oenofc : COXT&IBCTOEU. AU skaacst sftwer thsa4 aafcekr will be ehat«s«ai Bi. C. W. JUBSSOS. PERFECT THBOUGH SDFFEBISG. our

Size: px
Start display at page:

Download "oenofc : COXT&IBCTOEU. AU skaacst sftwer thsa4 aafcekr will be ehat«s«ai Bi. C. W. JUBSSOS. PERFECT THBOUGH SDFFEBISG. our"

Transcription

1 x V < x x 35 V? 3?/ -V 3 - ) - - [ Z8 - & Z x \ ( -? 9 { < - V 3 < < - - Z 7 - z 3 - [ } & _ 3 < 3 ( 5 7< ( % --- /? - / & - % 4 V V V ] _ - ( z 4 / < z z ( V x zx V x x x < - (\? q ) ( x / ( V -? ( - - x Q? 6 x - - Q q - - Q Z? 3 x 9 & - % V= ~3 x q q 39? _ 6 x 3 z - ~ ? -\ - V < V - ) 6 - q - z? 4 x 70 V 23 x- 0 Z z- - - x - x x V x \ { q = = x 7 z-? q )? Q - 30 x x - -(? -? < 2 z - { x 8 - x? - - q }? 5 -? - z -? - q - - ) - - ( 7-39 xx - q 3? x Q x - x x - x? < ( - x - -? q 2872 q & ( xx ) 76x x - 4z x x 872 ( x 2) x 3 - ( x 2) 8? q z - x ( & V -? x? -? x - <? )? x - x < 9 33 & 5 82

2 4 z - 8z x q x - x & <4& - / V #-{< <~ / - x - 7 x x??? -? - q x 6 - x z z x & x x -- 7 V )# - ( -? -? )3 q 4 Q - x x?? Q ( & ( z V / z q q ? q z x? -? Q q 3 - V q - x x -x V x \) z?? - - & - x- q? & 6 z 7 x q q - )?? - -z? 88 Qz? Q? x 4 q - < q x - Z z Z q q V x 773 ( 7 x x 0 7 0(4 4 _ xx - - $ - x z -- z x q \ ( ) z- x Z < ( 7 72 q ) [ - q q << z x < - -- x z - - ( ) z -- < ( - 3 q q - ( ) ( ) V?? - - ( ) & _ ) % ) ) x q 2? $50 8? { x 0 $200? x \ V xx 2 ) 8 $50 - x - $2500 x } x 4 4 V x 5 } ( - { ) 4 - q 6 V x 7 8 x V x V 0 - V - 8 x Q V 6 ( x 29 \ 8 4 ( ) x Z x ) % q ) V 6 q )] x 6 7x] ( &< 2 (- ) q x - ( q 4 - = ( z q 6 / x? ) = [ 2 /Z q [ - 8 [ x 4 x Z ( ) V \ ( ] ) - q \

3 - [ ? } & & ) x _ V x ] x & [ Q Q z x [ V- x & x - 4 x x 5 Q x z V 83 -V 3 - x 8 / - V x & x & - V 3 6 Z < 4 -< - &( 5 Q & - & & x - V << 6 x QQ ( ) < V < 8 z 4 < x -- 4 ( - x - & ) ( x ) q x <3 x Z V ] 4 5 % ( ( -- ( < ) ) / q -{- V V 7 ( 2 x ) - - ( - ) V x x q \ q z ( - 6 & - ( q -? V ? (2-3) 9? V? -? x 6 x z 7 x % z 2 - $ - - x - (< < - 3 x $60000? x \ $ q x z - (? V ) ( -3) q z x - - V - q x - ( - - x - $-< x x-? ( - - ) - \ V -? x ( x 5 - $ x q x ( - - x x ) - V ) $% < ( ( -- - <4 \V? - $ ( $ ) ) 30 q - V 3 [ & < q z - { }- 3< 60)4 $ V V - V - \ - 6 < { 8-V x x < - (2 - ) Q -4 x z ( x ) - q x x -?3 ( q q ) x q q - x V q x - ( < & < - / / x q q - < - x z - 4 -& x \\x\ x $5 $8 x? - < 86 V 873

4 < - 4 Z - 4 ( z -- x q 3 ( V 6 q & q Q ) $ V () x- z (2? 0) 8 6&] V- & - 7 x x - x)? & x - ) ] V -? 9 V / - 3 V 5 < - z x & # $20? ( 3) - % - & - Z x x - - x - z x - % - 8 x x - Q - V q 7 - [ q ( 0 q - () - ( (8 Q -? x 2 607) ] / z 6 (2)? 3873? x (3) (8 x z V _ (4 ) ) Qq ( x 2 4 $375 $ ) x x - x x q - q - - V x ( 7 - ( x 2 ) ( x 2 22 ) /#- - / z Q- 8 ( 9 ) - q / ( 48) x - q z q x 37 3? / V ) x & & -- )] / 5 - x $ V z Q z & V ( (z [ } - [ 6 & < V?? ] x qx VV V 7 - & x x - x z x $50 $50 x - & $60 V z x - $00 $ $50 - z $60 $50 Q $6 x $&0 $ q { 4 & ( ) -40 $ V? - $ $30 x V - $&0 - $000 $60 $5 $ $6000 x $25000 z & q? - Q x - $23000 x z & -- - z - $ x- z - < $00000 < x < - ( z - / x ] z Q q x #4 ) - < & x ) - z 9 x 0-- < x z < - - x V ( 0{ - - x x 5 [ V ] q - q ] Q ? (_ ] - - -? -

5 9 z z - (0 Q x xx & ( <& 820 (3) x - < x <5 [ - & & ? qz ) - & 6 - _ q ( ) V _ - V < 7 0 [ z q x & &??? q - x - x V x - q - x < - q << 6 z V q ] / ( - ] V z_ x - Q 6<3 x <3 & x ] < % % Q / - - Q x 3 z 9 4? - x - ( x q V( 7 x - /V z z & < - z ) x q - z z x 2 72 < Q & & - x z q x / <- 6 - x - x - V? < x {< q ) = x Q - x - - x -?? \ Q x x x z - - q q q x V /V 6 32 xx -? V V ) Q ? x - - \ q ( ) 7 < - x &?? -? 6%? ( ) q -? -?? - -- x ~ x x ( V? - ( 4 6 x q - x ) V - - 3? 7 (3 2 & Q ] 9 Q <V - V z - & x x ] 4x 6 Q V 6? _ - < 7 - z q && 9< & 6 $ 8 < &

6 0 ] - ) ($ - - V x - { VV 4 V V z x - VV - & 8 3V < Z 00 }? - 48 ( -? - - ) - V x< < x z 8 < x V ( x 0 z 7 % 7_ V x < 8 V x? V -23 ~ & 0 0 < V V 8 x ~ ( - < - x < -- V ] V < 3 <- z x z? x z < - & - < 9 6 V9 < - 72 \ - ~ Q {} Q 44- x Q < \ - - x - x < V - ( -? x 8 x < V 3<< - [ q Q ( ) < - - < 4 -? - )) ) < )< _ ~ & ] ) 8 < ) - = - < V - ) ---? x x \ \< - - zx \ - -? \-)\( x <-- z < <4 --? < ( / --\ < - -z? -V ( < < Q - < ( 4 - V <-< )- )-? x - \- - V / -- /V - < Z < V - x Q V- - (V x 4 ( ) _\ <) x - - \ ) ( (}5 - - x V< - z $ 6 00 V < - ( - ) \ V \ - { 2 5 qq - - ) - ) z 7 50 x < <- - x Q ( V -? z x 0 /- ]( x x - x 8 3 \ V x - & q - x 7V < < < x - <<-( < < x - V 4< Q-< -?? V x &x - V - - <? ) V % 88 Z < 0V- - <- V - - V Q & - < 3 - V - { < V Q - - V & - x? x -- () x () x V V & _ V q x --- V -x V - 5 xv - - x & x - z 8 _ ( x V ~ -V 4 [ - 8 x? x 3 ) V - 8 x - - V V - V V & / 90 \ 9 ( 6 - \ - V < & - -=-7- ~ & - x q - % ( V & q z < V - - x &< V V- 3 z V 87 3 V V x x ] 5 = - ( & - x - { 0 _ V q V { z q x - 22 x < ] x V - - ] $750 - < x (?( q ]

7 Q - V { z - z z --x- < } < - V q ( % { 00 x -- Z _ ( < - () < - -( _ ( 4 q < 4 <- -- & / V - <)< - - V ~ < < z ( ) ( < 89 - < < - Z - 8x- %4 q % - x x < ( )/ / 5 - Z -- x- ( z 0 x ( V \ \ - ( ) < - - V 4 - V z < ( ( Q ( V 94 -< - ) - (< ( \ - 5) < Q ~ - < x & x 4 ] 9 V [ V & ( - 3 Q [ (- ) V -< x & 3 & ( x -] <9 V --3-<-3 < < < -4 - % 4 <- -- V - ( x _ Z V - V V Q ~ 40 -Z 60 6Q0_ - - q z 4 2 ( ) < V & } V Z - 07 ~ - < - - <- ) - $()-{) \V( & - x q ) -- - < < - 87 & < 8 0 ) V & x < V \ \V\ - - V V V x ( ) x- 0000? V -V - - x (& - 4 4? ( / V V < -- <( ( Q V z x - -<- x Z - V x -- - x 8 - V 37 -(- - $ $ ) -- <? - - < - <- - < ~- ( - 9 < - ( 85) -- \ Q ( V ) - V - ( ] < - x < ) ( ) x < x x < x 05 - _ x < x x - x V - -< - \ x - & < - Q 3 V - % -- & - - _ Z V x V \ {{ <- Z 6 6 & 09 _ ) -- -< < <4 _ - q < V - V x - \ 4-) -? V - x 0 V - - < & x % &z V - 0 V z 99 q ( < - - $3 V / -9 < - 0 & -~ - - x 6 < ( ( - 3 ) 0( ---- x? 7 ( x q _ V / x 40 < -- - < ) -5 ( $75 \ V VZ 8# Vz x } )V Z z Q V x ] V ( << ( z 7 & q - ( ) V& 4 ( < --- -&-27 6

8 07 x x V x x ) V _ V - x - - (% & ] - ( &? q x- V x % x q < $ ( ) - - $ { ( ) V- 7 x V < & _ x - <7 --# & V V - q & V x x 03 Q - $3 &V V ( -- V x - ] )4 9 % 4 7? 0 x V- x V -& ) -V? V V - 8 9? < / - \ x - - ( - / V (9 ( - < - -- z x - 24 < - & $ x x - < 860 V x 4 x 6 Q - z & 50 4< q -3 x Z Q 377 & % x x x - z V ( ) x x - ( - - < -x - V -- ( z ( & V ( 8 x \% V & V < - < Q - V - V \ x <}x< ] < V q 0 x - 3 x V? x {3)9 V q - 4 < Q x _ V - q V - 3 q 2 V ($) 0 < 6 7 < x } - q 8< - < z V x < -V V 9 - ( ) x x % ? < x 9 V -? x? - - q?4 \ Q 6- _ -??- - \ 0 x? 3 ( < 4 \ Z -) 3 82 < & 3 - ( 2 x - =3 q x - x } 9< } - 7? ( x - - z 3 - () ) z x 2 73 Z - 873? < % < 6 x 72 xz V < V Z q < 2 ) & 9 70 & 9 ] 2 &? - ( V ( 0? / - 04? q? / -? ( ( & ) / --- z 4 4 / ( ) < ] ( V - q x - ( V <4 $5 < V x?< ( x ( / ( 7 V ~ 3 (} 4 4 V q )- V V 3 < & V /V V 7 % <- ( < \ < / --z (V < ( < - -- < x < 0 V V ] --? x () 3 { - < - 4 Q - Q q V ( V\ z q x () q - & 273

A. H. Hall, 33, 35 &37, Lendoi

A. H. Hall, 33, 35 &37, Lendoi 7 X x > - z Z - ----»»x - % x x» [> Q - ) < % - - 7»- -Q 9 Q # 5 - z -> Q x > z»- ~» - x " < z Q q»» > X»? Q ~ - - % % < - < - - 7 - x -X - -- 6 97 9

More information

P A L A C E P IE R, S T. L E O N A R D S. R a n n o w, q u a r r y. W WALTER CR O TC H, Esq., Local Chairman. E. CO O PER EVANS, Esq.,.

P A L A C E P IE R, S T. L E O N A R D S. R a n n o w, q u a r r y. W WALTER CR O TC H, Esq., Local Chairman. E. CO O PER EVANS, Esq.,. ? ( # [ ( 8? [ > 3 Q [ ««> » 9 Q { «33 Q> 8 \ \ 3 3 3> Q»«9 Q ««« 3 8 3 8 X \ [ 3 ( ( Z ( Z 3( 9 9 > < < > >? 8 98 ««3 ( 98 < # # Q 3 98? 98 > > 3 8 9 9 ««««> 3 «>

More information

' Liberty and Umou Ono and Inseparablo "

' Liberty and Umou Ono and Inseparablo 3 5? #< q 8 2 / / ) 9 ) 2 ) > < _ / ] > ) 2 ) ) 5 > x > [ < > < ) > _ ] ]? <

More information

i r-s THE MEMPHIS, TENN., SATURDAY. DEGfMBER

i r-s THE MEMPHIS, TENN., SATURDAY. DEGfMBER N k Q2 90 k ( < 5 q v k 3X3 0 2 3 Q :: Y? X k 3 : \ N 2 6 3 N > v N z( > > :}9 [ ( k v >63 < vq 9 > k k x k k v 6> v k XN Y k >> k < v Y X X X NN Y 2083 00 N > N Y Y N 0 \ 9>95 z {Q ]k3 Q k x k k z x X

More information

LOWELL WEEKLY JOURNAL

LOWELL WEEKLY JOURNAL Y -» $ 5 Y 7 Y Y -Y- Q x Q» 75»»/ q } # ]»\ - - $ { Q» / X x»»- 3 q $ 9 ) Y q - 5 5 3 3 3 7 Q q - - Q _»»/Q Y - 9 - - - )- [ X 7» -» - )»? / /? Q Y»» # X Q» - -?» Q ) Q \ Q - - - 3? 7» -? #»»» 7 - / Q

More information

LOWELL WEEKLY JOURNAL

LOWELL WEEKLY JOURNAL G $ G 2 G ««2 ««q ) q «\ { q «««/ 6 «««««q «] «q 6 ««Z q «««Q \ Q «q «X ««G X G ««? G Q / Q Q X ««/«X X «««Q X\ «q «X \ / X G XX «««X «x «X «x X G X 29 2 ««Q G G «) 22 G XXX GG G G G G G X «x G Q «) «G

More information

Educjatipnal. L a d ie s * COBNWALILI.S H IG H SCHOOL. I F O R G IR L S A n B k i n d e r g a r t e n.

Educjatipnal. L a d ie s * COBNWALILI.S H IG H SCHOOL. I F O R G IR L S A n B k i n d e r g a r t e n. - - - 0 x ] - ) ) -? - Q - - z 0 x 8 - #? ) 80 0 0 Q ) - 8-8 - ) x ) - ) -] ) Q x?- x - - / - - x - - - x / /- Q ] 8 Q x / / - 0-0 0 x 8 ] ) / - - /- - / /? x ) x x Q ) 8 x q q q )- 8-0 0? - Q - - x?-

More information

Two Posts to Fill On School Board

Two Posts to Fill On School Board Y Y 9 86 4 4 qz 86 x : ( ) z 7 854 Y x 4 z z x x 4 87 88 Y 5 x q x 8 Y 8 x x : 6 ; : 5 x ; 4 ( z ; ( ) ) x ; z 94 ; x 3 3 3 5 94 ; ; ; ; 3 x : 5 89 q ; ; x ; x ; ; x : ; ; ; ; ; ; 87 47% : () : / : 83

More information

LOWELL JOURNAL. MUST APOLOGIZE. such communication with the shore as Is m i Boimhle, noewwary and proper for the comfort

LOWELL JOURNAL. MUST APOLOGIZE. such communication with the shore as Is m i Boimhle, noewwary and proper for the comfort - 7 7 Z 8 q ) V x - X > q - < Y Y X V - z - - - - V - V - q \ - q q < -- V - - - x - - V q > x - x q - x q - x - - - 7 -» - - - - 6 q x - > - - x - - - x- - - q q - V - x - - ( Y q Y7 - >»> - x Y - ] [

More information

a s*:?:; -A: le London Dyers ^CleanefSt * S^d. per Y ard. -P W ..n 1 0, , c t o b e e d n e sd *B A J IllW6fAi>,EB. E D U ^ T IG r?

a s*:?:; -A: le London Dyers ^CleanefSt * S^d. per Y ard. -P W ..n 1 0, , c t o b e e d n e sd *B A J IllW6fAi>,EB. E D U ^ T IG r? ? 9 > 25? < ( x x 52 ) < x ( ) ( { 2 2 8 { 28 ] ( 297 «2 ) «2 2 97 () > Q ««5 > «? 2797 x 7 82 2797 Q z Q (

More information

Neatest and Promptest Manner. E d i t u r ami rul)lihher. FOIt THE CIIILDIIES'. Trifles.

Neatest and Promptest Manner. E d i t u r ami rul)lihher. FOIt THE CIIILDIIES'. Trifles. » ~ $ ) 7 x X ) / ( 8 2 X 39 ««x» ««! «! / x? \» «({? «» q «(? (?? x! «? 8? ( z x x q? ) «q q q ) x z x 69 7( X X ( 3»«! ( ~«x ««x ) (» «8 4 X «4 «4 «8 X «x «(» X) ()»» «X «97 X X X 4 ( 86) x) ( ) z z

More information

A DARK GREY P O N T, with a Switch Tail, and a small Star on the Forehead. Any

A DARK GREY P O N T, with a Switch Tail, and a small Star on the Forehead. Any Y Y Y X X «/ YY Y Y ««Y x ) & \ & & } # Y \#$& / Y Y X» \\ / X X X x & Y Y X «q «z \x» = q Y # % \ & [ & Z \ & { + % ) / / «q zy» / & / / / & x x X / % % ) Y x X Y $ Z % Y Y x x } / % «] «] # z» & Y X»

More information

Governor Green Triumphs Over Mudslinging

Governor Green Triumphs Over Mudslinging ; XXX 6 928 - x 22 5 Q 0 x 2- Q- & & x 30 - x 93000000 95000000 50 000 x 0:30 7 7 2 x q 9 0 0:30 2;00 7:30 9 ( 9 & ( ( - ( - 225000 x ( ( 800 ) - 70000 200000 - x ; 200-0: 3333 0850; 778: 5-38 090; 002;

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

lidmbtr Ftderal Dtposit Iniuranct C^rptratim

lidmbtr Ftderal Dtposit Iniuranct C^rptratim 3 6 2 v v v v v J J : : $3 $ v J v x z " " v v Q j v v z v 2 J v v v v v v v ( v v ) v v v v ( v v v x v v v v x x! v J v v x 3 v v v v v v " v 7 ( v ) z j 3 q J J v v j v v v v x z v v x v v j x v; v

More information

LOWELL WEEKI.Y JOURINAL

LOWELL WEEKI.Y JOURINAL / $ 8) 2 {!»!» X ( (!!!?! () ~ x 8» x /»!! $?» 8! ) ( ) 8 X x /! / x 9 ( 2 2! z»!!»! ) / x»! ( (»»!» [ ~!! 8 X / Q X x» ( (!»! Q ) X x X!! (? ( ()» 9 X»/ Q ( (X )!» / )! X» x / 6!»! }? ( q ( ) / X! 8 x»

More information

LOWELL. MICHIGAN, OCTOBER morning for Owen J. Howard, M last Friday in Blodpett hospital.

LOWELL. MICHIGAN, OCTOBER morning for Owen J. Howard, M last Friday in Blodpett hospital. G GG Y G 9 Y- Y 77 8 Q / x -! -} 77 - - # - - - - 0 G? x? x - - V - x - -? : : - q -8 : : - 8 - q x V - - - )?- X - - 87 X - ::! x - - -- - - x -- - - - )0 0 0 7 - - 0 q - V -

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

' '-'in.-i 1 'iritt in \ rrivfi pr' 1 p. ru

' '-'in.-i 1 'iritt in \ rrivfi pr' 1 p. ru V X X Y Y 7 VY Y Y F # < F V 6 7»< V q q $ $» q & V 7» Q F Y Q 6 Q Y F & Q &» & V V» Y V Y [ & Y V» & VV & F > V } & F Q \ Q \» Y / 7 F F V 7 7 x» > QX < #» > X >» < F & V F» > > # < q V 6 & Y Y q < &

More information

A L T O SOLO LOWCLL. MICHIGAN, THURSDAY. DECEMBER 10,1931. ritt. Mich., to T h e Heights. Bos" l u T H I S COMMl'NiTY IN Wilcox

A L T O SOLO LOWCLL. MICHIGAN, THURSDAY. DECEMBER 10,1931. ritt. Mich., to T h e Heights. Bos l u T H I S COMMl'NiTY IN Wilcox G 093 < 87 G 9 G 4 4 / - G G 3 -!! - # -G G G : 49 q» - 43 8 40 - q - z 4 >» «9 0-9 - - q 00! - - q q!! ) 5 / : \ 0 5 - Z : 9 [ -?! : ) 5 - - > - 8 70 / q - - - X!! - [ 48 - -!

More information

MANY BILLS OF CONCERN TO PUBLIC

MANY BILLS OF CONCERN TO PUBLIC - 6 8 9-6 8 9 6 9 XXX 4 > -? - 8 9 x 4 z ) - -! x - x - - X - - - - - x 00 - - - - - x z - - - x x - x - - - - - ) x - - - - - - 0 > - 000-90 - - 4 0 x 00 - -? z 8 & x - - 8? > 9 - - - - 64 49 9 x - -

More information

Ayuntamiento de Madrid

Ayuntamiento de Madrid 9 v vx-xvv \ ü - v q v ó - ) q ó v Ó ü " v" > - v x -- ü ) Ü v " ñ v é - - v j? j 7 Á v ü - - v - ü

More information

LOWELL WEEKLY JOURNAL

LOWELL WEEKLY JOURNAL : Y J G V $ 5 V V G Y 2 25 Y 2» 5 X # VG q q q 6 6 X J 6 $3 ( 6 2 6 2 6 25 3 2 6 Y q 2 25: JJ JJ < X Q V J J Y J Q V (» Y V X Y? G # V Y J J J G J»Y ) J J / J Y Y X ({ G #? J Y ~» 9? ) < ( J VY Y J G (

More information

Q SON,' (ESTABLISHED 1879L

Q SON,' (ESTABLISHED 1879L ( < 5(? Q 5 9 7 00 9 0 < 6 z 97 ( # ) $ x 6 < ( ) ( ( 6( ( ) ( $ z 0 z z 0 ) { ( % 69% ( ) x 7 97 z ) 7 ) ( ) 6 0 0 97 )( 0 x 7 97 5 6 ( ) 0 6 ) 5 ) 0 ) 9%5 z» 0 97 «6 6» 96? 0 96 5 0 ( ) ( ) 0 x 6 0

More information

E S T A B L IS H E D. n AT Tnn G.D.O. r.w.-bal'eu. e d n e s d a y. II GRANVILLE HOUSE. GATJDICK ROAD. MEADS. EASTBOUENk

E S T A B L IS H E D. n AT Tnn G.D.O. r.w.-bal'eu. e d n e s d a y. II GRANVILLE HOUSE. GATJDICK ROAD. MEADS. EASTBOUENk K q X k K 5 ) ) 5 / K K x x) )? //? q? k X z K 8 5 5? K K K / / $8 ± K K K 8 K / 8 K K X k k X ) k k /» / K / / / k / ] 5 % k / / k k? Z k K ] 8 K K K )» 5 ) # 8 q»)kk q»» )88{ k k k k / k K X 8 8 8 ]

More information

LOWELL WEEKLY JOURNAL

LOWELL WEEKLY JOURNAL W WY R G «( 5 R 5 Y q YG R ««W G WY Y 7 W \(\ 5 R ( W R R W ) W «W W W W< W ) W 53 R R Y 4 RR \ \ ( q ) W W X R R RY \ 73 «\ 2 «W R RG ( «q ) )[ 5 7 G ««R q ] 6 ) X 5 5 x / ( 2 3 4 W «(«\Y W Q RY G G )

More information

V o l u m e 5, N u m b e r 5 2, 1 6 P a g e s. Gold B e U ClUt Stamps Double Stamp D a y E v e r y Wednesday

V o l u m e 5, N u m b e r 5 2, 1 6 P a g e s. Gold B e U ClUt Stamps Double Stamp D a y E v e r y Wednesday 1 6 5 J 9 6 " " z k ; k x k k k z z k j " " ( k " " k 8 1959 " " x k j 5 25 ; ; k k qz ; x 13 x k * k ( ) k k : qz 13 k k k j ; q k x ; x 615 26 ( : k z 113 99751 z k k q ; 15 k k k j q " " k j x x ( *»

More information

Lowell Dam Gone Out. Streets Turned I n t o Rivers. No Cause For Alarm Now However As This Happened 35 Years A&o

Lowell Dam Gone Out. Streets Turned I n t o Rivers. No Cause For Alarm Now However As This Happened 35 Years A&o V ()\\ ))? K K Y 6 96 Y - Y Y V 5 Z ( z x z \ - \ - - z - q q x x - x 5 9 Q \ V - - Y x 59 7 x x - Y - x - - x z - z x - ( 7 x V 9 z q &? - 9 - V ( x - - - V- [ Z x z - -x > -) - - > X Z z ( V V V

More information

ACHD Roadways to Bikeways Update June Hills Gate Dr. Ec ho Summit Pl. Star Ridge Ln. Sunrise View Ln. Eagle Pointe Pl.

ACHD Roadways to Bikeways Update June Hills Gate Dr. Ec ho Summit Pl. Star Ridge Ln. Sunrise View Ln. Eagle Pointe Pl. v U v G G q G G z j v Q v v v v v v G v U v v v z K K z v J v v v G v v 16 z z v q v G v J J K:\_j\20\20987 - U\\ 1-4_24. - - 3:46 6/2/2017 O ( O) O z O O v v v v J J J G v O G J v z zz G v v Q zz / /

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

County Council Named for Kent

County Council Named for Kent \ Y Y 8 9 69 6» > 69 ««] 6 : 8 «V z 9 8 x 9 8 8 8?? 9 V q» :: q;; 8 x () «; 8 x ( z x 9 7 ; x >«\ 8 8 ; 7 z x [ q z «z : > ; ; ; ( 76 x ; x z «7 8 z ; 89 9 z > q _ x 9 : ; 6? ; ( 9 [ ) 89 _ ;»» «; x V

More information

LOWELL WEEKLY JOURNAL.

LOWELL WEEKLY JOURNAL. Y 5 ; ) : Y 3 7 22 2 F $ 7 2 F Q 3 q q 6 2 3 6 2 5 25 2 2 3 $2 25: 75 5 $6 Y q 7 Y Y # \ x Y : { Y Y Y : ( \ _ Y ( ( Y F [ F F ; x Y : ( : G ( ; ( ~ x F G Y ; \ Q ) ( F \ Q / F F \ Y () ( \ G Y ( ) \F

More information

Bidiagonal pairs, Tridiagonal pairs, Lie algebras, and Quantum Groups

Bidiagonal pairs, Tridiagonal pairs, Lie algebras, and Quantum Groups Bidiagonal pairs, Tridiagonal pairs, Lie algebras, and Quantum Groups Darren Funk-Neubauer Department of Mathematics and Physics Colorado State University - Pueblo Pueblo, Colorado, USA darren.funkneubauer@colostate-pueblo.edu

More information

LOWELL WEEKLY JOURNAL

LOWELL WEEKLY JOURNAL Y G q G Y Y 29 8 $ 29 G 6 q )

More information

L O W Z L L, M Z C B., W S D I T X S D J L T, JT7ITZ 2 6, O n # D o l l a r a T m t. L Cuiiveuiluu. BASEBALL.

L O W Z L L, M Z C B., W S D I T X S D J L T, JT7ITZ 2 6, O n # D o l l a r a T m t. L Cuiiveuiluu. BASEBALL. # Z Z B X 7Z 6 8 9 0 # F Y BB F x B- B B BV 5 G - V 84 B F x - G 6 x - F - 500000 Bx > -- z : V Y B / «- Q - 4«7 6 890 6 578 0 00 8: B! 0 677 F 574 BB 4 - V 0 B 8 5 5 0 5 Z G F Q 4 50 G B - 5 5-7 B z 7

More information

LOWHLL #WEEKLY JOURNAL.

LOWHLL #WEEKLY JOURNAL. # F 7 F --) 2 9 Q - Q - - F - x $ 2 F? F \ F q - x q - - - - )< - -? - F - - Q z 2 Q - x -- - - - 3 - % 3 3 - - ) F x - \ - - - - - q - q - - - - -z- < F 7-7- - Q F 2 F - F \x -? - - - - - z - x z F -

More information

.1 "patedl-righl" timti tame.nto our oai.c iii C. W.Fiak&Co. She ftowtt outnal,

.1 patedl-righl timti tame.nto our oai.c iii C. W.Fiak&Co. She ftowtt outnal, J 2 X Y J Y 3 : > Y 6? ) Q Y x J Y Y // 6 : : \ x J 2 J Q J Z 3 Y 7 2 > 3 [6 2 : x z (7 :J 7 > J : 7 (J 2 J < ( q / 3 6 q J $3 2 6:J : 3 q 2 6 3 2 2 J > 2 :2 : J J 2 2 J 7 J 7 J \ : q 2 J J Y q x ( ) 3:

More information

M E M P H I S, T E N N., S A T U E D A Y, OCTOBER 8, 1870.

M E M P H I S, T E N N., S A T U E D A Y, OCTOBER 8, 1870. 5 L V 8 5 x - L : L Q ) L - \ \ Q Q - V 84 z < L L 4 Y z ( (

More information

LOWELL JOURNAL NEWS FROM HAWAII.

LOWELL JOURNAL NEWS FROM HAWAII. U # 2 3 Z7 B 2 898 X G V ; U» VU UU U z z 5U G 75 G } 2 B G G G G X G U 8 Y 22 U B B B G G G Y «j / U q 89 G 9 j YB 8 U z U - V - 2 z j _ ( UU 9 -! V G - U GB 8 j - G () V B V Y 6 G B j U U q - U z «B

More information

I ' l A MEMPHIS, TENN., SATURDAY, AUGUST 23,1873.

I ' l A MEMPHIS, TENN., SATURDAY, AUGUST 23,1873. - P G& P P G» -» - P D - RP P R G GFFX G - 3 D G» R» G - G > D X >»» P -3 8 7 3-379 ( -» - F X P X X z» FR 0- P x X >»» P»( > ( 3 - - --5 - X- - x 25Z3 - - z - 37 - x -» x V5?» - > 3 x & 2» x z > - -»»

More information

ELECTRIC SUN NEW JERSEY'S OLDEST WEEKLY NEWSPAPER EST :30-5:30 DAILY SAT. 10>00-5:30 OPEN TILL 9:00 P.M. THURS. "A Unisex Boutique*'

ELECTRIC SUN NEW JERSEY'S OLDEST WEEKLY NEWSPAPER EST :30-5:30 DAILY SAT. 10>00-5:30 OPEN TILL 9:00 P.M. THURS. A Unisex Boutique*' G Y Y 9 ] v- j $ G - v $ F v F v v - v G / $ v z - -! v - )v - v ( -! - - j---- - - - v v- - - - -! / j v - v G -

More information

LOWELL WEEKLY JOURNAL

LOWELL WEEKLY JOURNAL Y G y G Y 87 y Y 8 Y - $ X ; ; y y q 8 y $8 $ $ $ G 8 q < 8 6 4 y 8 7 4 8 8 < < y 6 $ q - - y G y G - Y y y 8 y y y Y Y 7-7- G - y y y ) y - y y y y - - y - y 87 7-7- G G < G y G y y 6 X y G y y y 87 G

More information

A Memorial. Death Crash Branch Out. Symbol The. at Crossing Flaming Poppy. in Belding

A Memorial. Death Crash Branch Out. Symbol The. at Crossing Flaming Poppy. in Belding - G Y Y 8 9 XXX G - Y - Q 5 8 G Y G Y - - * Y G G G G 9 - G - - : - G - - ) G G- Y G G q G G : Q G Y G 5) Y : z 6 86 ) ; - ) z; G ) 875 ; ) ; G -- ) ; Y; ) G 8 879 99 G 9 65 q 99 7 G : - G G Y ; - G 8

More information

. ffflffluary 7, 1855.

. ffflffluary 7, 1855. x B B - Y 8 B > ) - ( vv B ( v v v (B/ x< / Y 8 8 > [ x v 6 ) > ( - ) - x ( < v x { > v v q < 8 - - - 4 B ( v - / v x [ - - B v B --------- v v ( v < v v v q B v B B v?8 Y X $ v x B ( B B B B ) ( - v -

More information

(EccL HUt, Mosheim, p. 40.) AGC3. Rgnres. We shall now proceed to show two things:

(EccL HUt, Mosheim, p. 40.) AGC3. Rgnres. We shall now proceed to show two things: P K K P / P V -K VX - x K D K GFF G D G DKX X P P F D K 8 6 Y X X X P 9 ] K V Y 0 - D 00 D P F G K K PXVK P > G K K V v v v v PK P v D > v Y v D P > P v v - v x V D - ()zx q - & 9 K x K > % x v - - P x

More information

Pithy P o i n t s Picked I ' p and Patljr Put By Our P e r i p a tetic Pencil Pusher VOLUME X X X X. Lee Hi^h School Here Friday Ni^ht

Pithy P o i n t s Picked I ' p and Patljr Put By Our P e r i p a tetic Pencil Pusher VOLUME X X X X. Lee Hi^h School Here Friday Ni^ht G G QQ K K Z z U K z q Z 22 x z - z 97 Z x z j K K 33 G - 72 92 33 3% 98 K 924 4 G G K 2 G x G K 2 z K j x x 2 G Z 22 j K K x q j - K 72 G 43-2 2 G G z G - -G G U q - z q - G x) z q 3 26 7 x Zz - G U-

More information

READ T H E DATE ON LABEL A blue m a r k a r o u n d this notice will call y o u r attention to y o u r LOWELL. MICHIGAN, THURSDAY, AUGUST 29.

READ T H E DATE ON LABEL A blue m a r k a r o u n d this notice will call y o u r attention to y o u r LOWELL. MICHIGAN, THURSDAY, AUGUST 29. B U D D B < / UDY UU 29 929 VU XXXV Y B 5 2 $25 25 25 U 6 B j 3 $8 D D D VD V D D V D B B % B 2 D - Q 22: 5 B 2 3 Z D 2 5 B V $ 2 52 2 $5 25 25 $ Y Y D - 8 q 2 2 6 Y U DD D D D Y!! B D V!! XU XX D x D

More information

Additional Practice Lessons 2.02 and 2.03

Additional Practice Lessons 2.02 and 2.03 Additional Practice Lessons 2.02 and 2.03 1. There are two numbers n that satisfy the following equations. Find both numbers. a. n(n 1) 306 b. n(n 1) 462 c. (n 1)(n) 182 2. The following function is defined

More information

Two-dimensional flow in a porous medium with general anisotropy

Two-dimensional flow in a porous medium with general anisotropy Two-dimensional flow in a porous medium with general anisotropy P.A. Tyvand & A.R.F. Storhaug Norwegian University of Life Sciences 143 Ås Norway peder.tyvand@umb.no 1 Darcy s law for flow in an isotropic

More information

1 h 9 e $ s i n t h e o r y, a p p l i c a t i a n

1 h 9 e $ s i n t h e o r y, a p p l i c a t i a n T : 99 9 \ E \ : \ 4 7 8 \ \ \ \ - \ \ T \ \ \ : \ 99 9 T : 99-9 9 E : 4 7 8 / T V 9 \ E \ \ : 4 \ 7 8 / T \ V \ 9 T - w - - V w w - T w w \ T \ \ \ w \ w \ - \ w \ \ w \ \ \ T \ w \ w \ w \ w \ \ w \

More information

Rural Women Get Invitations For Conference. Playground Opens With Enthusiasm

Rural Women Get Invitations For Conference. Playground Opens With Enthusiasm H M H M v v Y v v v v H 4-H 6 MH U 4 97 Y-H Y H v M U M M M 5 M 5? v -? v 7 q - v < v 9 q U H # v - M - v < M 75 8 v - v 8 M 4-H v U v v M v v - v - v M v v v 4-H 4-H 9 M v 5 v 5 6 - $6 M v - M - v \ v

More information

M e t ir c S p a c es

M e t ir c S p a c es A G M A A q D q O I q 4 78 q q G q 3 q v- q A G q M A G M 3 5 4 A D O I A 4 78 / 3 v D OI A G M 3 4 78 / 3 54 D D v M q D M 3 v A G M 3 v M 3 5 A 4 M W q x - - - v Z M * A D q q q v W q q q q D q q W q

More information

Polynomials. In many problems, it is useful to write polynomials as products. For example, when solving equations: Example:

Polynomials. In many problems, it is useful to write polynomials as products. For example, when solving equations: Example: Polynomials Monomials: 10, 5x, 3x 2, x 3, 4x 2 y 6, or 5xyz 2. A monomial is a product of quantities some of which are unknown. Polynomials: 10 + 5x 3x 2 + x 3, or 4x 2 y 6 + 5xyz 2. A polynomial is a

More information

" W I T H M: A. L I G E T O ' W ^ P L D IST O ISTE -A-IsTD G H! A-I^IT Y IPO PL A.LI-i. :

 W I T H M: A. L I G E T O ' W ^ P L D IST O ISTE -A-IsTD G H! A-I^IT Y IPO PL A.LI-i. : : D D! Y : V Y JY 4 96 J z z Y &! 0 6 4 J 6 4 0 D q & J D J» Y j D J & D & Y = x D D DZ Z # D D D D D D V X D DD X D \ J D V & Q D D Y D V D D? q ; J j j \V ; q» 0 0 j \\ j! ; \?) j: ; : x DD D J J j ;

More information

MEMORIAL UNIVERSITY OF NEWFOUNDLAND

MEMORIAL UNIVERSITY OF NEWFOUNDLAND MEMORIAL UNIVERSITY OF NEWFOUNDLAND DEPARTMENT OF MATHEMATICS AND STATISTICS Section 5. Math 090 Fall 009 SOLUTIONS. a) Using long division of polynomials, we have x + x x x + ) x 4 4x + x + 0x x 4 6x

More information

- >,- V v ' V" S.T T~T .. RAHWAY NEWS RECORD -CLARK PATRIOT PAGE 10 THURSDAY, JULY 22, 1971 THURSDAY, JULY 15 VOL. 149, NO. 29

- >,- V v ' V S.T T~T .. RAHWAY NEWS RECORD -CLARK PATRIOT PAGE 10 THURSDAY, JULY 22, 1971 THURSDAY, JULY 15 VOL. 149, NO. 29 > V V Y O K O G Y Y kj > «) > k : \ \\ V) Q K! \ : = < \ \ \ \V :! < VG O O OKO O O O OVG KO B K V G G O O $ G OK O Y V O >K K : j k k 6 Y OO >«Y k k k z : B OO G Bk k G k G O k > G! x OOO O k Y Y 6 }

More information

LOWELL WEEKLY JOURNAL.

LOWELL WEEKLY JOURNAL. > LLL KLY L L x L L L L G K Y F 7 2 K LKL Y K «F «««««q 5 $ ) / «2 K) ««) 74 «G > x «LY K «! «KL K K K K K! ««x > x K! K ) 2 K «X! «K LK >> < >«««) «< >>«K«KLK < «4! «««#> ««!

More information

Closed-Form Solution Of Absolute Orientation Using Unit Quaternions

Closed-Form Solution Of Absolute Orientation Using Unit Quaternions Closed-Form Solution Of Absolute Orientation Using Unit Berthold K. P. Horn Department of Computer and Information Sciences November 11, 2004 Outline 1 Introduction 2 3 The Problem Given: two sets of corresponding

More information

Una aad Ark«m*. I cuim tie la.-seit HTni«.ent 9. Twenty.? S 3 S 3 CLOTHS, MEMPHIS, TENN., SATURDAY. JANUARY 18, 1873.

Una aad Ark«m*. I cuim tie la.-seit HTni«.ent 9. Twenty.? S 3 S 3 CLOTHS, MEMPHIS, TENN., SATURDAY. JANUARY 18, 1873. 8! (!> > > ( v 7 q! v Y vq! >5! #! g k gg y y k Q G [x y k xv < zg > 9 _ 7 v ) 6 4 { k & x > 5! k & \ ) >% G > k k x k< G < q k>{> y k k kk k 2 k y y k ( y k y y Y g

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

1. A polynomial p(x) in one variable x is an algebraic expression in x of the form

1. A polynomial p(x) in one variable x is an algebraic expression in x of the form POLYNOMIALS Important Points 1. A polynomial p(x) in one variable x is an algebraic expression in x of the form p(x) = a nx n +a n-1x n-1 + a 2x 2 +a 1x 1 +a 0x 0 where a 0, a 1, a 2 a n are constants

More information

LOWELL JOURNAL. LOWSLL, MICK., WSSDNaSDAY", FEB 1% 1894:

LOWELL JOURNAL. LOWSLL, MICK., WSSDNaSDAY, FEB 1% 1894: ? jpv J V# 33 K DDY % 9 D Y D z K x p * pp J - jj Q D V Q< - j «K * j G»D K* G 3 zz DD V V K Y p K K 9 G 3 - G p! ( - p j p p p p Q 3 p ZZ - p- pp p- D p pp z p p pp G pp G pp J D p G z p _ YK G D xp p-

More information

Lecture 8 Analyzing the diffusion weighted signal. Room CSB 272 this week! Please install AFNI

Lecture 8 Analyzing the diffusion weighted signal. Room CSB 272 this week! Please install AFNI Lecture 8 Analyzing the diffusion weighted signal Room CSB 272 this week! Please install AFNI http://afni.nimh.nih.gov/afni/ Next lecture, DTI For this lecture, think in terms of a single voxel We re still

More information

There seems to be three different groups of students: A group around 6 A group around 12 A group around 16

There seems to be three different groups of students: A group around 6 A group around 12 A group around 16 10 5 0 0 5 10 15 20 25 30 There seems to be three different groups of students: A group around 6 A group around 12 A group around 16 Altuğ Özpineci ( METU ) Phys109-MECHANICS PHYS109 55 / 67 10 5 0 0 5

More information

acclamation. sophomores, their roomer, George P. Burdell, who

acclamation. sophomores, their roomer, George P. Burdell, who Z- V., X X H v H, 4 V w w w v. w v j w w z w w w, w H $.0, w w w J.,, x- Y w- w ; v H.. H. - 3.. w x 4 :00.., 0, 4. -. - x. - Yw J, q. 3. j...,, ( w U, v., w, v,,., v, v, v w w Y,, w z, v w w H. 3, v,

More information

THE I Establiifrad June, 1893

THE I Establiifrad June, 1893 89 : 8 Y Y 2 96 6 - - : - 2 q - 26 6 - - q 2 2 2 4 6 4«4 ' V () 8 () 6 64-4 '2" () 6 ( ) * 'V ( 4 ) 94-4 q ( / ) K ( x- 6% j 9*V 2'%" 222 27 q - - K 79-29 - K x 2 2 j - -% K 4% 2% 6% ' K - 2 47 x - - j

More information

Compatible Systems and Charpit s Method

Compatible Systems and Charpit s Method MODULE 2: FIRST-ORDER PARTIAL DIFFERENTIAL EQUATIONS 28 Lecture 5 Compatible Systems Charpit s Method In this lecture, we shall study compatible systems of first-order PDEs the Charpit s method for solving

More information

CONSERVATION OF ENERGY FOR ACONTINUUM

CONSERVATION OF ENERGY FOR ACONTINUUM Chapter 6 CONSERVATION OF ENERGY FOR ACONTINUUM Figure 6.1: 6.1 Conservation of Energ In order to define conservation of energ, we will follow a derivation similar to those in previous chapters, using

More information

JUST THE MATHS UNIT NUMBER ORDINARY DIFFERENTIAL EQUATIONS 3 (First order equations (C)) A.J.Hobson

JUST THE MATHS UNIT NUMBER ORDINARY DIFFERENTIAL EQUATIONS 3 (First order equations (C)) A.J.Hobson JUST THE MATHS UNIT NUMBER 15.3 ORDINARY DIFFERENTIAL EQUATIONS 3 (First order equations (C)) by A.J.Hobson 15.3.1 Linear equations 15.3.2 Bernouilli s equation 15.3.3 Exercises 15.3.4 Answers to exercises

More information

. L( )WE WEEKLY JOURNAL.

. L( )WE WEEKLY JOURNAL. ) Y R G V V VV ) V R R F RP : x 2 F VV V Ṅ : V \ \ : P R : G V Y F P 35 RP 8 G V : % \ V X Q V < \ V P R V \ V< R VRG : Y ) P [ < _ & V V 6 :: V } V x V V & x 2 ) 3 RR & 8 \ R < Y q GR : XR < R V R % 7

More information

IOAN ŞERDEAN, DANIEL SITARU

IOAN ŞERDEAN, DANIEL SITARU Romanian Mathematical Magazine Web: http://www.ssmrmh.ro The Author: This article is published with open access. TRIGONOMETRIC SUBSTITUTIONS IN PROBLEM SOLVING PART IOAN ŞERDEAN, DANIEL SITARU Abstract.

More information

DIFFERENTIAL EQUATIONS

DIFFERENTIAL EQUATIONS DIFFERENTIAL EQUATIONS DIFFERENTIAL EQUATIONS NON-LINEAR LINEAR (in y) LINEAR W/ CST COEFFs (in y) FIRST- ORDER 4(y ) 2 +x cos y = x 2 4x 2 y + y cos x = x 2 4y + 3y = cos x ORDINARY DIFF EQs SECOND- ORDER

More information

Sect Least Common Denominator

Sect Least Common Denominator 4 Sect.3 - Least Common Denominator Concept #1 Writing Equivalent Rational Expressions Two fractions are equivalent if they are equal. In other words, they are equivalent if they both reduce to the same

More information

u (surge) X o p (roll) Body-fixed r o v (sway) w (heave) Z o Earth-fixed X Y Z r (yaw) (pitch)

u (surge) X o p (roll) Body-fixed r o v (sway) w (heave) Z o Earth-fixed X Y Z r (yaw) (pitch) Nonlinear Modelling of Marine Vehicles in Degrees of Freedom Thor I. Fossen and Ola-Erik Fjellstad The Norwegian Institute of Technology Department of Engineering Cybernetics N-0 Trondheim, NORWAY (E-mail:tif@itk.unit.no)

More information

KEEP PACE WITH. Volume 3, Number.38, 12 Pages. at Michigan State university.

KEEP PACE WITH. Volume 3, Number.38, 12 Pages. at Michigan State university. 2 3, 98! W \G \ q vk \ b v \(, v v ;, ): j:!, ; W, j v ; ;, \ ;, : z W, x,, G, 38 G v W W WW Y G W X Q G 82, v v G b Y v : W G : Y G X W Y 32 WG G G WG G X x x v v k v x b b b b b b 3 (x ) x, b b, W, v

More information

AE/ME 339. K. M. Isaac Professor of Aerospace Engineering. 12/21/01 topic7_ns_equations 1

AE/ME 339. K. M. Isaac Professor of Aerospace Engineering. 12/21/01 topic7_ns_equations 1 AE/ME 339 Professor of Aerospace Engineering 12/21/01 topic7_ns_equations 1 Continuity equation Governing equation summary Non-conservation form D Dt. V 0.(2.29) Conservation form ( V ) 0...(2.33) t 12/21/01

More information

CHAPTER 7 DIV, GRAD, AND CURL

CHAPTER 7 DIV, GRAD, AND CURL CHAPTER 7 DIV, GRAD, AND CURL 1 The operator and the gradient: Recall that the gradient of a differentiable scalar field ϕ on an open set D in R n is given by the formula: (1 ϕ = ( ϕ, ϕ,, ϕ x 1 x 2 x n

More information

Homework problems from Chapters IV-VI: answers and solutions

Homework problems from Chapters IV-VI: answers and solutions Homework problems from Chapters IV-VI: answers and solutions IV.21.1. In this problem we have to describe the field F of quotients of the domain D. Note that by definition, F is the set of equivalence

More information

2326 Problem Sheet 1. Solutions 1. First Order Differential Equations. Question 1: Solve the following, given an explicit solution if possible:

2326 Problem Sheet 1. Solutions 1. First Order Differential Equations. Question 1: Solve the following, given an explicit solution if possible: 2326 Problem Sheet. Solutions First Order Differential Equations Question : Solve the following, given an explicit solution if possible:. 2 x = 4x3, () = 3, ( ) The given equation is a first order linear

More information

2.1 NUMERICAL SOLUTION OF SIMULTANEOUS FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS. differential equations with the initial values y(x 0. ; l.

2.1 NUMERICAL SOLUTION OF SIMULTANEOUS FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS. differential equations with the initial values y(x 0. ; l. Numerical Methods II UNIT.1 NUMERICAL SOLUTION OF SIMULTANEOUS FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS.1.1 Runge-Kutta Method of Fourth Order 1. Let = f x,y,z, = gx,y,z be the simultaneous first order

More information

Logic, Set Theory and Computability [M. Coppenbarger]

Logic, Set Theory and Computability [M. Coppenbarger] 7 Relations (Handout) Definition 7-1: A set r is a relation from X to Y if r X Y. If X = Y, then r is a relation on X. Definition 7-2: Let r be a relation from X to Y. The domain of r, denoted dom r, is

More information

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

M5 Simple Beam Theory (continued)

M5 Simple Beam Theory (continued) M5 Simple Beam Theory (continued) Reading: Crandall, Dahl and Lardner 7.-7.6 In the previous lecture we had reached the point of obtaining 5 equations, 5 unknowns by application of equations of elasticity

More information

5/2/2012 Miscellaneous exercises Orbital motion 1

5/2/2012 Miscellaneous exercises Orbital motion 1 5/2/22 Miscellaneous exercises Orbital motion Orbital motion This exercise explores the motion of a particle in a spherical Coulomb potential. The equations of motion are similar to those for a planet

More information

14 EE 2402 Engineering Mathematics III Solutions to Tutorial 3 1. For n =0; 1; 2; 3; 4; 5 verify that P n (x) is a solution of Legendre's equation wit

14 EE 2402 Engineering Mathematics III Solutions to Tutorial 3 1. For n =0; 1; 2; 3; 4; 5 verify that P n (x) is a solution of Legendre's equation wit EE 0 Engineering Mathematics III Solutions to Tutorial. For n =0; ; ; ; ; verify that P n (x) is a solution of Legendre's equation with ff = n. Solution: Recall the Legendre's equation from your text or

More information

Remarks on semi-algebraic functions

Remarks on semi-algebraic functions Remarks on semi-algebraic functions Seiichiro Wakabayashi April 5 2008 the second version on August 30 2010 In this note we shall give some facts and remarks concerning semi-algebraic functions which we

More information

In Class Problem Set #15

In Class Problem Set #15 In Class Problem Set #15 CSE 1400 and MTH 2051 Fall 2012 Relations Definitions A relation is a set of ordered pairs (x, y) where x is related to y. Let denote a relational symbol. Write x y to express

More information

3D Elasticity Theory

3D Elasticity Theory 3D lasticity Theory Many structural analysis problems are analysed using the theory of elasticity in which Hooke s law is used to enforce proportionality between stress and strain at any deformation level.

More information

Chapter 2: Basic Governing Equations

Chapter 2: Basic Governing Equations -1 Reynolds Transport Theorem (RTT) - Continuity Equation -3 The Linear Momentum Equation -4 The First Law of Thermodynamics -5 General Equation in Conservative Form -6 General Equation in Non-Conservative

More information

Course 2BA1: Hilary Term 2007 Section 8: Quaternions and Rotations

Course 2BA1: Hilary Term 2007 Section 8: Quaternions and Rotations Course BA1: Hilary Term 007 Section 8: Quaternions and Rotations David R. Wilkins Copyright c David R. Wilkins 005 Contents 8 Quaternions and Rotations 1 8.1 Quaternions............................ 1 8.

More information

Homework 1/Solutions. Graded Exercises

Homework 1/Solutions. Graded Exercises MTH 310-3 Abstract Algebra I and Number Theory S18 Homework 1/Solutions Graded Exercises Exercise 1. Below are parts of the addition table and parts of the multiplication table of a ring. Complete both

More information

CHAPTER 2 BOOLEAN ALGEBRA

CHAPTER 2 BOOLEAN ALGEBRA CHAPTER 2 BOOLEAN ALGEBRA This chapter in the book includes: Objectives Study Guide 2.1 Introduction 2.2 Basic Operations 2.3 Boolean Expressions and Truth Tables 2.4 Basic Theorems 2.5 Commutative, Associative,

More information