untitled
|
|
|
- おさむ はなだて
- 5 years ago
- Views:
Transcription
1 1
2 2
3 HUMAN( Socrates ) HUMAN( x) MORTAL( x) σ = { x Socrates} HUMAN( Socrates) MORTAL( Socrates) MORTAL(Socrates) x x x Socrates HUMAN(Socrates) HUMAN(Socrates) MORTAL(Socrates) x Socrates HUMAN(Socrates) HUMAN(x) x Socrates 3
4 σ = { x s, x s,, x s } n n x i ( i = 1,2,, n) s i σ = { xa, y gz ( )} x a y g(z) (substitution) 4
5 σ () t t σ = { xa, y gz ( )} t = g( x, f ( c, x, y), z) x a y g(z) σ ( t) = g( a, f( c, a, g( z)), z) ( ) 5
6 T T : T T σ = { xa, y gz ( )} σ ( f ( x, y) ) = f( a, g( z)) σ σ 1 2 ( σ σ )( t) = σ ( σ ( t)) ( ) ( ) 6
7 σ = { x y} g( x, y) g( y, y) τ = { yb} σ = τ σ = g( b, b) { xb, yb} (more general) σ = τ σ g(x,y) g(y,y) g(b,b) g(b,b) g(x,y) (more general) less general more specific 7
8 s, t σ σ( s) = σ( t) σ s, t (unifier) s, t (unifiable) (most general unifier: mgu) ( ) (more general) (most general) (most general unifier) mgu mgu mgu f(x) f(y) mgu {x/y} {y/x} 8
9 f( x, g( x )) f( h( y), z) σ = { xhy ( ), zghy ( ( ))} f( h( y), g( h( y))) σ = { xha ( ), ya, zgha ( ( ))} f ( ha ( ), gha ( ( ))) τ = { y a} mgu f(h(a),g(h(a))) f(h(y),g(h(y))) ={y/a} 9
10 f ( x, g( x)) = f ( h( y), z) x= h( y) σ = z = g( h( y)) mgu mgu 10
11 Step1. { s= t} f ( s1,, sn) = f ( t1,, tn) s 1 = t 1,, sn = tn f ( s1,, sn) = g( t1,, tm) ( f g; n, m 0) t x = x x = t = x x f(x) x = t t x x t x = t x t x { x t} 0 f(x)=a (occur check) 11
12 Step2. Step1 { x = u,, x = u } s, t 1 1 n 1 1 n σ = { x u,, x u } mgu n n mgu 12
13 f ( xgx, ( )) f ( hy ( ), z ) f( x, g( x)) = f( h( y), z) x= h() y g() x = z x= h() y z = g(()) h y σ = x= h() y z = g() x { x h( y ), z g ( h( y ))} 13
14 P( a, x), P( y, b) P( a, b), P( a, b) P( a, x), P( x, a) P( a, x), P( a, y) P( a, b), Q( a, b) P( a, x), P( b, y) P( a, x), P( x, b) P( x, x), P( y, f ( y)) { x b, y a} {} { xa} { x y} 14
15 P C P D C D (1) (2) (1) P (2) ( P (1) (2) P (3) (1),(2) (1) (2) (3) P P 15
16 HUMAN( Socrates ) HUMAN( x) MORTAL( x) σ = { x Socrates} MORTAL(Socrates) HUMAN( Socrates) MORTAL( Socrates) HUMAN(Socrates) HUMAN(x) mgu HUMAN(Socrates) HUMAN(Socrates) 16
17 P( x) Q( x) P( x) Q( x) P( f( x)) P( f( y)) 17
18 18
19 19
20 20
21 P(, exx, ) P( x, y, z): xiy = z P( xex,, ) ( xy i ) iz= xi( yz i ) P( x, y, u) P( y, zv, ) Puzw (,, ) Pxvw (,, ) P( x, y, u) P( y, zv, ) Pxvw (,, ) Puzw (,, ) ( x)( y)( z) ( P( xyz,, ) Pyxz (,, )) P( xxe,, ) Pabc (,, ) P(, bac,) x y z x y = z x e x = x e = x x, y, z (x y) z = x (y z ) ( x x = e) x, y x y = y x P(x,y,z) x y = z x,y,z,u,v,w x y = u y z = v u z = w x v = w ( x)( y)( P(x,y,z) P(y,x,z) ) ( x)( y)( P(x,y,z) P(y,x,z) ) = ( x) ( y) ( z) ( P(x,y,z) P(y,x,z) ) = ( x) ( y) ( z) ( P(x,y,z) P(y,x,z) ) = ( x) ( y) ( z) (P(x,y,z) P(y,x,z) ) a,b,c P(a,b,c) P(b,a,c) 21
22 Pexx (,, ) (1) Pxex (,, ) (2) Pxyu (,, ) Pyzv (,, ) Puzw (,, ) Pxvw (,, ) (3) Pxyu (,, ) Pyzv (,, ) Pxvw (,, ) Puzw (,, ) (4) Pxxe (,, ) (5) Pabc (,, ) (6) Pbac (,,) (7) from(6),(4.1): P( b, z, v) P( a, v, w) P( c, z, w) (8) from(5),(8.1) : P( aew,, ) Pcbw (,, ) (21) from(2),(21.1) : P( c, b, a) (30) from(30),(3.2) : Pxcu (,, ) Pubw (,, ) Pxaw (,, ) (32) from(5),(32.1) : P( e, b, w) P( c, a, w) (42) from(1), (42.1) : P( c, a, b) (55) from(55),(4.1): P( a, z, v) P( c, v, w) P( b, z, w) (62) from(7),(62.3) : Paav (,, ) Pcvc (,, ) (112) from(5),(112.1) : P( c, e, c) (130) from(2),(130):
23 HUMAN( x) MORTAL( x) HUMAN( Socrates) MORTAL( Socrates) Yes/No Yes Yes No I m sorry I don t know. 23
24 WIFE( Mary, John) WIFE( x, y) HUS( y, x) HUS( z, Mary) ANS( z) WIFE( Mary, z) ANS( z) ANS( John) Wh- ANS ANS(x) x ANS Mary John x y y x Mary z Mary z ANS ANS x y y x is-a 24
25 How s s act s s s =act(s) a s =act(a,s) 25
26 26
27 Pxyzs (,,, ) REACH () s walk(,) v s carry( w, s) climb() s P REACH P(x,y,z,s) s REACH(s) s walk, carry, climb s 27
28 Pxy (,, zs, ) Pvy (,, zwalkvs, (, )) Pxyxs (,,, ) Pwywcarryws (,,, (, )) Pxy (,, xs, ) Pxy (,, x, climb( s)) Pxxxs (,,, ) REACHclimbs ( ( )) P( a, b, c, InitialState) REACH () s ANS() s s,v,w,x,y,z s=(x,y,z) v walk(v,s)=(v,y,z) s=(x,y,x) x=z w carry(w,s)=(w,y,w) s=(x,y,x) x=z climb(w,s)=(x,y,x) s=(x,x,x) climb(s) InitialState=(a,b,c) REACH(s) s 28
29 Pxyzs (,,, ) Pvyzwalkvs (,,, (, )) (1) P( x, y, x, s) P( w, y, w, carry( w, s)) (2) P( x, x, x, s) REACH ( climb( s)) (3) P( a, b, c, InitialState) (4) REACH () s ANS() s (5) from(5),(3) : P( x, x, x, s) ANS( climb( s)) (6) from(6),(2) : P( x, w, x, s) ANS( climb( carry( w, s))) (7) from(7),(1) : P( x, w, v, s) ANS( climb( carry( w, walk( v, s)))) (8) from(8),(4) : ANS( climb( carry( b, walk( c, InitialState)))) (9) climb( carry( b, walk( c, InitialState))) 29
Q.5-1 Ans.
5 Q.5-1 Q.5-2 Q.5-3 Q.5-4 Q.5-5 Q.5-6 Q.5-7 Q.5-8 Q.5-9 Q.5-10 Q.5-11 Q.5-12 Q.5-13 Q.5-14 Q.5-15 Q.5-1 Ans. Q.4-5 1 Q.5-3 Check Q.5-2 200 203 197 199 Q.5-2 Ans. Check Q.5-3 Ans. Q.5-2 12 Q.6-4 69 56
7 27 7.1........................................ 27 7.2.......................................... 28 1 ( a 3 = 3 = 3 a a > 0(a a a a < 0(a a a -1 1 6
26 11 5 1 ( 2 2 2 3 5 3.1...................................... 5 3.2....................................... 5 3.3....................................... 6 3.4....................................... 7
II 1 3 2 5 3 7 4 8 5 11 6 13 7 16 8 18 2 1 1. x 2 + xy x y (1 lim (x,y (1,1 x 1 x 3 + y 3 (2 lim (x,y (, x 2 + y 2 x 2 (3 lim (x,y (, x 2 + y 2 xy (4 lim (x,y (, x 2 + y 2 x y (5 lim (x,y (, x + y x 3y
II Time-stamp: <05/09/30 17:14:06 waki> ii
II waki@cc.hirosaki-u.ac.jp 18 1 30 II Time-stamp: ii 1 1 1.1.................................................. 1 1.2................................................... 3 1.3..................................................
1.1 1 A
. A..2 2 2. () (xyz) ( xyz) ( xy z) = (x x)yz ( xy z) = yz ( xy z) = y(z ( x z)) = y((z x)(z z)) = y( x z) (2) (3) M aj (x, y, M aj ( x, ȳ, z)) = xy ȳm aj ( x, ȳ, z) M aj ( x, ȳ, z)x M aj (x, y, z) x =
ii
ii iii 1 1 1.1..................................... 1 1.2................................... 3 1.3........................... 4 2 9 2.1.................................. 9 2.2...............................
a q q y y a xp p q y a xp y a xp y a x p p y a xp q y x yaxp x y a xp q x p y q p x y a x p p p p x p
a a a a y y ax q y ax q q y ax y ax a a a q q y y a xp p q y a xp y a xp y a x p p y a xp q y x yaxp x y a xp q x p y q p x y a x p p p p x p y a xp q y a x p q p p x p p q p q y a x xy xy a a a y a x
1
1 - 2 - ... - 4 -... - 4 -... - 4 -... - 4 -... - 5 -... - 5 -... - 8 -... - 9 -... - 9 -... - 9 -... - 9 -... - 9 -... - 9 -... - 10 -... - 10 -... - 10 -... - 10 -... - 10 -... - 11 -... - 11 -... -
untitled
20 7 1 22 7 1 1 2 3 7 8 9 10 11 13 14 15 17 18 19 21 22 - 1 - - 2 - - 3 - - 4 - 50 200 50 200-5 - 50 200 50 200 50 200 - 6 - - 7 - () - 8 - (XY) - 9 - 112-10 - - 11 - - 12 - - 13 - - 14 - - 15 - - 16 -
untitled
19 1 19 19 3 8 1 19 1 61 2 479 1965 64 1237 148 1272 58 183 X 1 X 2 12 2 15 A B 5 18 B 29 X 1 12 10 31 A 1 58 Y B 14 1 25 3 31 1 5 5 15 Y B 1 232 Y B 1 4235 14 11 8 5350 2409 X 1 15 10 10 B Y Y 2 X 1 X
8 i, III,,,, III,, :!,,,, :!,,,,, 4:!,,,,,,!,,,, OK! 5:!,,,,,,,,,, OK 6:!, 0, 3:!,,,,! 7:!,,,,,, ii,,,,,, ( ),, :, ( ), ( ), :... : 3 ( )...,, () : ( )..., :,,, ( ), (,,, ),, (ϵ δ ), ( ), (ˆ ˆ;),,,,,,!,,,,.,,
1 A A.1 G = A,B,C, A,B, (1) A,B AB (2) (AB)C = A(BC) (3) 1 A 1A = A1 = A (4) A A 1 A 1 A = AA 1 = 1 AB = BA ( ) AB BA ( ) 3 SU(N),N 2 (Lie) A(θ 1,θ 2,
1 A A.1 G = A,B,C, A,B, (1) A,B AB (2) (AB)C = A(BC) (3) 1 A 1A = A1 = A (4) A A 1 A 1 A = AA 1 = 1 AB = BA ( ) AB BA ( ) 3 SU(N),N 2 (Lie) A(θ 1,θ 2,θ n ) = exp(i n i=1 θ i F i ) (A.1) F i 2 0 θ 2π 1
6. Euler x
...............................................................................3......................................... 4.4................................... 5.5......................................
FX ) 2
(FX) 1 1 2009 12 12 13 2009 1 FX ) 2 1 (FX) 2 1 2 1 2 3 2010 8 FX 1998 1 FX FX 4 1 1 (FX) () () 1998 4 1 100 120 1 100 120 120 100 20 FX 100 100 100 1 100 100 100 1 100 1 100 100 1 100 101 101 100 100
II (10 4 ) 1. p (x, y) (a, b) ε(x, y; a, b) 0 f (x, y) f (a, b) A, B (6.5) y = b f (x, b) f (a, b) x a = A + ε(x, b; a, b) x a 2 x a 0 A = f x (
II (1 4 ) 1. p.13 1 (x, y) (a, b) ε(x, y; a, b) f (x, y) f (a, b) A, B (6.5) y = b f (x, b) f (a, b) x a = A + ε(x, b; a, b) x a x a A = f x (a, b) y x 3 3y 3 (x, y) (, ) f (x, y) = x + y (x, y) = (, )
2
2007 8 12 1 Q&A Q1 A 2007 6 29 2008 1 1 14 1 12 1 2 3 1 1 13 1 2 15 1 1 2 Q2 A 627 1 20 1 1 3 15 2003 18 2 3 4 5 3 406 44 2 1997 7 16 5 1 1 15 4 52 1 31 268 17 5 60 55 50 1999 3 9 1999 3 39 40 44 100 1
xyr x y r x y r u u
xyr x y r x y r u u y a b u a b a b c d e f g u a b c d e g u u e e f yx a b a b a b c a b c a b a b c a b a b c a b c a b c a u xy a b u a b c d a b c d u ar ar a xy u a b c a b c a b p a b a b c a
A
A05-132 2010 2 11 1 1 3 1.1.......................................... 3 1.2..................................... 3 1.3..................................... 3 2 4 2.1............................... 4 2.2
2003 10 2003.10.21 70.400 YES NO NO YES YES NO YES NO YES NO YES NO NO 20 20 50m 12m 12m 0.1 ha 4.0m 6.0m 0.3 ha 4.0m 6.0m 6.0m 0.3 0.6ha 4.5m 6.0m 6.0m 0.6 1.0ha 5.5m 6.5m 6.0m 50m 18 OK a a a a b a
P072-076.indd
3 STEP0 STEP1 STEP2 STEP3 STEP4 072 3STEP4 STEP3 STEP2 STEP1 STEP0 073 3 STEP0 STEP1 STEP2 STEP3 STEP4 074 3STEP4 STEP3 STEP2 STEP1 STEP0 075 3 STEP0 STEP1 STEP2 STEP3 STEP4 076 3STEP4 STEP3 STEP2 STEP1
1
1 2 3 4 5 6 7 8 9 0 1 2 6 3 1 2 3 4 5 6 7 8 9 0 5 4 STEP 02 STEP 01 STEP 03 STEP 04 1F 1F 2F 2F 2F 1F 1 2 3 4 5 http://smarthouse-center.org/sdk/ http://smarthouse-center.org/inquiries/ http://sh-center.org/
STEP1 STEP3 STEP2 STEP4 STEP6 STEP5 STEP7 10,000,000 2,060 38 0 0 0 1978 4 1 2015 9 30 15,000,000 2,060 38 0 0 0 197941 2016930 10,000,000 2,060 38 0 0 0 197941 2016930 3 000 000 0 0 0 600 15
, = = 7 6 = 42, =
http://www.ss.u-tokai.ac.jp/~mahoro/2016autumn/alg_intro/ 1 1 2016.9.26, http://www.ss.u-tokai.ac.jp/~mahoro/2016autumn/alg_intro/ 1.1 1 214 132 = 28258 2 + 1 + 4 1 + 3 + 2 = 7 6 = 42, 4 + 2 = 6 2 + 8
応力とひずみ.ppt
in yukawa@numse.nagoya-u.ac.jp 2 3 4 5 x 2 6 Continuum) 7 8 9 F F 10 F L L F L 1 L F L F L F 11 F L F F L F L L L 1 L 2 12 F L F! A A! S! = F S 13 F L L F F n = F " cos# F t = F " sin# S $ = S cos# S S
Jacobson Prime Avoidance
2016 2017 2 22 1 1 3 2 4 2.1 Jacobson................. 4 2.2.................... 5 3 6 3.1 Prime Avoidance....................... 7 3.2............................. 8 3.3..............................
技術流出防止指針公表用.PDF
15 3 1 4 .. 2 2.. 4. 6.10 10.14.16.19.24.26.28 1 2 1 2002 7 3 2002 3 4 2 3 5 4 4 6 7 8 5 5 9 plan (do) (check) (act) 1) 2) 3) 4) 5) 6) 7) 10 11 12 13 14 15 16 17 18 6 6 19 / / 20 21 22 7 23 8 24 25 26
1. A0 A B A0 A : A1,...,A5 B : B1,...,B12 2. 5 3. 4. 5. A0 (1) A, B A B f K K A ϕ 1, ϕ 2 f ϕ 1 = f ϕ 2 ϕ 1 = ϕ 2 (2) N A 1, A 2, A 3,... N A n X N n X N, A n N n=1 1 A1 d (d 2) A (, k A k = O), A O. f
( 28 ) ( ) ( ) 0 This note is c 2016, 2017 by Setsuo Taniguchi. It may be used for personal or classroom purposes, but not for commercial purp
( 28) ( ) ( 28 9 22 ) 0 This ote is c 2016, 2017 by Setsuo Taiguchi. It may be used for persoal or classroom purposes, but ot for commercial purposes. i (http://www.stat.go.jp/teacher/c2epi1.htm ) = statistics
/02/18
3 09/0/8 i III,,,, III,?,,,,,,,,,,,,,,,,,,,,?,?,,,,,,,,,,,,,,!!!,? 3,,,, ii,,,!,,,, OK! :!,,,, :!,,,,,, 3:!,, 4:!,,,, 5:!,,! 7:!,,,,, 8:!,! 9:!,,,,,,,,, ( ),, :, ( ), ( ), 6:!,,, :... : 3 ( )... iii,,
18 5 10 1 1 1.1 1.1.1 P Q P Q, P, Q P Q P Q P Q, P, Q 2 1 1.1.2 P.Q T F Z R 0 1 x, y x + y x y x y = y x x (y z) = (x y) z x + y = y + x x + (y + z) = (x + y) + z P.Q V = {T, F } V P.Q P.Q T F T F 1.1.3
..0.._0807...e.qxp
4 6 0 4 6 0 4 6 8 30 34 36 38 40 4 44 46 8 8 3 3 5 4 6 7 3 4 6 7 5 9 8 3 4 0 3 3 4 3 5 3 4 4 3 4 7 6 3 9 8 Check 3 4 6 5 3 4 0 3 5 3 3 4 4 7 3 3 4 6 9 3 3 4 8 3 3 3 4 30 33 3 Check Check Check Check 35
h01
P03 P05 P10 P13 P18 P21 1 2 Q A Q A Q A Q A Q A 3 1 check 2 1 2-1 2-2 2-3 2-4 2-5 2-5-1 2-6 2-6-1 2-6-2 2-6-3 3 3-1 3-2 3-3 3-4 3 check 4 5 3-5 3-6 3-7 3-8 3-9 4-1 4-1-1 4-2 4-3 4-4 4-5 4-6 5-1 5-2 4
1 2 3 4 1 2 1 2 3 4 5 6 7 8 9 10 11 27 29 32 33 1 2 3 7 9 11 13 15 17 19 21 23 26 CHECK! 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
26 2 3 4 5 8 9 6 7 2 3 4 5 2 6 7 3 8 9 3 0 4 2 4 3 4 4 5 6 5 7 6 2 2 A B C ABC 8 9 6 3 3 4 4 20 2 6 2 2 3 3 4 4 5 5 22 6 6 7 7 23 6 2 2 3 3 4 4 24 2 2 3 3 4 4 25 6 2 2 3 3 4 4 26 2 2 3 3 27 6 4 4 5 5
mogiJugyo_slide_full.dvi
a 2 + b 2 = c 2 (a, b, c) a 2 a 2 = a a a 1/ 78 2/ 78 3/ 78 4/ 78 180 5/ 78 http://www.kaijo.ed.jp/ 6/ 78 a, b, c ABC C a b B c A C 90 a 2 + b 2 = c 2 7/ 78 C a b a 2 +b 2 = c 2 B c A a 2 a a 2 = a a 8/
1 2 3 4 5 6 X Y ABC A ABC B 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 13 18 30 P331 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 ( ) 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
2005
20 30 8 3 190 60 A,B 67,2000 98 20 23,600 100 60 10 20 1 3 2 1 2 1 12 1 1 ( ) 340 20 20 30 50 50 ( ) 6 80 5 65 17 21 5 5 12 35 1 5 20 3 3,456,871 2,539,950 916,921 18 10 29 5 3 JC-V 2 ( ) 1 17 3 1 6
untitled
1 ( 12 11 44 7 20 10 10 1 1 ( ( 2 10 46 11 10 10 5 8 3 2 6 9 47 2 3 48 4 2 2 ( 97 12 ) 97 12 -Spencer modulus moduli (modulus of elasticity) modulus (le) module modulus module 4 b θ a q φ p 1: 3 (le) module
III No (i) (ii) (iii) (iv) (v) (vi) x 2 3xy + 2 lim. (x,y) (1,0) x 2 + y 2 lim (x,y) (0,0) lim (x,y) (0,0) lim (x,y) (0,0) 5x 2 y x 2 + y 2. xy x2 + y
III No (i) (ii) (iii) (iv) (v) (vi) x 2 3xy + 2. (x,y) (1,0) x 2 + y 2 5x 2 y x 2 + y 2. xy x2 + y 2. 2x + y 3 x 2 + y 2 + 5. sin(x 2 + y 2 ). x 2 + y 2 sin(x 2 y + xy 2 ). xy (i) (ii) (iii) 2xy x 2 +
IA hara@math.kyushu-u.ac.jp Last updated: January,......................................................................................................................................................................................
- 8 -. 1 (1) (2) (3) (4) (5) (6) (7) (8)
- 7 - (1) (2).. ha 43 ( (1) ( ) (2).. 18 11 30 43 (1).. (2).. 0.5. () () A) B) C) - 8 -. 1 (1) (2) (3) (4) (5) (6) (7) (8) (1) (2) 43-9 - - 10 - (1).. 43.. 43... 43 - 11 - (2) (1).. A B A A B A - 12 -.
- 111 -
- 110 - - 111 - - 112 - - 113 - - 114 - - 115 - - 116 - - 117 - - 118 - - 119 - - 120 - - 121 - - 122 - - 123 - - 124 - - 125 - - 126 - - 127 - - 128 - - 129 - - 130 - - 131 - - 132 - - 133 - - 134 - -
100 26331 26331 7,082ha(6.9% 9,027ha(8.8) 903ha(0.9%) 1,2292.5% 5,45711.2% 2,916(6.0%) 80,622ha79.0 4,507ha4.4% 18,277(37.4) 2949 (42.9% ( ) !! 1008940 (03)3581-4111 http://www.mof.go.jp/ 0608579
2 3 2
1 2 3 2 ha ha ha 3 4 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 5 5 ( ) ( ) 3 ( ) ( ),,, 5 6 7 ( ) ( ) ( ) ( ) ( ) ( ) 6 36.3% ( ) 8 ( ) ( ) ( ) ( ) ( ) ( ) 3 5 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
300 10
300 10 16 1695 4 2 44 7 3 1 2 2 1869 11 192210 506.75ha 3 (1594) (1596) 16 17 7 1630 2 14 1637 16 17 4 1664 5 6 1678 6 1678 6 3 8 16954 8 (1758) 7 (1770) 17 2 (1745) 2 (1765) 4 11 11 10 12 1 12 12 12 2
untitled
2 23 3 28 10 12 1 2 3 18 6 1 1 2 9 9 5 22 1 22 10 2 100 9 9 9 1 11 2,300 22 10 8 90 5 80 90 100 5,000 100 90 5 90 8 90 13 1 22 20 / 14 / 10 / 1 13 80 8 80 80 7 8 13 80 7 90 2 200 300 3 4 10 1 1 90 5 90
- 1 - - 2 - - 3 - - 4 - - 5 - - 6 - - 7 - - 8 - ) () ( 0
... 1... 2... 3... 5... 10... 13... 15... 19... 22... 24... 26... 27 0 0 1 2 H13 12 3 4 H21 15.7 5 29.8 10 1 6 4 1 10 1 50,284 48,834 46,185 41,056 33,892 26,726 7 8 9 1012 10 11 12 136ha 80.7ha 13 14
untitled
1,985ha 41.5 2,799ha 58.5 4,784ha 100.0 3 14,210 0 0.0 27 57,590 37,140 64.5 3 1,800 930 51.7 6 1,150 1,150 31.0 39 77,310 39,220 50.7 34 8-3 34 8-4 52 1-6 52 2-3 53 1-6 56 1-2 56 1 18 12 17 30 50
9 5 1 9 30 17 10 1 21 30 18 10 1 22 30 18 10 1 20 30 16 10 1 20 30 31 16 60 9 63 9 65 9 3 14 1 2 3 4 19 10 1 5,600 20,000 21,500 10 10 1,540 1,540 950 950 178 15 5,329 19 1,900 200 19 12 1 200 3,429
０．表紙
60 10 11 11 11,600 36,500 10,500 7,900 +1,500+1,500+9,000+18,0003,70041,600 12 3.84ha 3,100 3,100 4,400 2,785 5,000 50 70 3,500 3,500 2,600 30 2,600 45 3,375 40 4,500 20 2,000 12 1,500 12 2,300 7,500
1 4 8 19 65 87 108 132 142 156 - 1 - - 2 - - 3 - - 4 - - 5 - - 6 - - 7 - - 8 - - 9 - - 10 - - 11 - - 12 - - 13 - - 14 - - 15 - - 16 - - 17 - - 18 - 30-19 - - 20 - ( ) - 21 - - 22 - - 23 - - 24 -
-2-
-1- -2- -3-24 32ha 13-4- 30-5- -6- -7- 100-8- 20 20 100-9- 100-10- 100 100-11- -12-30 -13- 10-14- 52 71 59-15- 30-16- -17- -18- 31 31-19- -20- 47 52 71 29 41 59 306 88 348-21- -22- -23- -24- 12-25- 1,300
総務委員会会議録
29 28 29 29 () 121 1 111 11928 3 () () () () 11928 3 1,320 32,7897,000 () 1 23725,000 9 1,320 313 2,7897,000 2 2 2 5.5 16 15200 31 29 2931 3110 21 21 5 6 8,2195,000 2134,1097,000 1,320 32,7897,000 31 ()
14 12 ( 17 4 2 ) 2004
14 12 ( 17 4 2 ) 2004 1 4,700 1980 1,757 1,150 25,000ha 6,000ha 10 10 10 2 1981 56 90 4,700 1980 1,757 1,150 2003 187,614 96,940 51.7 17 102,128 54.7 2004 545 76 14 2004 4 13 49.1 1981 84,638 38,272 17,570
,
34 29 5 29 6 29 7 30 28 26 1 1-71 - , - 72 - 27 3 1, - 73 - 5811 5821 5822 5831 58 2 5841 5851 5861 5862 5863 5864 5892 5896 5897 5898 5891 5895 7711 622 6311 6312 6314 6324 6032 6033 7611 7621 7623 7624
変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy,
変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy, z + dz) Q! (x + d x + u + du, y + dy + v + dv, z +
,2,4
2005 12 2006 1,2,4 iii 1 Hilbert 14 1 1.............................................. 1 2............................................... 2 3............................................... 3 4.............................................
平成 22 年度 ( 第 32 回 ) 数学入門公開講座テキスト ( 京都大学数理解析研究所, 平成 ~8 22 月年 58 日開催月 2 日 ) V := {(x,y) x n + y n 1 = 0}, W := {(x,y,z) x 3 yz = x 2 y z 2
3 90 2006 1. V := {(x,y) x n + y n 1 = 0}, W := {(x,y,z) x 3 yz = x 2 y z 2 = xz y 2 = 0} V (x,y) n = 1 n = 2 (x,y) V n = 1 n = 2 (3/5,4/5),(5/13,12/13)... n 3 V (0,±1),(±1,0) ( ) n 3 x n + y n = z n,
9 2 1 f(x, y) = xy sin x cos y x y cos y y x sin x d (x, y) = y cos y (x sin x) = y cos y(sin x + x cos x) x dx d (x, y) = x sin x (y cos y) = x sin x
2009 9 6 16 7 1 7.1 1 1 1 9 2 1 f(x, y) = xy sin x cos y x y cos y y x sin x d (x, y) = y cos y (x sin x) = y cos y(sin x + x cos x) x dx d (x, y) = x sin x (y cos y) = x sin x(cos y y sin y) y dy 1 sin