INRIA Sophia Antipolis France. TEITP p.1
|
|
- Peregrine Dorsey
- 6 years ago
- Views:
Transcription
1 ÌÖÙ Ø ÜØ Ò ÓÒ Ò ÓÕ Ä ÙÖ ÒØ Ì ÖÝ INRIA Sophia Antipolis France TEITP p.1
2 ÅÓØ Ú Ø ÓÒ Ï Ý ØÖÙ Ø Ó ÑÔÓÖØ ÒØ Å ÒÐÝ ÈÖÓÚ Ò ÌÖÙØ Ø Ò ÑÔÐ Ã Ô ÈÖÓÚ Ò ÌÖÙ Ø È Ó ÖÖÝ Ò ÈÖÓÓ µ Ò Ö ØÝ ÓÑ Ò ËÔ ÔÔÐ Ø ÓÒ TEITP p.2
3 ÇÙØÐ Ò ÇÚ ÖÚ Û Ó ÓÕ Ê Ð Ø ÓÒ ÜØ Ò ÓÒ Î Ö ÓÙ Ð ÚÓÙÖ ÅÓÖ ÜØ Ò ÓÒ ÓÒÐÙ ÓÒ TEITP p.3
4 ÓÕ ÐÙÐÙ Ó ÁÒ ÙØ Ú ÓÒ ØÖÙØ ÓÒ ÄÓ Ú Ö ÓÒ ÒÓÛ v8.2 Ö Ø ÌÖÙ Ø Ò ÓÕ ÜÔÐ Ø ÈÖÓÓ Ç Ø ÌÖÙ Ø ÓÑÔÓÒ ÒØ coqchk TEITP p.4
5 ÓÕ Inductive N:Type := O S (n:n). Inductive _ = _ : T:Type, T T Prop := refl_equal: T:Type, x:t, x = x. Fact triv:2 = 2. Proof. apply refl_equal. Qed. Print triv. triv = (refl_equal N 2) TEITP p.5
6 ÓÕ Function x + y := if x is S x then S(x + y) else y. Fact triv :1 + 2 = 3. Proof. apply refl_equal. Qed. Print triv. triv = (refl_equal N 3) TEITP p.6
7 Ê Ð Ø ÓÒ ÓÙØ Ò ³ µ Ë ÑÙ Ð Ö Ð Ø ÓÒ ØÓ Ù Ð ÒØ Ò Í Ò ÖØ ÓÒ ÔÖÓ ÙÖ (a 2 + b 2 + c 2 + d 2 + e 2 + f 2 + g 2 + h 2 )(m 2 + n 2 + o 2 + p 2 + q 2 + r 2 + s 2 + t 2 ) = (am bn co dp eq fr gs ht) 2 + (bm + an + do cp + fq er hs + gt) 2 + (cm dn + ao + bp + gq + hr es ft) 2 + (dm + cn bo + ap + hq gr + fs et) 2 + (em fn go hp + aq + br + cs + dt) 2 + (fm + en ho + gp bq + ar ds + ct) 2 + (gm + hn + eo fp cq + dr + as bt) 2 + (hm gn + fo + ep dq cr + bs + at) 2 TEITP p.7
8 Ê Ð Ø ÓÒ ÖÓÙÔ Ð Ò Inductive expr:type := add (e 1 e 2 :expr) opp (e:expr) var (n: N) zero. (x + y) y (add (add (var 1) (var 2)) (opp (var 1))) Ä Ø Ó ÒØ Ö Function l 1 ++ l 2 := if l 1 is a:: l 3 then if l 2 is b:: l 4 then if a < b then a::(l 3 ++ l 2 ) else if b < a then b::(l 1 ++ l 4 ) else if a == b then a:: b::(l 3 ++ l 4 ) else (l 3 ++ l 4 ) else l 1 else l 2 [1,1,2] ++ [-1,2] [1,2,2] TEITP p.8
9 Ê Ð Ø ÓÒ ÆÓÖÑ Ð Ø ÓÒ Function e2l e := match e with add e 1 e 2 e2l e 1 ++ e2l e 2 opp e 1 map (fun x x) (e2l e 1 ) var n [+n] zero [] end e2l (add (add (var 1) (var 2)) (opp (var 2))) ([1] ++ [2]) ++ (map (fun x x) [2]) [1,2] ++ (map (fun x x) [2]) [1,2] ++ [-2] [1] TEITP p.9
10 Ê Ð Ø ÓÒ ÁÒØ ÖÔÖ Ø Ø ÓÒ Structure Group := { T: Type; add: T -> T -> T; opp: T -> T; zero: T; assoc: x y z, add (add x y) = add x (add y z); com: x y, add x y = add y x; lefti: x, add x zero = x; lefto: x, add x (opp x) = zero; } Definition zgroup := mkgroup {Z,+,,0,...} Definition ogroup := mkgroup {bool,,,true,...} TEITP p.10
11 Ê Ð Ø ÓÒ ÁÒØ ÖÔÖ Ø Ø ÓÒ Function [ e ] g,env := match e with add e 1 e 2 g.add [ e 1 ] g,env [ e 2 ] g,env opp e 1 g.opp [ e 1 ] g,env var n env n zero g.zero end [ add (add (var 1) (var 2)) (opp (var 2)) ] zgroup,{1 x,2 y} (x + y) + y [ add (add (var 1) (var 2)) (opp (var 2)) ] ogroup,{1 x,2 y} (x y) y TEITP p.11
12 Ê Ð Ø ÓÒ ÁÒØ ÖÔÖ Ø Ø ÓÒ Definition < z > g,env := if 0 < z then env z else g.opp (env z) Function { l } g,env := match l with [] g.zero [z] < z > g,env z::l 1 g.add < z > g,env { l 1 } g,env end { [1] } zgroup,{1 x,2 y} x { [1] } ogroup,{1 x,2 y} x TEITP p.12
13 Ê Ð Ø ÓÒ ÓÖÖ ØÒ Lemma e2l_cor: g env e, [ e ] g,env = { e2l e } g,env. Ý ØÖÙØÙÖ Ð Ò ÙØ ÓÒ ÓÒ e ÈÖÓÓ Ó x y, (x + y) + y = x : ÈÖÓÓ (fun x y (e2l_cor zgroup {1 x,2 y} (add (add (var 1) (var 2)) (opp (var 2))))) Ó x y, (x y) y = x : ÈÖÓÓ (fun x y (e2l_cor ogroup {1 x,2 y} (add (add (var 1) (var 2)) (opp (var 2))))) TEITP p.13
14 Ê Ð Ø ÓÒ ËÙÑÑ ÖÝ e2l add (add (var 1) (var 2)) (opp (var 2)) [2] { } (x + y) + y = x Ö Ø ÓÒ TEITP p.14
15 Ê Ð Ø ÓÒ Ò³ ÒØ ØÝ ³ µ Ñ v8.2µ ¼ ½ Ö Ó Ö Å ÓÙ ³¼ µ Ò Ñ Ò ÕÙ Ð Ø Ò ÓÑÑÙØ Ø Ú Ö Ò ÓÒ Ö Ø Ò ÓÕä ãèöóú Ò Ö Ó Ö Ú Ö Ä ÖÓÝ ³¼¾µ Ò Ñ Ò ÓÑÔ Ð ÑÔÐ Ñ ÒØ Ø ÓÒ Ó ØÖÓÒ Ö ÙØ ÓÒä ã TEITP p.15
16 Ð Ý Å Ð Å Ý ÖÓ ³¼ µ Ú Ð Ò Û Ø Ð Ö ÜÔÖ ÓÒ ÓÚ Ö Ð Ò ÓÕ Ù Ò ã ÜØ Ò ÓÒ Å ÔÐ ä Coq expand, factor,... ring Maple TEITP p.16
17 Ì ÖÝ ³¼ µ Ä ÙÖ ÒØ ÈÓÐÝÒÓÑ Ð ÜÔÖ ÓÒ Ò ÈÖÓÓ Ø ÒØä ãë ÑÔÐ Ý Ò ÜØ Ò ÓÒ y(3x + y + 2) < x(3y + 1) + z(x + y) ÆÓÖÑ Ð Ø ÓÒ 0 < x yy 2y + zx + zy ÁÒØ Ö Ø Ú y(y + 2) < x + z(x + y) TEITP p.17
18 ÓÒ ³¼ µ Ö Ö Ê Ð Ü Ú Ö Ø Ñ Ø Ì Ø Ø Ð Ò Ö Ò ã Ø ÜØ Ò ÓÒ ÝÓÒ ä E = c cx E 1 + E 2 E 1 E 2 E 1 < E 2 E 1 = E 2 2x y 1 x + y 2 y 1 TEITP p.18
19 Ä ÑÑ Ö ³ ÓÒ Ó Ø ÓÐÐÓÛ Ò Ø Ø Ñ ÒØ ÓÐ Ü ØÐÝ ÜØ Ò ÓÒ x,a.x b y,y 0 A y.y = 0 b t.y > 0 2x y 1 1 x + y 2 2 y TEITP p.19
20 À ÖÖ ÓÒ ³¼ µ ÂÓ Ò ÒÓÒÐ Ò Ö Ö Ð ÓÖÑÙÐ Ú ÙÑ Ó ÕÙ Ö ä ãî Ö Ý Ò ÜØ Ò ÓÒ x 1,...,x n, P 1 (x 1,...,x n ) 0... P k (x 1,...,x n ) 0 P(x 1,...,x n ) 0 TEITP p.20
21 ÜØ Ò ÓÒ Á P(x 1,...,x n ) 2 0 P(x 1,...,x n ) 0 P(x 1,...,x n ) 0 P(x 1,...,x n ) + Q(x 1,...,x n ) 0 P(x 1,...,x n ) 0 Q(x 1,...,x n ) 0 P(x 1,...,x n ) Q(x 1,...,x n ) 0 Ü ÑÔÐ abcx, ax 2 + bx + c = 0 b 2 4ac 0 b 2 4ac = (2ax + b) 2 4a(ax 2 + bx + c) TEITP p.21
22 ÜØ Ò ÓÒ Coq external g P i p i Sos-Wrapper A Csdp L U TEITP p.22
23 ˺ ÓÝ Ö Â ËØÖÓØ Ö ÅÓÓÖ ³ ½µ ÊÓ ÖØ Å Ò Ð Î Ö Ø ÓÒ Ó ÓÖØÖ Ò ËÕÙ Ö ÊÓÓØ ãì ÜØ Ò ÓÒ ÈÖÓ Ö Ñä INTEGER FUNCTION ISQRT(I) INTEGER I IF ((I.LT. O)) STOP IF ((I.GT. 1)) GOTO 100 ISQRT = I RETURN 100 ISQRT = (I / 2) 200 CONTINUE IF (((I / ISQRT).GE. ISQRT)) RETURN ISQRT = ((ISQRT + (I / ISQRT)) / 2) GOTO 200 END TEITP p.23
24 ÜØ Ò ÓÒ Ø ÓÖ Ñ Å Ò ij, 0 i 0 < j i < ((j + i/j)/2 + 1) 2 k = i/j Ò l = (j + k)/2 Ê ÙØ ÓÒ j k l, 0 j 0 k 0 l 2l j+k j + k < 2(l + 1) jk + j (l + 1) 2 Ó ËÕÙ Ö ËÙÑ 4((l + 1) 2 (jk + j)) = (k j + 1) 2 + (2(l + 1) (j + k + 1))(3 + j + k + 2l)) TEITP p.24
25 Ö Ó Ö ÄÓ ÈÓØØ Ö Ä ÙÖ ÒØ Ì ÖÝ ³¼ µ Ò Ñ Ò ÖØ Ø ÓÖ Ð Ö Ò Ø Ö ÔÔÐ Ø ÓÒ ØÓ ãèöóó ÜØ Ò ÓÒ ÓÑ ØÖÝ Ì ÓÖ Ñ ÈÖÓÚ Ò ä ÙØÓÑ Ø x 1,...,x n, P 1 (x 1,...,x n ) = 0... P k (x 1,...,x n ) = 0 P(x 1,...,x n ) = 0 ÆÙÐÐ Ø ÐÐ Ò ØÞ À Ð Öس cp(x 1,...,x n ) r = i Q i (x 1,...,x n )P i (x 1,...,x n ) TEITP p.25
26 ÜØ Ò ÓÒ Á P(x 1,...,x n ) r {P 1 (x 1,...,x n ),...,P k (x 1,...,x n )} Ü ÑÔÐ x 2 y 2 y 4 {x 2 + 1,xy 1} Ú ÓÒ x 2 y 2 y 4 = y 2 (x 2 + 1) y 4 y 2 x 2 y 2 y 4 = (xy + 1)(xy 1) y ËÔÓÐÝÒÓÑ Ð x 2 y = y(x 2 + 1) = x(xy 1) spoly(x 2 + 1,xy + 1) = y(x 2 + 1) x(xy 1) = x + y TEITP p.26
27 ÜØ Ò ÓÒ Ö Ò Ö spoly(x 2 + 1,xy + 1) = x + y {x 2 + 1,xy 1} {x 2 + 1,xy 1,x + y} spoly(x 2 + 1,x + y) = x x(x + y) = (xy 1) spoly(xy 1,x + y) = xy 1 y(x + y) = y 2 1 {x 2 + 1,xy 1,x + y, y 2 1} spoly(xy 1, y 2 1) = y(xy 1) ( x)( y 2 1) = (x + y) TEITP p.27
28 ÜØ Ò ÓÒ ÖØ Ø x 2 y 2 y 4 {x 2 + 1,xy 1} x 2 y 2 y 4 {x 2 + 1,xy 1,x + y, y 2 1} x 2 y 2 y 4 = y 2 (x 2 + 1) y 4 y 2 y 4 y 2 = y 2 ( y 2 1) + 0 x 2 y 2 y 4 = y 2 (x 2 + 1) + y 2 ( y 2 1) x 2 y 2 y 4 = y 2 (x 2 + 1) + y 2 (xy 1 y(x + y)) x 2 y 2 y 4 = y 2 (x 2 +1) +y 2 (xy 1 y(y(x 2 +1) x(xy 1))) x 2 y 2 y 4 = ( y 4 + y 2 )(x 2 + 1) + (xy 3 + y 2 )(xy 1) TEITP p.28
29 ÜØ Ò ÓÒ ÈÖÓ Ö Ñ ËØÖ Ø Ä Ò X f n+1 1 = 0 X f n 1 = 0 X 1 = 0 Û Ö f n f 0 = 0, f 1 = 1, f n+2 = f n+1 + f n X 1 = P n 2 (X f n+1 1) + P n 1 (X f n 1) Û Ö P n P 0 = 0,P 1 = 1,P n = X f n P n 1 + P n 2 P 1 = X f n+1 1 P 2 = X f n 1 C = [[1, X f n 1 ] P 3 = P 1 X f n 1 P 2 [0, 1, X f n 2 ], P 4 = P 2 X f n 2 P [0,...,0, 1, X f 2 ]] P n = P n 2 X f 2 P n 1 CR = [0,...,0, 1] X 1 = P n TEITP p.29
30 ÜØ Ò ÓÒ Coq P {P 1,..., P 2 } SLP Gb + TEITP p.30
31 ÜØ Ò ÓÒ P S A 1 A B C C 1 Q B 1 Record point := {x: R, y: R}. Definition collinear (A B C:point):= (A.x - B.x) * (C.y - B.y) - (A.y - B.y) * (C.x - B.x) = 0. Definition parallel (A B C D:point):= (A.x - B.x) * (C.y - D.y) = (A.y - B.y) * (C.x - D.x). R TEITP p.31
32 ÜØ Ò ÓÒ Ì Ñ ÓÒ µ Ë Þ Ö Ø Ö µ Ë Þ ÒÓ µ Ì ÓÖ Ñ ÓÑÔÙØ Ò Î Ö Ý Ò ÈÓÐÝÒÓÑ Ð ÖØ Ø ËÄÈ Ú ½ ½ ¾º ½ Ö Ù ¼º ¼º¼½ ½ ½½ Ù Ö ¼º ¼º ¾ ½ È ÔÔÙ ½º ¼º¾ ¾ ¾½ ½ ¼ ½ È Ð ½¾ ¾ ¾ ¼ ½ ¼ ÈØÓÐ ÑÝ ¾¼¼ ¾º ½ ½ ½ ½ ¾ Ë Ñ ÓÒ ¼º ¼º¾ ½ ½ ½¾ ½ Ì Ð ¼º¼ ¼º½ ¾¾ ½ ½ ¾ TEITP p.32
33 ÖÑ Ò Ò Ñ Ò Ö Ó Ö ÖÒ Ù ËÔ Û Å Ð Ä ÙÖ ÒØ Ì ÖÝ ³½¼µ Ò ÓÕ Û Ø ÁÑÔ Ö Ø Ú ØÙÖ Ò Ø ÜØ Ò Ò ØÓ Ë Ì Î Ö Ø ÓÒ ÔÔÐ Ø ÓÒ Ã ÐÐ Ö Ò Ò Ñ Ò Ï ÖÒ Ö ³½¼µ ÒØ Ð ÀÇÄ Ä Ø ÒØÓ ÓÕ ÁÑÔÓÖØ Ò ÅÓÖ ÜØ Ò ÓÒ TEITP p.33
34 ÜØ Ò ÓÒ Coq ÒØ ÒØ ÒØ ÒØ SAT TEITP p.34
35 ÅÓÖ ÜØ Ò ÓÒ p cnf p cnf TEITP p.35
36 Ê ÓÐÙØ ÓÒ ÅÓÖ ÜØ Ò ÓÒ x C x C C C TEITP p.36
37 ÅÓÖ ÜØ Ò ÓÒ ÈÖÓ Ð Ñ Î Ö Ð Ù Þ ÞÎ Ö Ý Ù Ó ¼ ½ ¼ ¼¼ ¼º¼¼ ¼º¼½ ÖÖ Ð ½ ¼ ¼º ¼ ¼º¼ ÖÖ Ð ¾ ¼ ½ ½º ¼º½ ÖÖ Ð ¾ ½ º¾¼ ¼º¾ Ô Ô ½ ¼¼ ¾º¾½ ¾º ÐÓÒ ÑÙÐؽ ½ ¾¾ ¼ ¼ º º ÓÐ ½½ ½ ¾ ½ º ¾ ¼º ¼ ÓÐ ½¾ ½ ½ º º ÓÐ ½ ½ ¾ ½½ ¼ º¾ æ TEITP p.37
38 ÅÓÖ ÜØ Ò ÓÒ ÈÖÓ Ð Ñ zverify Coq ÖØ ÌÝÔ Ò Ù Ó ¼ ¼º¼½ ¼º¼ ¼º¼¼ ¼º¼¾ ¼º¼¾ ÖÖ Ð ¼º¼ ¼º ¼º¼¼ ¼º ¾ ¼º½ ÖÖ Ð ¼º½ ½º½ ¼º¼ ¼º ¾ ¼º ÖÖ Ð ¼º¾ ½º ¼º½ ¼º ¼ ¼º Ô Ô ¾º ¾ º ¼º ½ º ¾ º ÐÓÒ ÑÙÐؽ º º º ¾ ¾ º¼ º ÓÐ ½½ ¼º ¼ ¼º ½ ¾º º½ ½º ÓÐ ½¾ º º¾ ¾º ½ º º ÓÐ ½ æ ½¼ º ¼ º½ º ¾º ¾ TEITP p.38
39 ÅÓÖ ÜØ Ò ÓÒ Coq DEF Hol TEITP p.39
40 ÅÓÖ ÜØ Ò ÓÒ ÆÙÑ Ö Ì Ñ Å ÑÓÖÝ Ò º Ì ÓÖ Ñ Ä ÑÑ Ê º ÜÔº ÓÑÔº Àº º º Î Öغ ÓÕ ËØ Ð ½ ¾ ½ ½ ¾ Ñ Ò ¼ Ñ Ò ¼ ½¼ ¾½ Å º ÅÓ Ð ¾ ½¾½ ¾¾ ¾ Ñ Ò ¼ ¾ Ñ Ò ¾ Å º Î ØÓÖ ¾ ¼ ¼ Ñ Ò ¼ ¾½ Ñ Ò ¾ Å º TEITP p.40
41 ÓÒÐÙ ÓÒ Ã Ý ÊÓÐ Ó ÖØ Ø Ö ÒÙÐ Ö ØÝ Ð Ö Ë Ô Ö Ø ÓÒ ÊÓÓÑ ÓÖ ÁÑÔÖÓÚ Ñ ÒØ TEITP p.41
ÇÙÐ Ò ½º ÅÙÐ ÔÐ ÔÓÐÝÐÓ Ö Ñ Ò Ú Ö Ð Ú Ö Ð ¾º Ä Ò Ö Ö Ù Ð Ý Ó ËÝÑ ÒÞ ÔÓÐÝÒÓÑ Ð º Ì ÛÓ¹ÐÓÓÔ ÙÒÖ Ö Ô Û Ö Ö ÖÝ Ñ ¹ ÝÓÒ ÑÙÐ ÔÐ ÔÓÐÝÐÓ Ö Ñ
ÅÙÐ ÔÐ ÔÓÐÝÐÓ Ö Ñ Ò ÝÒÑ Ò Ò Ö Ð Ö Ò Ó Ò Ö ÀÍ ÖÐ Òµ Ó Ò ÛÓÖ Û Ö Ò ÖÓÛÒ Ö Ú ½ ¼¾º ¾½ Û Åº Ä Ö Ö Ú ½ ¼¾º ¼¼ Û Äº Ñ Ò Ëº Ï ÒÞ ÖÐ Å ÒÞ ½ º¼ º¾¼½ ÇÙÐ Ò ½º ÅÙÐ ÔÐ ÔÓÐÝÐÓ Ö Ñ Ò Ú Ö Ð Ú Ö Ð ¾º Ä Ò Ö Ö Ù Ð Ý Ó ËÝÑ
More informationRadu Alexandru GHERGHESCU, Dorin POENARU and Walter GREINER
È Ö Ò Ò Ù Ò Ò Ò ÖÝ ÒÙÐ Ö Ý Ø Ñ Radu Alexandru GHERGHESCU, Dorin POENARU and Walter GREINER Radu.Gherghescu@nipne.ro IFIN-HH, Bucharest-Magurele, Romania and Frankfurt Institute for Advanced Studies, J
More informationF(jω) = a(jω p 1 )(jω p 2 ) Û Ö p i = b± b 2 4ac. ω c = Y X (jω) = 1. 6R 2 C 2 (jω) 2 +7RCjω+1. 1 (6jωRC+1)(jωRC+1) RC, 1. RC = p 1, p
ÓÖ Ò ÊÄ Ò Ò Û Ò Ò Ö Ý ½¾ Ù Ö ÓÖ ÖÓÑ Ö ÓÒ Ò ÄÈ ÐØ Ö ½¾ ½¾ ½» ½½ ÓÖ Ò ÊÄ Ò Ò Û Ò Ò Ö Ý ¾ Á b 2 < 4ac Û ÒÒÓØ ÓÖ Þ Û Ö Ð Ó ÒØ Ó Û Ð Ú ÕÙ Ö º ËÓÑ Ñ ÐÐ ÕÙ Ö Ö ÓÒ Ò º Ù Ö ÓÖ ½¾ ÓÖ Ù Ö ÕÙ Ö ÓÖ Ò ØÖ Ò Ö ÙÒØ ÓÒ
More information2 Hallén s integral equation for the thin wire dipole antenna
Ú Ð Ð ÓÒÐ Ò Ø ØØÔ»» Ѻ Ö Ùº º Ö ÁÒغ º ÁÒ Ù ØÖ Ð Å Ø Ñ Ø ÎÓк ÆÓº ¾ ¾¼½½µ ½ ¹½ ¾ ÆÙÑ Ö Ð Ñ Ø Ó ÓÖ Ò ÐÝ Ó Ö Ø ÓÒ ÖÓÑ Ø Ò Û Ö ÔÓÐ ÒØ ÒÒ Ëº À Ø ÑÞ ¹Î ÖÑ ÞÝ Ö Åº Æ Ö¹ÅÓ Êº Ë Þ ¹Ë Ò µ Ô ÖØÑ ÒØ Ó Ð ØÖ Ð Ò Ò
More informationPH Nuclear Physics Laboratory Gamma spectroscopy (NP3)
Physics Department Royal Holloway University of London PH2510 - Nuclear Physics Laboratory Gamma spectroscopy (NP3) 1 Objectives The aim of this experiment is to demonstrate how γ-ray energy spectra may
More informationProving observational equivalence with ProVerif
Proving observational equivalence with ProVerif Bruno Blanchet INRIA Paris-Rocquencourt Bruno.Blanchet@inria.fr based on joint work with Martín Abadi and Cédric Fournet and with Vincent Cheval June 2015
More informationLars Schmidt-Thieme, Information Systems and Machine Learning Lab (ISMLL), Institute BW/WI & Institute for Computer Science, University of Hildesheim
Course on Information Systems 2, summer term 2010 0/29 Information Systems 2 Information Systems 2 5. Business Process Modelling I: Models Lars Schmidt-Thieme Information Systems and Machine Learning Lab
More informationThis document has been prepared by Sunder Kidambi with the blessings of
Ö À Ö Ñ Ø Ò Ñ ÒØ Ñ Ý Ò Ñ À Ö Ñ Ò Ú º Ò Ì ÝÊ À Å Ú Ø Å Ê ý Ú ÒØ º ÝÊ Ú Ý Ê Ñ º Å º ² ºÅ ý ý ý ý Ö Ð º Ñ ÒÜ Æ Å Ò Ñ Ú «Ä À ý ý This document has been prepared by Sunder Kidambi with the blessings of Ö º
More informationx 0, x 1,...,x n f(x) p n (x) = f[x 0, x 1,..., x n, x]w n (x),
ÛÜØ Þ ÜÒ Ô ÚÜ Ô Ü Ñ Ü Ô Ð Ñ Ü ÜØ º½ ÞÜ Ò f Ø ÚÜ ÚÛÔ Ø Ü Ö ºÞ ÜÒ Ô ÚÜ Ô Ð Ü Ð Þ Õ Ô ÞØÔ ÛÜØ Ü ÚÛÔ Ø Ü Ö L(f) = f(x)dx ÚÜ Ô Ü ÜØ Þ Ü Ô, b] Ö Û Þ Ü Ô Ñ ÒÖØ k Ü f Ñ Df(x) = f (x) ÐÖ D Ü Ü ÜØ Þ Ü Ô Ñ Ü ÜØ Ñ
More informationParts 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 informationLecture 16: Modern Classification (I) - Separating Hyperplanes
Lecture 16: Modern Classification (I) - Separating Hyperplanes Outline 1 2 Separating Hyperplane Binary SVM for Separable Case Bayes Rule for Binary Problems Consider the simplest case: two classes are
More informationAn Example file... log.txt
# ' ' Start of fie & %$ " 1 - : 5? ;., B - ( * * B - ( * * F I / 0. )- +, * ( ) 8 8 7 /. 6 )- +, 5 5 3 2( 7 7 +, 6 6 9( 3 5( ) 7-0 +, => - +< ( ) )- +, 7 / +, 5 9 (. 6 )- 0 * D>. C )- +, (A :, C 0 )- +,
More informationÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ÁÒÜ ½ ÁÒØÖÓÙØÓÒ ¾ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ
ÁÒØÖÓÙØÓÒ ÈÖÓÐÑ ØØÑÒØ ÓÚÖÒ¹ ÐØÖ Ò ËÑÙÐØÓÒ Ê ÙÐØ ÓÒÐÙ ÓÒ ÙÑÔ ÐØÖ ÓÖ ÙÒÖØÒ ÝÒÑ Ý ØÑ ÛØ ÖÓÔÓÙØ º ÓÐÞ ½ º º ÉÙÚÓ ¾ Áº ÈÖÖÓ ½ ʺ ËÒ ½ ½ ÔÖØÑÒØ Ó ÁÒÙ ØÖÐ ËÝ ØÑ ÒÒÖÒ Ò Ò ÍÒÚÖ ØØ ÂÙÑ Á ØÐÐ ËÔÒ ¾ ËÓÓÐ Ó ÐØÖÐ ÒÒÖÒ
More informationLecture 11: Regression Methods I (Linear Regression)
Lecture 11: Regression Methods I (Linear Regression) 1 / 43 Outline 1 Regression: Supervised Learning with Continuous Responses 2 Linear Models and Multiple Linear Regression Ordinary Least Squares Statistical
More informationµ(, y) Computing the Möbius fun tion µ(x, x) = 1 The Möbius fun tion is de ned b y and X µ(x, t) = 0 x < y if x6t6y 3
ÈÖÑÙØØÓÒ ÔØØÖÒ Ò Ø ÅÙ ÙÒØÓÒ ÙÖ ØÒ ÎØ ÂÐÒ Ú ÂÐÒÓÚ Ò ÐÜ ËØÒÖÑ ÓÒ ÒÖ Ì ØÛÓµ 2314 ½¾ ½ ¾ ¾½ ¾ ½ ½¾ ¾½ ½¾ ¾½ ½ Ì ÔÓ Ø Ó ÔÖÑÙØØÓÒ ÛºÖºØº ÔØØÖÒ ÓÒØÒÑÒØ ½ 2314 ½¾ ½ ¾ ¾½ ¾ ½ ½¾ ¾½ ½¾ ¾½ Ì ÒØÖÚÐ [12,2314] ½ ¾ ÓÑÔÙØÒ
More informationLecture 11: Regression Methods I (Linear Regression)
Lecture 11: Regression Methods I (Linear Regression) Fall, 2017 1 / 40 Outline Linear Model Introduction 1 Regression: Supervised Learning with Continuous Responses 2 Linear Models and Multiple Linear
More informationArbeitstagung: Gruppen und Topologische Gruppen Vienna July 6 July 7, Abstracts
Arbeitstagung: Gruppen und Topologische Gruppen Vienna July 6 July 7, 202 Abstracts ÁÒÚ Ö Ð Ñ Ø Ó Ø¹Ú ÐÙ ÙÒØ ÓÒ ÁÞØÓ Ò ÞØÓ º Ò ÙÒ ¹Ñ º ÙÐØÝ Ó Æ ØÙÖ Ð Ë Ò Ò Å Ø Ñ Ø ÍÒ Ú Ö ØÝ Ó Å Ö ÓÖ ÃÓÖÓ ½ ¼ Å Ö ÓÖ ¾¼¼¼
More informationSME 3023 Applied Numerical Methods
UNIVERSITI TEKNOLOGI MALAYSIA SME 3023 Applied Numerical Methods Ordinary Differential Equations Abu Hasan Abdullah Faculty of Mechanical Engineering Sept 2012 Abu Hasan Abdullah (FME) SME 3023 Applied
More informationProblem 1 (From the reservoir to the grid)
ÈÖÓ º ĺ ÙÞÞ ÐÐ ÈÖÓ º ʺ ³ Ò Ö ½ ½¹¼ ¹¼¼ ËÝ Ø Ñ ÅÓ Ð Ò ÀË ¾¼½ µ Ü Ö ËÓÐÙØ ÓÒ ÌÓÔ ÀÝ ÖÓ Ð ØÖ ÔÓÛ Ö ÔÐ ÒØ À Èȵ ¹ È ÖØ ÁÁ Ð ÖÒ Ø Þº ÇØÓ Ö ¾ ¾¼½ Problem 1 (From the reservoir to the grid) The causality diagram
More informationProblem 1 (From the reservoir to the grid)
ÈÖÓ º ĺ ÙÞÞ ÐÐ ÈÖÓ º ʺ ³ Ò Ö ½ ½¹¼ ¼¹¼¼ ËÝ Ø Ñ ÅÓ Ð Ò ÀË ¾¼½ µ Ü Ö ÌÓÔ ÀÝ ÖÓ Ð ØÖ ÔÓÛ Ö ÔÐ ÒØ À Èȵ ¹ È ÖØ ÁÁ Ð ÖÒ Ø Þº ÇØÓ Ö ½ ¾¼½ Problem (From the reservoir to the grid) The causality diagram of the
More informationSKMM 3023 Applied Numerical Methods
UNIVERSITI TEKNOLOGI MALAYSIA SKMM 3023 Applied Numerical Methods Ordinary Differential Equations ibn Abdullah Faculty of Mechanical Engineering Òº ÙÐÐ ÚºÒÙÐÐ ¾¼½ SKMM 3023 Applied Numerical Methods Ordinary
More informationLund Institute of Technology Centre for Mathematical Sciences Mathematical Statistics
Lund Institute of Technology Centre for Mathematical Sciences Mathematical Statistics STATISTICAL METHODS FOR SAFETY ANALYSIS FMS065 ÓÑÔÙØ Ö Ü Ö Ì ÓÓØ ØÖ Ô Ð ÓÖ Ø Ñ Ò Ý Ò Ò ÐÝ In this exercise we will
More information! " # $! % & '! , ) ( + - (. ) ( ) * + / 0 1 2 3 0 / 4 5 / 6 0 ; 8 7 < = 7 > 8 7 8 9 : Œ Š ž P P h ˆ Š ˆ Œ ˆ Š ˆ Ž Ž Ý Ü Ý Ü Ý Ž Ý ê ç è ± ¹ ¼ ¹ ä ± ¹ w ç ¹ è ¼ è Œ ¹ ± ¹ è ¹ è ä ç w ¹ ã ¼ ¹ ä ¹ ¼ ¹ ±
More informationFramework for functional tree simulation applied to 'golden delicious' apple trees
Purdue University Purdue e-pubs Open Access Theses Theses and Dissertations Spring 2015 Framework for functional tree simulation applied to 'golden delicious' apple trees Marek Fiser Purdue University
More information519.8 ýý ½ ¹¼½¹¾¼¼ ¼º üº üº þ üº º Á ¹ ÇÊž¼½ µ ¾¾ ¾ ¾¼½ º º Á» º º üº üº þ üº º º º ü ¾¼½ º º ÁË Æ þ Á ¹ º ¹ º ºþº ¹ ú û ü ü µ ¹ µ ¹ ü ü µ ¹ µ
þ ü þ þ º þº þü ü þü ú ü ü üþ û ü ü ü þ ¹ ý üþ ü ý þ þü ü ü ý þ þü ü Á ÇÊž¼½ µ ¾¾ ¾ ¾¼½ Á Á ÅÓ ÓÛ ÁÒØ ÖÒ Ø ÓÒ Ð ÓÒ Ö Ò ÓÒ ÇÔ Ö Ø ÓÒ Ê Ö ÇÊž¼½ µ ÅÓ ÓÛ ÇØÓ Ö ¾¾¹¾ ¾¼½ ÈÊÇ ÁÆ Ë ÎÇÄÍÅ Á þü ¾¼½ 519.8 ýý 22.18
More informationSKMM 3023 Applied Numerical Methods
SKMM 3023 Applied Numerical Methods Solution of Nonlinear Equations ibn Abdullah Faculty of Mechanical Engineering Òº ÙÐÐ ÚºÒÙÐÐ ¾¼½ SKMM 3023 Applied Numerical Methods Solution of Nonlinear Equations
More informationSME 3023 Applied Numerical Methods
UNIVERSITI TEKNOLOGI MALAYSIA SME 3023 Applied Numerical Methods Solution of Nonlinear Equations Abu Hasan Abdullah Faculty of Mechanical Engineering Sept 2012 Abu Hasan Abdullah (FME) SME 3023 Applied
More informationÆÓÒ¹ÒØÖÐ ËÒÐØ ÓÙÒÖÝ
ÁÒØÖÐ ÓÙÒÖ Ò Ë»Ì Î ÊÐ ÔÖØÑÒØ Ó ÅØÑØ ÍÒÚÖ ØÝ Ó ÓÖ Á̳½½ ØÝ ÍÒÚÖ ØÝ ÄÓÒÓÒ ÔÖÐ ½ ¾¼½½ ÆÓÒ¹ÒØÖÐ ËÒÐØ ÓÙÒÖÝ ÇÙØÐÒ ËÙÔÖ ØÖÒ Ò Ë»Ì Ì ØÙÔ ÏÓÖÐ Ø Ë¹ÑØÖÜ ÍÒÖÐÝÒ ÝÑÑØÖ ÁÒØÖÐ ÓÙÒÖ ÁÒØÖÐØÝ Ø Ø ÓÙÒÖÝ» ÖÒ Ò ØÛ Ø ÒÒ Ú»Ú
More informationLecture 10, Principal Component Analysis
Principal Cmpnent Analysis Lecture 10, Principal Cmpnent Analysis Ha Helen Zhang Fall 2017 Ha Helen Zhang Lecture 10, Principal Cmpnent Analysis 1 / 16 Principal Cmpnent Analysis Lecture 10, Principal
More information½ ÅÝ Ò ØØÙØÓÒ ¾ ÁÒØÖÓÙØÓÒ ÓÒ ØØÙØÚ ÑÓÐÐÒ ÆÙÑÖÐ ÑÔÐÑÒØØÓÒ ÓÒÐÙ ÓÒ Ò ÔÖ ÔØÚ ¾»¾
ÓÖ ÁÒ ØØÙØ Ó ÌÒÓÐÓÝ ¹ ÇØÓÖ Ø ¾¼½¾ ÓÒ ØØÙØÚ ÑÓÐ ÓÙÔÐÒ Ñ Ò ÔÐ ØØÝ ÓÖ ÙÒ ØÙÖØ ÓÑØÖÐ ËÓÐÒÒ Ä ÈÆË È ËÙÔÖÚ ÓÖ Ñ ÈÇÍ ÖÓÙÞ ÌÅÁÊÁ ½ ÅÝ Ò ØØÙØÓÒ ¾ ÁÒØÖÓÙØÓÒ ÓÒ ØØÙØÚ ÑÓÐÐÒ ÆÙÑÖÐ ÑÔÐÑÒØØÓÒ ÓÒÐÙ ÓÒ Ò ÔÖ ÔØÚ ¾»¾ ½
More informationALLEN. Pre Nurture & Career Foundation Division For Class 6th to 10th, NTSE & Olympiads. å 7 3 REGIONAL MATHEMATICAL OLYMPIAD-2017 SOLUTION
For Class 6th to 0th, NTSE & Olympiads REGIONAL MATHEMATICAL OLYMPIAD-07. Let AOB be a given angle less than 80 and let P be an interior point of the angular region determined by ÐAOB. Show, with proof,
More informationOH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9
OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at
More informationF(q 2 ) = 1 Q Q = d 3 re i q r ρ(r) d 3 rρ(r),
ÁÒØÖÓÙØÓÒ ÖÐ ÕÙÖ ÑÓÐ Ê ÙÐØ ËÙÑÑÖÝ ÌÖÒ ÚÖ ØÝ ØÖÙØÙÖ Ó Ø ÔÓÒ Ò ÖÐ ÕÙÖ ÑÓÐ ÏÓ ÖÓÒÓÛ ÂÒ ÃÓÒÓÛ ÍÒÚÖ ØÝ ÃÐ ÁÒ ØØÙØ Ó ÆÙÐÖ ÈÝ ÈÆ ÖÓÛ ÛØ º ÊÙÞ ÖÖÓÐ Ò º º ÓÖÓÓÚ ÅÒ¹ÏÓÖ ÓÔ Ð ¾¼½½ ÍÒÖ ØÒÒ ÀÖÓÒ ËÔØÖ Ð ËÐÓÚÒµ ¹½¼ ÂÙÐÝ
More information«Û +(2 )Û, the total charge of the EH-pair is at most «Û +(2 )Û +(1+ )Û ¼, and thus the charging ratio is at most
ÁÑÔÖÓÚ ÇÒÐÒ ÐÓÖØÑ ÓÖ Ù«Ö ÅÒÑÒØ Ò ÉÓË ËÛØ ÅÖ ÖÓ ÏÓ ÂÛÓÖ ÂÖ ËÐÐ Ý ÌÓÑ ÌÝ Ý ØÖØ We consider the following buffer management problem arising in QoS networks: packets with specified weights and deadlines arrive
More informationTHE 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 informationF O R SOCI AL WORK RESE ARCH
7 TH EUROPE AN CONFERENCE F O R SOCI AL WORK RESE ARCH C h a l l e n g e s i n s o c i a l w o r k r e s e a r c h c o n f l i c t s, b a r r i e r s a n d p o s s i b i l i t i e s i n r e l a t i o n
More informationT h e C S E T I P r o j e c t
T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T
More informationu x + u y = x u . u(x, 0) = e x2 The characteristics satisfy dx dt = 1, dy dt = 1
Õ 83-25 Þ ÛÐ Þ Ð ÚÔÜØ Þ ÝÒ Þ Ô ÜÞØ ¹ 3 Ñ Ð ÜÞ u x + u y = x u u(x, 0) = e x2 ÝÒ Þ Ü ÞØ º½ dt =, dt = x = t + c, y = t + c 2 We can choose c to be zero without loss of generality Note that each characteristic
More informationMulti-electron and multi-channel effects on Harmonic Generation
Multi-electron and multi-channel effects on Harmonic Generation Contact abrown41@qub.ac.uk A.C. Brown and H.W. van der Hart Centre for Theoretical Atomic, Molecular and Optical Physics, Queen s University
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 informationpage 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$%! & (, -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 informationh : 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 information18.06 Quiz 2 April 7, 2010 Professor Strang
8.06 Quiz 2 April 7, 200 Professor Strang Your PRINTED name is:. Your recitation number or instructor is 2. 3.. (33 points) (a) Find the matrix P that projects every vector b in R 3 onto the line in the
More informationI118 Graphs and Automata
I8 Graphs and Automata Takako Nemoto http://www.jaist.ac.jp/ t-nemoto/teaching/203--.html April 23 0. Û. Û ÒÈÓ 2. Ø ÈÌ (a) ÏÛ Í (b) Ø Ó Ë (c) ÒÑ ÈÌ (d) ÒÌ (e) É Ö ÈÌ 3. ÈÌ (a) Î ÎÖ Í (b) ÒÌ . Û Ñ ÐÒ f
More informationPeriodic monopoles and difference modules
Periodic monopoles and difference modules Takuro Mochizuki RIMS, Kyoto University 2018 February Introduction In complex geometry it is interesting to obtain a correspondence between objects in differential
More informationMATH 6101 Fall 2008 Newton and Differential Equations
MATH 611 Fall 8 Newto ad Differetial Equatios A Differetial Equatio What is a differetial equatio? A differetial equatio is a equatio relatig the quatities x, y ad y' ad possibly higher derivatives of
More informationP 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 informationVectors. Teaching Learning Point. Ç, where OP. l m n
Vectors 9 Teaching Learning Point l A quantity that has magnitude as well as direction is called is called a vector. l A directed line segment represents a vector and is denoted y AB Å or a Æ. l Position
More informationSubspace angles and distances between ARMA models
ÔÖØÑÒØ ÐØÖÓØÒ Ë̹ËÁËÌ»ÌÊ ß ËÙ Ô ÒÐ Ò ØÒ ØÛÒ ÊÅ ÑÓÐ ÃØÖÒ Ó Ò ÖØ ÅÓÓÖ ÅÖ ÈÙÐ Ò ÈÖÓÒ Ó Ø ÓÙÖØÒØ ÁÒØÖÒØÓÒÐ ËÝÑÔÓ ÙÑ Ó ÅØÑØÐ ÌÓÖÝ Ó ÆØÛÓÖ Ò ËÝ ØÑ ÅÌÆË µ ÈÖÔÒÒ ÖÒ ÂÙÒ ß Ì ÖÔÓÖØ ÚÐÐ Ý ÒÓÒÝÑÓÙ ØÔ ÖÓÑ ØÔº غÙÐÙÚÒºº
More informationQUESTIONS ON QUARKONIUM PRODUCTION IN NUCLEAR COLLISIONS
International Workshop Quarkonium Working Group QUESTIONS ON QUARKONIUM PRODUCTION IN NUCLEAR COLLISIONS ALBERTO POLLERI TU München and ECT* Trento CERN - November 2002 Outline What do we know for sure?
More informationFront-end. Organization of a Modern Compiler. Middle1. Middle2. Back-end. converted to control flow) Representation
register allocation instruction selection Code Low-level intermediate Representation Back-end Assembly array references converted into low level operations, loops converted to control flow Middle2 Low-level
More informationStochastic invariances and Lamperti transformations for Stochastic Processes
Stochastic invariances and Lamperti transformations for Stochastic Processes Pierre Borgnat, Pierre-Olivier Amblard, Patrick Flandrin To cite this version: Pierre Borgnat, Pierre-Olivier Amblard, Patrick
More informationLoop parallelization using compiler analysis
Loop parallelization using compiler analysis Which of these loops is parallel? How can we determine this automatically using compiler analysis? Organization of a Modern Compiler Source Program Front-end
More information0# E % D 0 D - C AB
5-70,- 393 %& 44 03& / / %0& / / 405 4 90//7-90/8/3 ) /7 0% 0 - @AB 5? 07 5 >0< 98 % =< < ; 98 07 &? % B % - G %0A 0@ % F0 % 08 403 08 M3 @ K0 J? F0 4< - G @ I 0 QR 4 @ 8 >5 5 % 08 OF0 80P 0O 0N 0@ 80SP
More informationApplication of ICA and PCA to extracting structure from stock return
2014 3 Å 28 1 Ð Mar. 2014 Communication on Applied Mathematics and Computation Vol.28 No.1 DOI 10.3969/j.issn.1006-6330.2014.01.012 Ç ÖÇ Ú ¾Ä Î Þ Ý ( 200433) Ç È ß ³ Õº º ÅÂÞÐÆÈÛ CAC40 Õ Û ËÛ ¾ ÆÄ (ICA)
More informationLA PRISE DE CALAIS. çoys, çoys, har - dis. çoys, dis. tons, mantz, tons, Gas. c est. à ce. C est à ce. coup, c est à ce
> ƒ? @ Z [ \ _ ' µ `. l 1 2 3 z Æ Ñ 6 = Ð l sl (~131 1606) rn % & +, l r s s, r 7 nr ss r r s s s, r s, r! " # $ s s ( ) r * s, / 0 s, r 4 r r 9;: < 10 r mnz, rz, r ns, 1 s ; j;k ns, q r s { } ~ l r mnz,
More informationOC330C. Wiring Diagram. Recommended PKH- P35 / P50 GALH PKA- RP35 / RP50. Remarks (Drawing No.) No. Parts No. Parts Name Specifications
G G " # $ % & " ' ( ) $ * " # $ % & " ( + ) $ * " # C % " ' ( ) $ * C " # C % " ( + ) $ * C D ; E @ F @ 9 = H I J ; @ = : @ A > B ; : K 9 L 9 M N O D K P D N O Q P D R S > T ; U V > = : W X Y J > E ; Z
More informationJournal of Singularities
Journal of Singularities Volume 12 2015 Singularities in Geometry and Applications III, 2-6 September 2013, Edinburgh, Scotland Editors: Jean-Paul Brasselet, Peter Giblin, Victor Goryunov ISSN: # 1949-2006
More informationFinal exam: Automatic Control II (Reglerteknik II, 1TT495)
Uppsala University Department of Information Technology Systems and Control Professor Torsten Söderström Final exam: Automatic Control II (Reglerteknik II, TT495) Date: October 22, 2 Responsible examiner:
More informationMulti-agent learning
Multi-agent learning Ê Ò ÓÖ Ñ ÒØ Ä ÖÒ Ò Gerard Vreeswijk, Intelligent Systems Group, Computer Science Department, Faculty of Sciences, Utrecht University, The Netherlands. Gerard Vreeswijk. Last modified
More informationTurbulence and Aeroacoustics Research Team of the Centre Acoustique Laboratoire des Fluides et d Acoustique UMR CNRS 5509, Ecole Centrale de Lyon MUSAF II Colloquium Toulouse, September 2013 Ö Ø ÓÑÔÙØ
More informationLecture 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 informationPersonalizing Declarative Repairing Policies for Curated KBs. Ioannis Roussakis Master s Thesis Computer Science Department, University of Crete
ÍÒ Ú Ö ØÝ Ó Ö Ø ÓÑÔÙØ Ö Ë Ò Ô ÖØÑ ÒØ È Ö ÓÒ Ð Þ Ò Ð Ö Ø Ú Ê Ô Ö Ò ÈÓÐ ÓÖ ÙÖ Ø Ã ÁÓ ÒÒ ÊÓÙ Å Ø Ö³ Ì À Ö Ð ÓÒ Ñ Ö ¾¼½¼ È Æ ÈÁËÌÀÅÁÇ ÃÊÀÌÀË ËÉÇÄÀ Â ÌÁÃÏÆ Ã Á Ì ÉÆÇÄÇ ÁÃÏÆ ÈÁËÌÀÅÏÆ ÌÅÀÅ ÈÁËÌÀÅÀË ÍÈÇÄÇ ÁËÌÏÆ
More informationGreen s function, wavefunction and Wigner function of the MIC-Kepler problem
Green s function, wavefunction and Wigner function of the MIC-Kepler problem Tokyo University of Science Graduate School of Science, Department of Mathematics, The Akira Yoshioka Laboratory Tomoyo Kanazawa
More information176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s
A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps
More informationExecutive Committee and Officers ( )
Gifted and Talented International V o l u m e 2 4, N u m b e r 2, D e c e m b e r, 2 0 0 9. G i f t e d a n d T a l e n t e d I n t e r n a t i o n a2 l 4 ( 2), D e c e m b e r, 2 0 0 9. 1 T h e W o r
More informationDifferentiating Functions & Expressions - Edexcel Past Exam Questions
- Edecel Past Eam Questions. (a) Differentiate with respect to (i) sin + sec, (ii) { + ln ()}. 5-0 + 9 Given that y =, ¹, ( -) 8 (b) show that = ( -). (6) June 05 Q. f() = e ln, > 0. (a) Differentiate
More informationCalculating β Decay for the r Process
Calculating β Decay for the r Process J. Engel with M. Mustonen, T. Shafer C. Fröhlich, G. McLaughlin, M. Mumpower, R. Surman D. Gambacurta, M. Grasso January 8, 7 R-Process Abundances Nuclear Landscape
More informationOutline. Calorimeters. E.Chudakov 1. 1 Hall A, JLab. JLab Summer Detector/Computer Lectures http: // gen/talks/calor lect.
Outline Calorimeters E.Chudakov 1 1 Hall A, JLab JLab Summer Detector/Computer Lectures http: //www.jlab.org/ gen/talks/calor lect.pdf Outline Outline 1 Introduction 2 Physics of Showers 3 Calorimeters
More informationRadiative Electroweak Symmetry Breaking with Neutrino Effects in Supersymmetric SO(10) Unifications
KEKPH06 p.1/17 Radiative Electroweak Symmetry Breaking with Neutrino Effects in Supersymmetric SO(10) Unifications Kentaro Kojima Based on the work with Kenzo Inoue and Koichi Yoshioka (Department of Physics,
More information! -., THIS PAGE DECLASSIFIED IAW EQ t Fr ra _ ce, _., I B T 1CC33ti3HI QI L '14 D? 0. l d! .; ' D. o.. r l y. - - PR Pi B nt 8, HZ5 0 QL
H PAGE DECAFED AW E0 2958 UAF HORCA UD & D m \ Z c PREMNAR D FGHER BOMBER ARC o v N C o m p R C DECEMBER 956 PREPARED B HE UAF HORCA DVO N HRO UGH HE COOPERAON O F HE HORCA DVON HEADQUARER UAREUR DEPARMEN
More informationVisit our WWW site:
For copies of this Booklet and of the full Review to be sent to addresses in the Americas, Australasia, or the Far East, visit http://pdg.lbl.gov/pdgmail or write to Particle Data Group MS 50R6008 Lawrence
More informationChebyshev Spectral Methods and the Lane-Emden Problem
Numer. Math. Theor. Meth. Appl. Vol. 4, No. 2, pp. 142-157 doi: 10.4208/nmtma.2011.42s.2 May 2011 Chebyshev Spectral Methods and the Lane-Emden Problem John P. Boyd Department of Atmospheric, Oceanic and
More informationx 9 or x > 10 Name: Class: Date: 1 How many natural numbers are between 1.5 and 4.5 on the number line?
1 How many natural numbers are between 1.5 and 4.5 on the number line? 2 How many composite numbers are between 7 and 13 on the number line? 3 How many prime numbers are between 7 and 20 on the number
More informationA Language for Task Orchestration and its Semantic Properties
DEPARTMENT OF COMPUTER SCIENCES A Language for Task Orchestration and its Semantic Properties David Kitchin, William Cook and Jayadev Misra Department of Computer Science University of Texas at Austin
More informationOverview in Images. 5 nm
Overview in Images 5 nm K.S. Min et al. PhD Thesis K.V. Vahala et al, Phys. Rev. Lett, 85, p.74 (000) J. D. Joannopoulos, et al, Nature, vol.386, p.143-9 (1997) S. Lin et al, Nature, vol. 394, p. 51-3,
More informationSection 3.1 Homework Solutions. 1. y = 5, so dy dx = y = 3x, so dy dx = y = x 12, so dy. dx = 12x11. dx = 12x 13
Math 122 1. y = 5, so dx = 0 2. y = 3x, so dx = 3 3. y = x 12, so dx = 12x11 4. y = x 12, so dx = 12x 13 5. y = x 4/3, so dx = 4 3 x1/3 6. y = 8t 3, so = 24t2 7. y = 3t 4 2t 2, so = 12t3 4t 8. y = 5x +
More informationExamination paper for TFY4240 Electromagnetic theory
Department of Physics Examination paper for TFY4240 Electromagnetic theory Academic contact during examination: Associate Professor John Ove Fjærestad Phone: 97 94 00 36 Examination date: 16 December 2015
More informationComputer Algebra in Coq using reflection
, 2 Computer Algebra in using reflection INRIA, team Marelle and Éducation Nationale 26-07-2012 Automatization in proof assistants, 2 From Computer Algebra Systems to Proof Assistants : certified computations.
More information" #$ P UTS W U X [ZY \ Z _ `a \ dfe ih j mlk n p q sr t u s q e ps s t x q s y i_z { U U z W } y ~ y x t i e l US T { d ƒ ƒ ƒ j s q e uˆ ps i ˆ p q y
" #$ +. 0. + 4 6 4 : + 4 ; 6 4 < = =@ = = =@ = =@ " #$ P UTS W U X [ZY \ Z _ `a \ dfe ih j mlk n p q sr t u s q e ps s t x q s y i_z { U U z W } y ~ y x t i e l US T { d ƒ ƒ ƒ j s q e uˆ ps i ˆ p q y h
More informationDynamics and Bifurcations in Predator-Prey Models with Refuge, Dispersal and Threshold Harvesting
Dynamics and Bifurcations in Predator-Prey Models with Refuge, Dispersal and Threshold Harvesting August 2012 Overview Last Model ẋ = αx(1 x) a(1 m)xy 1+c(1 m)x H(x) ẏ = dy + b(1 m)xy 1+c(1 m)x (1) where
More informationNon-Stationary Spatial Modeling
BAYESIAN STATISTICS 6, pp. 000 000 J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith (Eds.) Oxford University Press, 1998 Non-Stationary Spatial Modeling D. HIGDON, J. SWALL, and J. KERN Duke
More informationThe University of Bath School of Management is one of the oldest established management schools in Britain. It enjoys an international reputation for
The University of Bath School of Management is one of the oldest established management schools in Britain. It enjoys an international reputation for the quality of its teaching and research. Its mission
More informationJEE-ADVANCED MATHEMATICS. Paper-1. SECTION 1: (One or More Options Correct Type)
JEE-ADVANCED MATHEMATICS Paper- SECTION : (One or More Options Correct Type) This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR
More informationPlanning 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 informationA L A BA M A L A W R E V IE W
A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N
More informationApplications of Discrete Mathematics to the Analysis of Algorithms
Applications of Discrete Mathematics to the Analysis of Algorithms Conrado Martínez Univ. Politècnica de Catalunya, Spain May 2007 Goal Given some algorithm taking inputs from some set Á, we would like
More informationOn the Stability and Accuracy of the BGK, MRT and RLB Boltzmann Schemes for the Simulation of Turbulent Flows
Commun. Comput. Phys. doi: 10.4208/cicp.OA-2016-0229 Vol. 23, No. 3, pp. 846-876 March 2018 On the Stability and Accuracy of the BGK, MRT and RLB Boltzmann Schemes for the Simulation of Turbulent Flows
More informationIn this section, mathematical description of the motion of fluid elements moving in a flow field is
Jun. 05, 015 Chapter 6. Differential Analysis of Fluid Flow 6.1 Fluid Element Kinematics In this section, mathematical description of the motion of fluid elements moving in a flow field is given. A small
More informationStandard Model or New Physics?
Σ + pµ + µ Standard Model or New Physics? Jusak Tandean National Taiwan University in collaboration with XG He & G Valencia High Energy Physics Seminar National Tsing Hua University 25 September 2008 Outline
More informationJuan Juan Salon. EH National Bank. Sandwich Shop Nail Design. OSKA Beverly. Chase Bank. Marina Rinaldi. Orogold. Mariposa.
( ) X é X é Q Ó / 8 ( ) Q / ( ) ( ) : ( ) : 44-3-8999 433 4 z 78-19 941, #115 Z 385-194 77-51 76-51 74-7777, 75-5 47-55 74-8141 74-5115 78-3344 73-3 14 81-4 86-784 78-33 551-888 j 48-4 61-35 z/ zz / 138
More informationDifferential Equations Class Notes
Differential Equations Class Notes Dan Wysocki Spring 213 Contents 1 Introduction 2 2 Classification of Differential Equations 6 2.1 Linear vs. Non-Linear.................................. 7 2.2 Seperable
More informationLecture 2. Distributions and Random Variables
Lecture 2. Distributions and Random Variables Igor Rychlik Chalmers Department of Mathematical Sciences Probability, Statistics and Risk, MVE300 Chalmers March 2013. Click on red text for extra material.
More informationFactors and processes controlling climate variations at different time scales: supporting documents
Factors and processes controlling climate variations at different time scales: supporting documents Camille Risi LMD/IPSL/CNRS 3 july 2012 Outline Goals understand factors and processes controlling climate
More informationP a g e 3 6 of R e p o r t P B 4 / 0 9
P a g e 3 6 of R e p o r t P B 4 / 0 9 p r o t e c t h um a n h e a l t h a n d p r o p e r t y fr om t h e d a n g e rs i n h e r e n t i n m i n i n g o p e r a t i o n s s u c h a s a q u a r r y. J
More information:,,.. ;,..,.,. 90 :.. :, , «-»,, -. : -,,, -, -., ,, -, -. - «-»:,,, ,.,.
.,.,. 2015 1 614.8 68.9 90 :,,.. ;,. 90.,.,. :.. :, 2015. 164. - - 280700, «-»,, -. : -,,, -, -.,. -. -. -,, -, -. - «-»:,,, -. 614.8 68.9.,.,., 2015, 2015 2 ... 5... 7 1.... 7 1.1.... 7 1.2.... 9 1.3....
More informationHousing Market Monitor
M O O D Y È S A N A L Y T I C S H o u s i n g M a r k e t M o n i t o r I N C O R P O R A T I N G D A T A A S O F N O V E M B E R İ Ī Ĭ Ĭ E x e c u t i v e S u m m a r y E x e c u t i v e S u m m a r y
More informationSurface Modification of Nano-Hydroxyapatite with Silane Agent
ß 23 ß 1 «Ã Vol. 23, No. 1 2008 Ç 1 Journal of Inorganic Materials Jan., 2008» : 1000-324X(2008)01-0145-05 Þ¹ Ò À Đ³ Ù Å Ð (ÎÄÅ Ç ÂÍ ËÊÌÏÁÉ È ÃÆ 610064) Ì É (KH-560) ¼ ³ (n-ha) ³ ËØ ÌË n-ha KH-560 Õ Ì»Þ
More informationSynopsis of Numerical Linear Algebra
Synopsis of Numerical Linear Algebra Eric de Sturler Department of Mathematics, Virginia Tech sturler@vt.edu http://www.math.vt.edu/people/sturler Iterative Methods for Linear Systems: Basics to Research
More information