178 Course Notes QUATERNIONS Kenneth I. Joy Institute for Data Analysis and Visualization Department of Computer Science University of California, Davis Overview The quaternion number system was discovered

More information

ELEMENTARY LINEAR ALGEBRA

ELEMENTARY LINEAR ALGEBRA ELEMENTARY LINEAR ALGEBRA K R MATTHEWS DEPARTMENT OF MATHEMATICS UNIVERSITY OF QUEENSLAND First Printing, 99 Chapter LINEAR EQUATIONS Introduction to linear equations A linear equation in n unknowns x,

More information

Chapter 1. Describing the Physical World: Vectors & Tensors. 1.1 Vectors

Chapter 1. Describing the Physical World: Vectors & Tensors. 1.1 Vectors Chapter 1 Describing the Physical World: Vectors & Tensors It is now well established that all matter consists of elementary particles 1 that interact through mutual attraction or repulsion. In our everyday

More information

The European. Ombudsman. for business

The European. Ombudsman. for business G O D O Th E Ob f b EN Whh b SME, wh h EU b, h E Ob b f h EU. If b h fwk f EU-f j, f f fw wh h EU h f,, bb, f, h E Ob h. E O R E Ob Pb f b b wh h EU : L C Pb wh f Lk f /f f P U V f f h I h, h E Ob f b.

More information

NACC Uniform Data Set (UDS) FTLD Module

NACC Uniform Data Set (UDS) FTLD Module NACC Uniform Data Set (UDS) FTLD Module Data Template For Initial Visit Packet Version 2.0, January 2012 Copyright 2013 University of Washington Created and published by the FTLD work group of the ADC

More information

Answers Investigation 3

Answers Investigation 3 Answers Investigation Applications. a., b. s = n c. The numbers seem to be increasing b a greater amount each time. The square number increases b consecutive odd integers:,, 7,, c X X=. a.,,, b., X 7 X=

More information

See, Sketch, Shoot. A Study Abroad program offered by Coastline Community College and ACCENT International Consortium for Academic Programs Abroad

See, Sketch, Shoot. A Study Abroad program offered by Coastline Community College and ACCENT International Consortium for Academic Programs Abroad R 17!! 0 2 5 2 l J 5 2 J S, Sk, S A S A ff Cl C Cll ACCENT Il C f A P A ROME Il Y I Wk 1 J 24 J 28 Av R, Il f -l. O ACCENT f lv R. L, PS. Il l l.* S v Nl M, Nl Gll f M A, Gll B, V, Cl R F. T v f l k Il

More information

Symbols and dingbats. A 41 Α a 61 α À K cb ➋ à esc. Á g e7 á esc. Â e e5 â. Ã L cc ➌ ã esc ~ Ä esc : ä esc : Å esc * å esc *

Symbols and dingbats. A 41 Α a 61 α À K cb ➋ à esc. Á g e7 á esc. Â e e5 â. Ã L cc ➌ ã esc ~ Ä esc : ä esc : Å esc * å esc * Note: Although every effort ws tken to get complete nd ccurte tble, the uhtor cn not be held responsible for ny errors. Vrious sources hd to be consulted nd MIF hd to be exmined to get s much informtion

More information

Two conventions for coordinate systems. Left-Hand vs Right-Hand. x z. Which is which?

Two conventions for coordinate systems. Left-Hand vs Right-Hand. x z. Which is which? walters@buffalo.edu CSE 480/580 Lecture 2 Slide 3-D Transformations 3-D space Two conventions for coordinate sstems Left-Hand vs Right-Hand (Thumb is the ais, inde is the ais) Which is which? Most graphics

More information

Creative Communications Sample

Creative Communications Sample P f L D f h Scd S C Cc S j wk ASH WEDNESDAY L: P 136 G hk h Ld, f h gd, f h df d f. PSALM 136:1 L. I wh Ah Wddy b? Wh b dy fc h g gf f g h gf f Gd w S, J, b S f. Ech dy L, w x dff, cdg h h f h w fc d fc

More information

HOMEPAGE. The. Inside. Beating the MARCH New Faces & Anniversaries. Spring Recipes. Beating the Winter Blues. ADP Rollout

HOMEPAGE. The. Inside. Beating the MARCH New Faces & Anniversaries. Spring Recipes. Beating the Winter Blues. ADP Rollout T ARCH 2015 HOEPAGE A i f l f Oi H i ffili izi i 2 3 4 6 7 8 8 N F & Aivi Si Ri Bi Wi Bl AP Rll G Hl S N! HR C Tivi Bi T xil 89 f i l i v vi ll i fl lik 189! T illi ki; i f fi v i i l l f f i k i fvi lk

More information

MetroCount Traffic Executive Individual Vehicles

MetroCount Traffic Executive Individual Vehicles Individual-34 Page 1 MetroCount Traffic Executive Individual Vehicles Individual-34 -- English (ENA) Datasets: Site: [00001] Old Coast Rd 4km N of Od Bunbury Rd Direction: 5 - South bound A>B, North bound

More information

LIGHT DUTY DIFFERENTIAL

LIGHT DUTY DIFFERENTIAL B F FF PP P # /............................4...................................4-5 F.....................................5.....................................6-7 P PP Z.....................................7...................................7

More information

University of Technology, Building and Construction Engineering Department (Undergraduate study) PROBABILITY THEORY

University of Technology, Building and Construction Engineering Department (Undergraduate study) PROBABILITY THEORY ENGIEERING STATISTICS (Lectures) University of Technology, Building and Construction Engineering Department (Undergraduate study) PROBABILITY THEORY Dr. Maan S. Hassan Lecturer: Azhar H. Mahdi Probability

More information

wi& be demonstrated. Ilexbert Arkro,

wi& be demonstrated. Ilexbert Arkro, 8( P C B E L B A k> D A 10 O N O k jk \ CH 12 B R Z G kxj7~53> P C C 20 A A P O P 3 x G H kv 7 B5! &$ L N M k APO HM M B / Bk K j R 3(330 C BH& B k C j 2jB A D C & Dk M L 12 H R > APO k L E k M k APO M

More information

Annual report on voting activities and active ownership

Annual report on voting activities and active ownership Annual report on voting activities and active ownership 2017 !"#$%#$?"(%/ B("56.'"$,#-!

More information

Spring Newsletter 2016

Spring Newsletter 2016 2016 S Nw R T L 10 f 2 I bv ff f. I kw w w v w w I w f. f 2 10 w w 10 f 2 w v 10 f 2 b I k. f w 10 x x 2 b w b f. S v: Hw f v b k I k v w f b w w? Hw w b b? H k f w w f k f? 16 b 20 S k w w v w v f f b

More information

Interest Growing In Big Parade. Distribution of Covert Rd. Costs 4-H Club Boys Will Go to Camp

Interest Growing In Big Parade. Distribution of Covert Rd. Costs 4-H Club Boys Will Go to Camp C- C D C- C A 6 7 8 9 3 A 6 7 8 9 3 A j CGA DAY Y 9 93 XXXX CA A AD A K AGA jc C D AK BG A CG 7 K ACY BG A AY DAY - - - - - - A DA A ACCD D B ( q - {] /» K 2 B C - B C C - - - ; 4 G - 7 GAD AXAY CCA -

More information

Chapter 7. Linear Algebra: Matrices, Vectors,

Chapter 7. Linear Algebra: Matrices, Vectors, Chapter 7. Linear Algebra: Matrices, Vectors, Determinants. Linear Systems Linear algebra includes the theory and application of linear systems of equations, linear transformations, and eigenvalue problems.

More information

P i [B k ] = lim. n=1 p(n) ii <. n=1. V i :=

P i [B k ] = lim. n=1 p(n) ii <. n=1. V i := 2.7. Recurrence and transience Consider a Markov chain {X n : n N 0 } on state space E with transition matrix P. Definition 2.7.1. A state i E is called recurrent if P i [X n = i for infinitely many n]

More information

4.3 Analog Value Representation

4.3 Analog Value Representation 4.3 Analog Value Representation Introduction This section describes the analog values for all the measuring ranges and output ranges which you can use with the analog modules. Converting analog values

More information

MULTIPLE PRODUCTS OBJECTIVES. If a i j,b j k,c i k, = + = + = + then a. ( b c) ) 8 ) 6 3) 4 5). If a = 3i j+ k and b 3i j k = = +, then a. ( a b) = ) 0 ) 3) 3 4) not defined { } 3. The scalar a. ( b c)

More information

Structural Steel Design Project

Structural Steel Design Project Job No: Sheet 1 of 6 Rev Worked Example - 1 Made by Date 4-1-000 Checked by PU Date 30-4-000 Analyse the building frame shown in Fig. A using portal method. 15 kn C F I L 4 m 0 kn B E H K 6 m A D G J 4

More information