K e sub x e sub n s i sub o o f K.. w ich i sub s.. u ra to the power of m i sub fi ed.. a sub t to the power of a
|
|
- Kristian McBride
- 5 years ago
- Views:
Transcription
1 - ; ; ˆ ; q x ; j [ ; ; ˆ ˆ [ ˆ ˆ ˆ - x - - ; x j ˆ x j ˆ ˆ ; x ; j κ ˆ ; ; ˆ σ x j ; ˆ [ ; ] q x σ; x - ˆ - ; J -- F - - ; x - -x - - x - - ; ; 9 S j P R S 3 q 47 q F x j x ; [ ] 9 S j P R S ; x 3 [ 47] ; [ ˆ ˆ ˆ ˆ ] ˆ ˆ x ; R J F x x ˆ x & ˆ
2 B [ [ ; S z P ; z4 σ σ ; S z 6 7 I κ ; ; z 5 S z 9 z 6 ; Y I ; ; x 4 z ; ε εσ I ε ζ ζ ζε ζε σ S α α σ ε ε ζ x σ ζ ε σ
3 [ ˆ ] B ˆ ˆ q q ˆ q S z * q B q U P - - ; σ ˆ q ˆ ˆ q z 4 F - ; - [ ˆ [ ; ˆ S z ˆ ˆ -S z 6 7 I - P z 5 ˆ ; S z 9 R R - z 6 z 4 ˆ - Y I ; - x 4 q -z - q - - S z 6 7 I - ; - ˆ ; z I S z z 9 z z - & z & z 6 S- [ - - ; ] Y I ; z [ x - & - & z ; ] U x 4 q - ˆ z - - q q F - [ ; ] ˆ &
4 ε σ I ζ ζ σ ζ S ζ F x ζ ζ ζ x α I µ ζ α x x z B ζ I ; α α B - ζ α x α α x S ; q
5 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ - ˆ ˆ ˆ ˆ I - - z - 4 I - α z ˆ z z S z ˆ ˆ z z ˆ F S [ z - F ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ - ] x - - z ˆ z - x z ˆ x z I - z ˆ z q -x - - ˆ z - - x q x [ ˆ -z ˆ ] B z I - ˆ -- I z q q - x - - ˆ ˆ - - B q x z z ˆ B [ ˆ z ] x - I - ˆ x q S - q 4 [ ] - [ ]
6 z [ z - z 8 ˆ q 4 I ˆ z & & - ] I ˆ ζ8 - π q - 4 ˆ I q ζ q R R I - ˆ - ˆ ˆ I ˆ ˆ I I I κ I α q κ - I q q P I q I I π q κ - ] - z x z π σ [ I ] z β π q z q z z z I P β πσ β π q β π π P - β ζ; A σ - x - ζβ q 4 β ζ σ ζ ζ ζ ζ q P A 4 ] ˆ ˆ ˆ ˆ ˆ q q P z ; x z
7 - ˆ ˆ - - ˆ I & & I I α - - P - - ˆ ˆ β I A σ q ε q α β ε ε ε ˆ I A q- I q α P - ˆ A A κ q I - P π q q P q - q I q A ] ηβ P π q - - q - q - - z ˆ q A π q ηβ π ζ - η - R q F ˆ - R F - q - q S S z z q - ζ z - ˆ J F - - -J- R F R -x--- x x - ˆ π ˆ - - q I π ˆ q - x - q - - ˆ ˆ [ x ˆ ] ˆ P x x q x S z κ z x x ˆ ˆ q ˆ - - ˆ ˆ ˆ I ˆ ˆ ˆ x ˆ - q z S z - ˆ µ ˆ ζ ˆ z - ˆ x q 4 -z I S z 7 x -q - - P I ˆ - ˆ F F κ F - - z- ˆ - - z - x ˆ R q- ˆ 4 ˆ F - 3 I ˆ ˆ S - z 7 x q ˆ - S P ˆ z - F - F q z F ˆ R J - F ˆ x x q ˆ q
8 - R R -- x x j x 3 ˆ x x j P j x 3 ˆ q P q S ˆ z 9 j x x j P x 3 ˆ ˆ x ˆ - P x - j q q Sz 4 F - - x S z 9 P F κ S ˆ z F 9 ˆ P ˆ x x F - - Sz 4 F - x F F - S F - x x S x x Sz 4 F x F F F F x x 3 F I x S x - x 3 I ˆ q - A R R - ˆ ζ I A ˆ ˆ - q I z ˆ ˆ - ˆ ζ I ζ ˆ q ; q F ˆ x A I P ˆ x 3 x 8 z z - S I ˆ ; ε q ˆ ˆ P A P 4 x x [ 4 [ Y ] ˆ - q ˆ ˆ ˆ q A ˆ -S - ζ ˆ - ζ q z P - ˆ I ˆ ˆ ˆ I 4 ˆ q x ˆ ˆ q - 4 q Y q z ˆ z ˆ ˆ - ˆ ; q- ˆ ˆ - q - q
9 P P ˆ ˆ -- - x x [ x 3 ˆ ˆ ˆ - ˆ x x x P ν ] x q ν - - xx x ˆ ˆ ˆ ν J F x - x - ˆ x ˆ q R R x - q R R x q- [ ˆ ] - q J F [ ˆR J F x x - ] - x q - -- J q q- -- x ˆ q ˆ ˆ j ˆ q S J q z 8 q κ U q I j κ S z 8] F x x -- U I -F x- F - F x x - D x D ν x x q S ; x [ q ˆ S ˆ ˆ x ] ˆ [ ˆ R ˆ J q ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ j ˆ ˆ ˆ ˆ ˆ q ˆ ˆ S ˆ z 8 ]
10 [ ˆ q ] ] P - F * - J F -q [ -x x--- ; - ] - - q ] P - ˆ F - A - R - J F q ˆ ; x x S P F JF q x x q q q ˆ q R A A ˆ α F α S q α - ˆ - ˆ [ ] - ˆ ˆ S ˆ ˆ S- R R R ; F ˆ [ ] ˆ ˆ [ ˆ ] I q ˆ q I ˆ P q 0 4 ˆ P S R R ˆ S j j j j j - - R ˆ ; ˆ ˆ ˆ F q ˆ - ˆ ˆ ˆ ˆ ; ˆ ˆ ˆ 4 ˆ 8 q S q q ˆ q q 3 ˆ 4 P ˆ ˆ κ x 4 J q F x P - J x F - - [ ˆ ] I - x J -q F - [ x - ] x J --x -F - -- P ˆ S j ˆ j κ ] x J qf 8 j - - ˆ ˆ - q ˆ ˆ - ˆ x - - J q-f -- ; - -x- --- J - ˆ 4 8 q ˆ q q 3 ˆ 4
11 κ
12 - [ - - G - ] q V 4 x - q - G q V 4 q x P 3 q q - ; - - F Gq F V 4 q x q ; P V- x ˆ [ ] [ P [ 3 P ] 3 ] P - -q q F F ] - P V x ; F ˆ ˆ [ F ] ˆ 0 P P V x j ˆ - ; κ υ q [ ] - - ; - P 3 V ε x P I 4 υ 0 ; ˆ q [ P q ] j 3 3 ˆ ; ; [ ] P 3 V x I 4 - ˆ ˆ ˆ ˆ 0 ; ˆ ˆ P ˆ [ ] 33 j ˆ ˆ ˆ ˆ ˆ & & [ ˆ ] ˆ ; P 3 V x I 4
13 3 j - 3 j j * 3 ˆ 3 q j 3 3 [ ˆ 3 ; R R - -q 3 ˆ ˆ ˆ ˆ 3 33 j ] P j ; q F x [ - * q x * * ˆ ] - * P υ q * 3 ˆ P ˆ 3 ; ˆ P ˆ * q 3 ; J * F ˆ ˆ F - [ q S 3 P R F ˆ ; P x ε ] εσ 3 ε ; V 4 -x - - ˆ ˆ J F - 3 q ˆ x S 3 P q R R ˆ - ; 3 ˆ P - ; V 4 x 3 I R R ; -- - [ -q q F -- 3 R J F ] J- -q x-- x -- S 3 P J -- -F - -x -x - 3 I - - κ κ ; V 4 x J q x ˆ 3 ˆ I [ ˆ ˆ ˆ R ˆ q F R ˆ ˆ ˆ ˆ J q x ˆ x ˆ ˆ J ˆ ˆ x ˆ x
14 x7 x7 x7 x7 x7 x43 x43 x7 x7 [ x4 3 x43 4 x7 x7-x7 x7 x7 x4-x4-x4-x4 x7 5 x4 6 x7 q------z------q--- x7 x7 ˆ x 43 x x7 x7 ˆ ˆ x 4 x7-x4-x4-x7----x40-x40-x40-x40-x40 x43 - x4-q-x4--x4-x4----x7-x7- x7x7 x7 x7 x4x4x4x x7 4 x4 x7 ˆ q z q ˆ x7x4 x7 3 ] x 4 S - - x7x7x7 - - x7x7 q x43 x43 x7x7 x4 [ ] x43 - x7 q x7x7x4 x4 x4 x4 z- - q 3 x x4-4 x7 qzq S q x7x4x4x7x40x40x40x40x40 - x4qx4x4x4x7x7 x7 x7 ˆ ˆ I R R 0 q q q 3κ B x 4 S - - q ˆ z q µ ˆ qz ν ; q ˆ q ˆ ; [ I 0 [ ] ] B I ˆ ˆ 0 ˆ [ ] ˆ ˆ B ˆ ˆ ˆ ˆ
15 - - [ - ˆ ˆ ˆ - x - ] X X X - X x X X X ˆ X χ X * * χ x χ - X [ X X ˆ X x χ X X * - - ˆ X X X ] 3 X X χ X χ χ χ [ ] 0 X x χ X X - X S - X ˆ x ˆ X - ˆ X U - ˆ ˆ R X ˆ χ X q F q B F Z [ q - χ X X A J -z 98 -z 447 ˆ X ˆ ˆ ] χ χ 0 S é [ U ˆ ] R [ F ] B F Z q ˆ ˆ A J z98 z ˆ ˆ S ˆ ˆ U R [ F ] B F Z q A J z 98 z [ 5 ]
16 z - q z U F z [ A ˆ U A F z q ˆ J ˆ A A R R q J R A 86 [ J z q U 3 9 [ U 5 5 F z A q ˆ A J q [ J 9 3 J R A ˆ 86 q J R A 86 q A S z U G D [ R R U Z 39 q 93 [ 9 5 J U 9 ˆ q 5 5 U U ˆ I q q [ A J S z U R R G D ḣz39 93 J q [ U U I q I [ F S Y 9 A ĥ S S 4 J z 9 3 U 0 [ I G F S YD 9 R R 4 D S4 S Z R ˆ ID R G GR A Y 9-5 ˆ B - R RI X U D R S R Z 9 U I I D B R G D [ U R U ID R G GR A Y I q ˆ B IX U R Z U I I D B R G D R ˆ ˆ ˆ J 4 9 ˆ [ ˆ I ˆ ˆ F S ˆ Y 9 S 4 ˆ [ R R D ˆ S R 9 ] ID R G GR A Y ˆ B I X U R Z ˆ U I I D B R G D R
b e i ga set s oane f dast heco mm on n va ns ing lo c u soft w section
66 M M Eq: 66 - -I M - - - -- -- - - - - -- - S I T - I S W q - I S T q ] q T G S W q I ] T G ˆ Gα ˆ ˆ ] H Z ˆ T α 6H ; Z - S G W [6 S q W F G S W F S W S W T - I ] T ˆ T κ G Gα ±G κ α G ˆ + G > H O T
More informationPanHomc'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 informationMANY 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 informationLOWELL 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 informationCHAPTER 6 : LITERATURE REVIEW
CHAPTER 6 : LITERATURE REVIEW Chapter : LITERATURE REVIEW 77 M E A S U R I N G T H E E F F I C I E N C Y O F D E C I S I O N M A K I N G U N I T S A B S T R A C T A n o n l i n e a r ( n o n c o n v e
More informationP E R E N C O - C H R I S T M A S P A R T Y
L E T T I C E L E T T I C E I S A F A M I L Y R U N C O M P A N Y S P A N N I N G T W O G E N E R A T I O N S A N D T H R E E D E C A D E S. B A S E D I N L O N D O N, W E H A V E T H E P E R F E C T R
More informationa 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 informationIDEAL CLASS GROUPS OF CYCLOTOMIC NUMBER FIELDS I
IDEA CASS GROUPS OF CYCOTOMIC NUMBER FIEDS I FRANZ EMMERMEYER Abstract. Following Hasse s example, various authors have been deriving divisibility properties of minus class numbers of cyclotomic fields
More information. α β γ δ ε ζ η θ ι κ λ μ Aμ ν(x) ξ ο π ρ ς σ τ υ φ χ ψ ω. Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω. Friday April 1 ± ǁ
. α β γ δ ε ζ η θ ι κ λ μ Aμ ν(x) ξ ο π ρ ς σ τ υ φ χ ψ ω. Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω Friday April 1 ± ǁ 1 Chapter 5. Photons: Covariant Theory 5.1. The classical fields 5.2. Covariant
More informationTwo 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 informationP 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 informationNeatest 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 informationand in each case give the range of values of x for which the expansion is valid.
α β γ δ ε ζ η θ ι κ λ µ ν ξ ο π ρ σ τ υ ϕ χ ψ ω Mathematics is indeed dangerous in that it absorbs students to such a degree that it dulls their senses to everything else P Kraft Further Maths A (MFPD)
More informationGovernor 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 informationA2 Assignment lambda Cover Sheet. Ready. Done BP. Question. Aa C4 Integration 1 1. C4 Integration 3
A Assignment lambda Cover Sheet Name: Question Done BP Ready Topic Comment Drill Mock Exam Aa C4 Integration sin x+ x+ c 4 Ab C4 Integration e x + c Ac C4 Integration ln x 5 + c Ba C Show root change of
More informationIdeal class groups of cyclotomic number fields I
ACTA ARITHMETICA XXII.4 (1995) Ideal class groups of cyclotomic number fields I by Franz emmermeyer (Heidelberg) 1. Notation. et K be number fields; we will use the following notation: O K is the ring
More informationLong-wave Instability in Anisotropic Double-Diffusion
Long-wave Instability in Anisotropic Double-Diffusion Jean-Luc Thiffeault Institute for Fusion Studies and Department of Physics University of Texas at Austin and Neil J. Balmforth Department of Theoretical
More information. α β γ δ ε ζ η θ ι κ λ μ Aμ ν(x) ξ ο π ρ ς σ τ υ φ χ ψ ω. Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω. Wednesday March 30 ± ǁ
. α β γ δ ε ζ η θ ι κ λ μ Aμ ν(x) ξ ο π ρ ς σ τ υ φ χ ψ ω. Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω Wednesday March 30 ± ǁ 1 Chapter 5. Photons: Covariant Theory 5.1. The classical fields 5.2. Covariant
More informationOWELL WEEKLY JOURNAL
Y \»< - } Y Y Y & #»»» q ] q»»»>) & - - - } ) x ( - { Y» & ( x - (» & )< - Y X - & Q Q» 3 - x Q Y 6 \Y > Y Y X 3 3-9 33 x - - / - -»- --
More informationd A L. T O S O U LOWELL, MICHIGAN. THURSDAY, DECEMBER 5, 1929 Cadillac, Nov. 20. Indignation
) - 5 929 XXX - $ 83 25 5 25 $ ( 2 2 z 52 $9285)9 7 - - 2 72 - - 2 3 zz - 9 86 - - - - 88 - q 2 882 q 88 - - - - - - ( 89 < - Q - 857-888 - - - & - - q - { q 7 - - - - q - - - - - - q - - - - 929 93 q
More informationRANDOM PROCESSES. THE FINAL TEST. Prof. R. Liptser and P. Chigansky 9:00-12:00, 18 of October, Student ID:
RANDOM PROCESSES. THE FINAL TEST. Prof. R. Liptser and P. Chigansky 9:00-12:00, 18 of October, 2001 Student ID: any supplementary material is allowed duration of the exam is 3 hours write briefly the main
More informationLOWELL 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 informationFinite Elements for Elastic Shell Models in
Elastic s in Advisor: Matthias Heinkenschloss Computational and Applied Mathematics Rice University 13 April 2007 Outline Elasticity in Differential Geometry of Shell Geometry and Equations The Plate Model
More informationCounty 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 informationLOWELL 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 informationx 1 = x i1 x i2 y = x 1 β x K β K + ε, x i =
x k T x k k = 1,, K T K X X 1 1 1 x 1 = 1 β 1 y T y 1 y T ε T T 1 x i1 x i2 y = x 1 β 1 + + x K β K + ε, x i = y T 1 = X T K β K 1 + ε T 1. x it T 1 y x 1 x K y = Xβ + ε X T K K E[ε i x j1, x j2,, x jk
More informationRenormalization group in stochastic theory of developed turbulence 4
Renormalization group in stochastic theory of developed turbulence 4 p. 1/14 Renormalization group in stochastic theory of developed turbulence 4 Low-dimensional fluctuations and improved ε expansion Juha
More informationFurther Maths A2 (M2FP2D1) Assignment ψ (psi) A Due w/b 19 th March 18
α β γ δ ε ζ η θ ι κ λ µ ν ξ ο π ρ σ τ υ ϕ χ ψ ω The mathematician s patterns, like the painter s or the poet s, must be beautiful: the ideas, like the colours or the words, must fit together in a harmonious
More informationSymbols 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 informationA n.. a l y.. s i s.. a n.. d.. G.. e.. o.. m.. e.. t r y.. i.. n.. M.. e t r i c.. S.. p a.. c e.. s \ centerline
G O I : 4 8 G 3 v- G G 6 9 4 O I : 4 8 / 3 v O I : G 4 3 8 / 6 94 3 v G 3 9 4 - J K w * w - J K v w w : - - v - - w wv w w - F I6 FI F 6 Uv w F Uv ˆ v v ˆ wv wk W w - - : W w - v - w v w H w - v w v 8
More information4sec 2xtan 2x 1ii C3 Differentiation trig
A Assignment beta Cover Sheet Name: Question Done Backpack Topic Comment Drill Consolidation i C3 Differentiation trig 4sec xtan x ii C3 Differentiation trig 6cot 3xcosec 3x iii C3 Differentiation trig
More informationA. 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 informationLOWHLL #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,
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 information3% 5% 1% 2% d t = 1,, T d i j J i,d,t J i,d,t+ = J i,d,t j j a i,d,t j i t d γ i > 0 i j t d U i,j,d,t = μ i,j,d + β i,j,d,t γ i + ε i,j,d,t ε i,j,d,t t ε i,,d,t μ β μ μ i,j,d d t d, t j μ i,j,d i j d
More informationMathematics Review Exercises. (answers at end)
Brock University Physics 1P21/1P91 Mathematics Review Exercises (answers at end) Work each exercise without using a calculator. 1. Express each number in scientific notation. (a) 437.1 (b) 563, 000 (c)
More informationOn corrections of classical multivariate tests for high-dimensional data
On corrections of classical multivariate tests for high-dimensional data Jian-feng Yao with Zhidong Bai, Dandan Jiang, Shurong Zheng Overview Introduction High-dimensional data and new challenge in statistics
More informationoenofc : COXT&IBCTOEU. AU skaacst sftwer thsa4 aafcekr will be ehat«s«ai Bi. C. W. JUBSSOS. PERFECT THBOUGH SDFFEBISG. our
x V - --- < x x 35 V? 3?/ -V 3 - ) - - [ Z8 - & Z - - - - - x 0-35 - 3 75 3 33 09 33 5 \ - - 300 0 ( -? 9 { - - - -- - < - V 3 < < - - Z 7 - z 3 - [ } & _ 3 < 3 ( 5 7< ( % --- /? - / 4-4 - & - % 4 V 2
More informationPHIL 50 INTRODUCTION TO LOGIC 1 FREE AND BOUND VARIABLES MARCELLO DI BELLO STANFORD UNIVERSITY DERIVATIONS IN PREDICATE LOGIC WEEK #8
PHIL 50 INTRODUCTION TO LOGIC MARCELLO DI BELLO STANFORD UNIVERSITY DERIVATIONS IN PREDICATE LOGIC WEEK #8 1 FREE AND BOUND VARIABLES Before discussing the derivation rules for predicate logic, we should
More informationA 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 informationOutline. Logic. Definition. Theorem (Gödel s Completeness Theorem) Summary of Previous Week. Undecidability. Unification
Logic Aart Middeldorp Vincent van Oostrom Franziska Rapp Christian Sternagel Department of Computer Science University of Innsbruck WS 2017/2018 AM (DCS @ UIBK) week 11 2/38 Definitions elimination x φ
More informationASSIGNMENT COVER SHEET omicron
ASSIGNMENT COVER SHEET omicron Name Question Done Backpack Ready for test Drill A differentiation Drill B sketches Drill C Partial fractions Drill D integration Drill E differentiation Section A integration
More informationComplex Variables. Chapter 1. Complex Numbers Section 1.2. Basic Algebraic Properties Proofs of Theorems. December 16, 2016
Complex Variables Chapter 1. Complex Numbers Section 1.2. Basic Algebraic Properties Proofs of Theorems December 16, 2016 () Complex Variables December 16, 2016 1 / 12 Table of contents 1 Theorem 1.2.1
More informationECE 636: Systems identification
ECE 636: Systems identification Lectures 7 8 onparametric identification (continued) Important distributions: chi square, t distribution, F distribution Sampling distributions ib i Sample mean If the variance
More informationThermo-electric transport in holographic systems with moment
Thermo-electric Perugia 2015 Based on: Thermo-electric gauge/ models with, arxiv:1406.4134, JHEP 1409 (2014) 160. Analytic DC thermo-electric conductivities in with gravitons, arxiv:1407.0306, Phys. Rev.
More informationExogeneity tests and weak identification
Cireq, Cirano, Départ. Sc. Economiques Université de Montréal Jean-Marie Dufour Cireq, Cirano, William Dow Professor of Economics Department of Economics Mcgill University June 20, 2008 Main Contributions
More information1 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 informationOn corrections of classical multivariate tests for high-dimensional data. Jian-feng. Yao Université de Rennes 1, IRMAR
Introduction a two sample problem Marčenko-Pastur distributions and one-sample problems Random Fisher matrices and two-sample problems Testing cova On corrections of classical multivariate tests for high-dimensional
More informationY1 Double Maths Assignment λ (lambda) Exam Paper to do Core 1 Solomon C on the VLE. Drill
α β γ δ ε ζ η θ ι κ λ µ ν ξ ο π ρ σ τ υ ϕ χ ψ ω Nature is an infinite sphere of which the centre is everywhere and the circumference nowhere Blaise Pascal Y Double Maths Assignment λ (lambda) Tracking
More informationthermo-viscoelasticity using
thermo-viscoelasticity Chair of Computational Mechanics University of Siegen Chair of Applied Mechanics and Dynamics Chemnitz University of Technology ECCOMAS, 13.9.1 1 Thermoviscoelastic continuum framework
More informationChromatically Unique Bipartite Graphs With Certain 3-independent Partition Numbers III ABSTRACT
Malaysian Chromatically Journal of Mathematical Unique Biparte Sciences Graphs with 1(1: Certain 139-16 3-Independent (007 Partition Numbers III Chromatically Unique Bipartite Graphs With Certain 3-independent
More informationLOWER AND UPPER SOLUTIONS TO SEMILINEAR BOUNDARY VALUE PROBLEMS: AN ABSTRACT APPROACH. Alessandro Fonda Rodica Toader. 1.
Topological Methods in Nonlinear Analysis Journal of the Juliusz Schauder University Centre Volume 38, 2011, 59 93 LOWER AND UPPER SOLUTIONS TO SEMILINEAR BOUNDARY VALUE PROBLEMS: AN ABSTRACT APPROACH
More informationLOWELL 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 information16.20 HANDOUT #2 Fall, 2002 Review of General Elasticity
6.20 HANDOUT #2 Fall, 2002 Review of General Elasticity NOTATION REVIEW (e.g., for strain) Engineering Contracted Engineering Tensor Tensor ε x = ε = ε xx = ε ε y = ε 2 = ε yy = ε 22 ε z = ε 3 = ε zz =
More informationSlow Modulation & Large-Time Dynamics Near Periodic Waves
Slow Modulation & Large-Time Dynamics Near Periodic Waves Miguel Rodrigues IRMAR Université Rennes 1 France SIAG-APDE Prize Lecture Jointly with Mathew Johnson (Kansas), Pascal Noble (INSA Toulouse), Kevin
More informationFission of a longitudinal strain solitary wave in a delaminated bar
Fission of a longitudinal strain solitary wave in a delaminated bar Karima Khusnutdinova Department of Mathematical Sciences, Loughborough University, UK K.Khusnutdinova@lboro.ac.uk and G.V. Dreiden, A.M.
More informationMidterm Review. Name: Class: Date: ID: A. Short Answer. 1. For each graph, write the equation of a radical function of the form y = a b(x h) + k.
Name: Class: Date: ID: A Midterm Review Short Answer 1. For each graph, write the equation of a radical function of the form y = a b(x h) + k. a) b) c) 2. Determine the domain and range of each function.
More informationT m / A. Table C2 Submicroscopic Masses [2] Symbol Meaning Best Value Approximate Value
APPENDIX C USEFUL INFORMATION 1247 C USEFUL INFORMATION This appendix is broken into several tables. Table C1, Important Constants Table C2, Submicroscopic Masses Table C3, Solar System Data Table C4,
More informationA2 Assignment zeta Cover Sheet. C3 Differentiation all methods. C3 Sketch and find range. C3 Integration by inspection. C3 Rcos(x-a) max and min
A Assignment zeta Cover Sheet Name: Question Done Backpack Ready? Topic Comment Drill Consolidation M1 Prac Ch all Aa Ab Ac Ad Ae Af Ag Ah Ba C3 Modulus function Bb C3 Modulus function Bc C3 Modulus function
More information1 Integration of Rational Functions Using Partial Fractions
MTH Fall 008 Essex County College Division of Mathematics Handout Version 4 September 8, 008 Integration of Rational Functions Using Partial Fractions In the past it was far more usual to simplify or combine
More informationStorm Open Library 3.0
S 50% off! 3 O L Storm Open Library 3.0 Amor Sans, Amor Serif, Andulka, Baskerville, John Sans, Metron, Ozdoby,, Regent, Sebastian, Serapion, Splendid Quartett, Vida & Walbaum. d 50% f summer j sale n
More informationPRELIMINARIES FOR GENERAL TOPOLOGY. Contents
PRELIMINARIES FOR GENERAL TOPOLOGY DAVID G.L. WANG Contents 1. Sets 2 2. Operations on sets 3 3. Maps 5 4. Countability of sets 7 5. Others a mathematician knows 8 6. Remarks 9 Date: April 26, 2018. 2
More informationMATH443 PARTIAL DIFFERENTIAL EQUATIONS Second Midterm Exam-Solutions. December 6, 2017, Wednesday 10:40-12:30, SA-Z02
1 MATH443 PARTIAL DIFFERENTIAL EQUATIONS Second Midterm Exam-Solutions December 6 2017 Wednesday 10:40-12:30 SA-Z02 QUESTIONS: Solve any four of the following five problems [25]1. Solve the initial and
More informationSoliton solutions to the ABS list
to the ABS list Department of Physics, University of Turku, FIN-20014 Turku, Finland in collaboration with James Atkinson, Frank Nijhoff and Da-jun Zhang DIS-INI, February 2009 The setting CAC The setting
More informationR k. t + 1. n E t+1 = ( 1 χ E) W E t+1. c E t+1 = χ E Wt+1 E. Γ E t+1. ) R E t+1q t K t. W E t+1 = ( 1 Γ E t+1. Π t+1 = P t+1 /P t
R k E 1 χ E Wt E n E t+1 t t + 1 n E t+1 = ( 1 χ E) W E t+1 c E t+1 = χ E Wt+1 E t + 1 q t K t Rt+1 E 1 Γ E t+1 Π t+1 = P t+1 /P t W E t+1 = ( 1 Γ E t+1 ) R E t+1q t K t Π t+1 Γ E t+1 K t q t q t K t j
More informationPerfect simulation algorithm of a trajectory under a Feynman-Kac law
Perfect simulation algorithm of a trajectory under a Feynman-Kac law Data Assimilation, 24th-28th September 212, Oxford-Man Institute C. Andrieu, N. Chopin, A. Doucet, S. Rubenthaler University of Bristol,
More informationLeast squares: introduction to the network adjustment
Least squares: introduction to the network adjustment Experimental evidence and consequences Observations of the same quantity that have been performed at the highest possible accuracy provide different
More informationK(ζ) = 4ζ 2 x = 20 Θ = {θ i } Θ i=1 M = {m i} M i=1 A = {a i } A i=1 M A π = (π i ) n i=1 (Θ) n := Θ Θ (a, θ) u(a, θ) E γq [ E π m [u(a, θ)] ] C(π, Q) Q γ Q π m m Q m π m a Π = (π) U M A Θ
More informationTight-Binding Model of Electronic Structures
Tight-Binding Model of Electronic Structures Consider a collection of N atoms. The electronic structure of this system refers to its electronic wave function and the description of how it is related to
More informationlast name ID 1 c/cmaker/cbreaker 2012 exam version a 6 pages 3 hours 40 marks no electronic devices SHOW ALL WORK
last name ID 1 c/cmaker/cbreaker 2012 exam version a 6 pages 3 hours 40 marks no electronic devices SHOW ALL WORK 8 a b c d e f g h i j k l m n o p q r s t u v w x y z 1 b c d e f g h i j k l m n o p q
More informationModified Theories of Gravity in Cosmology
Modified Theories of Gravity in Cosmology Gonzalo J. Olmo University of Wisconsin-Milwaukee (USA) Gonzalo J. Olmo About this talk... Motivation: General Relativity by itself seems unable to justify the
More informationNumerical Approximation of Phase Field Models
Numerical Approximation of Phase Field Models Lecture 2: Allen Cahn and Cahn Hilliard Equations with Smooth Potentials Robert Nürnberg Department of Mathematics Imperial College London TUM Summer School
More informationΜια προσπαθεια για την επιτευξη ανθρωπινης επιδοσης σε ρομποτικές εργασίες με νέες μεθόδους ελέγχου
Μια προσπαθεια για την επιτευξη ανθρωπινης επιδοσης σε ρομποτικές εργασίες με νέες μεθόδους ελέγχου Towards Achieving Human like Robotic Tasks via Novel Control Methods Zoe Doulgeri doulgeri@eng.auth.gr
More informationOptimality conditions for unconstrained optimization. Outline
Optimality conditions for unconstrained optimization Daniel P. Robinson Department of Applied Mathematics and Statistics Johns Hopkins University September 13, 2018 Outline 1 The problem and definitions
More informationSemi-formal solution and monodromy of some confluent hypergeometric equations
RIMS Kôyûrou Bessatsu 4x (20XX), 000 000 Semi-formal solution and monodromy of some confluent hypergeometric equations Dedicated to Professor Taashi AOKI for his sixtieth birthday By MasafumiYoshino Abstract
More informationMagnetic wells in dimension three
Magnetic wells in dimension three Yuri A. Kordyukov joint with Bernard Helffer & Nicolas Raymond & San Vũ Ngọc Magnetic Fields and Semiclassical Analysis Rennes, May 21, 2015 Yuri A. Kordyukov (Ufa) Magnetic
More informationLOWELL, MICHIGAN, NOVEMBER 27, Enroute to Dominican Republic
LDG L G L Y Y LLL G 7 94 D z G L D! G G! L $ q D L! x 9 94 G L L L L L q G! 94 D 94 L L z # D = 4 L ( 4 Q ( > G D > L 94 9 D G z ] z ) q 49 4 L [ ( D x ] LY z! q x x < G 7 ( L! x! / / > ( [ x L G q x!
More informationLight Pseudoscalar Higgs boson in NMSSM
K. Cheung 1 Light Pseudoscalar Higgs boson in NMSSM Kingman Cheung NTHU, December 2006 (with Abdesslam Arhrib, Tie-Jiun Hou, Kok-Wee Song, hep-ph/0606114 K. Cheung 2 Outline Motivations for NMSSM The scenario
More informationWELL-POSEDNESS OF DISCONTINUOUS BOUNDARY-VALUE PROBLEMS FOR NONLINEAR ELLIPTIC COMPLEX EQUATIONS IN MULTIPLY CONNECTED DOMAINS
Electronic Journal of Differential Equations, Vol. 2013 (2013), No. 247, pp. 1 21. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu WELL-POSEDNESS
More informationA 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 informationA geometric solution of the Kervaire Invariant One problem
A geometric solution of the Kervaire Invariant One problem Petr M. Akhmet ev 19 May 2009 Let f : M n 1 R n, n = 4k + 2, n 2 be a smooth generic immersion of a closed manifold of codimension 1. Let g :
More informationParallel KS Block-Step Method. Sverre Aarseth. Institute of Astronomy, Cambridge
Parallel KS Block-Step Method Sverre Aarseth Institute of Astronomy, Cambridge Code Overview Hermite KS Prediction & Correction Iteration Time-Steps Decision-Making Binary Project Code Overview Directories
More informationEXPOSITORY NOTES ON DISTRIBUTION THEORY, FALL 2018
EXPOSITORY NOTES ON DISTRIBUTION THEORY, FALL 2018 While these notes are under construction, I expect there will be many typos. The main reference for this is volume 1 of Hörmander, The analysis of liner
More informationDavid Burns and Matthias Flach. t y
4 Dv B F v 4 b Dv 4 B Dv B F v b F bk bk R F R q v q b R F L L - b q q - Eq: L T C O b q ˆ bk bk * T C O b TΩ bk + ψ T Ω bk T Ω T C T O bk bk + ˆ O w w ψ * R ˆ R T bk Ω bk T O ˆ w R k R bk bk R T C O bk
More informationSubstitution in two symbols and transcendence. Kumiko Nishioka, Taka-aki Tanaka and Zhi-Ying Wen
Research Report KSTS/RR-97/007 Substitution in two symbols and transcendence by Kumiko Nishioka, Taka-aki Tanaka and Zhi-Ying Wen Kumiko Nishioka Mathematics, Hiyoshi Campus Keio University Taka-aki Tanaka
More informationConsequences of measurement error. Psychology 588: Covariance structure and factor models
Consequences of measurement error Psychology 588: Covariance structure and factor models Scaling indeterminacy of latent variables Scale of a latent variable is arbitrary and determined by a convention
More informationSupplementary Figures. Measuring Similarity Between Dynamic Ensembles of Biomolecules
Supplementary Figures Measuring Similarity Between Dynamic Ensembles of Biomolecules Shan Yang, Loïc Salmon 2, and Hashim M. Al-Hashimi 3*. Department of Chemistry, University of Michigan, Ann Arbor, MI,
More informationEntities for Symbols and Greek Letters
Entities for Symbols and Greek Letters The following table gives the character entity reference, decimal character reference, and hexadecimal character reference for symbols and Greek letters, as well
More information( ). Expanding the square and keeping in mind that
One-electron atom in a Magnetic Field When the atom is in a magnetic field the magnetic moment of the electron due to its orbital motion and its spin interacts with the field and the Schrodinger Hamiltonian
More information5 n N := {1, 2,...} N 0 := {0} N R ++ := (0, ) R + := [0, ) a, b R a b := max{a, b} f g (f g)(x) := f(x) g(x) (Z, Z ) bz Z Z R f := sup z Z f(z) κ: Z R ++ κ f : Z R f(z) f κ := sup z Z κ(z). f κ < f κ
More informationA density theorem for parameterized differential Galois theory
A density theorem for parameterized differential Galois theory Thomas Dreyfus University Paris 7 The Kolchin Seminar in Differential Algebra, 31/01/2014, New York. In this talk, we are interested in the
More informationEvent-sampled direct adaptive neural network control of uncertain strict-feedback system with application to quadrotor unmanned aerial vehicle
Scholars' Mine Masters Theses Student Research & Creative Works Fall 2016 Event-sampled direct adaptive neural network control of uncertain strict-feedback system with application to quadrotor unmanned
More informationM 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 informationCSE 1400 Applied Discrete Mathematics Definitions
CSE 1400 Applied Discrete Mathematics Definitions Department of Computer Sciences College of Engineering Florida Tech Fall 2011 Arithmetic 1 Alphabets, Strings, Languages, & Words 2 Number Systems 3 Machine
More informationEE-559 Deep learning 9. Autoencoders and generative models
EE-559 Deep learning 9. Autoencoders and generative models François Fleuret https://fleuret.org/dlc/ [version of: May 1, 2018] ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE Embeddings and generative models
More informationGraduate Econometrics Lecture 4: Heteroskedasticity
Graduate Econometrics Lecture 4: Heteroskedasticity Department of Economics University of Gothenburg November 30, 2014 1/43 and Autocorrelation Consequences for OLS Estimator Begin from the linear model
More informationINFANCY AND CHILDHOOD IN ANCIENT GREEK PHILOSOPHY. Malcolm Schofield
INFANCYANDCHILDHOODINANCIENTGREEKPHILOSOPHY MalcolmSchofield TheancientGreeksaren tusuallythoughttohavemuchofinteresttotellus aboutchildhoodorinfancy.butthisisinfactasubjectonwhichgreek philosophysaysquitealot,whoseattractionsishallbehopingtorecommendto
More informationarxiv: v2 [nlin.si] 4 Nov 2015
Self-Consistent Sources for Integrable Equations via Deformations of Binary Darboux Transformations O. Chvartatskyi a,b, A. Dimakis c and F. Müller-Hoissen b a Mathematisches Institut, Georg-August Universität
More informationExact Computation of Pearson Statistics Distribution and Some Experimental Results
AUSTRIAN JOURNAL OF STATISTICS Volume 37 (28), Number 1, 129 135 Exact Computation of Pearson Statistics Distribution and Some Experimental Results Marina V. Filina and Andrew M. Zubkov Steklov Mathematical
More informationWeak solutions to the incompressible Euler equations
Weak solutions to the incompressible Euler equations Antoine Choffrut Seminar Talk - 2014 Motivation Time-dependent Euler equations: t v + (v )v + p = 0 div v = 0 Onsager s conjecture: conservation vs.
More information