Size: px
Start display at page:

Download ""

Transcription

1

2

3 N

4

5 N

6

7 N

8

9 N

10

11 N

12

13 N

14

15 N

16

17 N

18

19 N

20

21 N

22 Q A

23 N

24 N{ N

25 N{

26

27 N{ N{

28 { NN N

29 { N { N{ N { N { N {

30 N

31 N{

32 N { {

33

34 N{

35 N{

36 { N {

: : : : ) ) 1. d ij f i e i x i v j m a ij m f ij n x i =

: : : : ) ) 1. d ij f i e i x i v j m a ij m f ij n x i = 1 1980 1) 1 2 3 19721960 1965 2) 1999 1 69 1980 1972: 55 1999: 179 2041999: 210 211 1999: 211 3 2003 1987 92 97 3) 1960 1965 1970 1985 1990 1995 4) 1. d ij f i e i x i v j m a ij m f ij n x i = n d ij

More information

c a a ca c c% c11 c12 % s & %

c a a ca c c% c11 c12 % s & % c a a ca c c% c11 c12 % s & % c13 c14 cc c15 %s & % c16 c211 c21% c212 c21% c213 c21% c214 c21% c215 c21% c216 c21% c23 & & % c24 c25 c311 c312 % c31 c315 c32 c33 c34 % c35 c36 c37 c411 c N N c413 c c414c

More information

橡魅力ある数学教材を考えよう.PDF

橡魅力ある数学教材を考えよう.PDF Web 0 2 2_1 x y f x y f f 2_2 2 1 2_3 m n AB A'B' x m n 2 1 ( ) 2_4 1883 5 6 2 2_5 2 9 10 2 1 1 1 3 3_1 2 2 2 16 2 1 0 1 2 2 4 =16 0 31 32 1 2 0 31 3_2 2 3_3 3_4 1 1 GO 3 3_5 2 5 9 A 2 6 10 B 3 7 11 C

More information

四校_目次~巻頭言.indd

四校_目次~巻頭言.indd 107 25 1 2016 3 Key Words : A 114 67 58.84 Mann-Whitney 6 1. 2. 3. 4. 5. 6. I. 21 4 B 23 11 1 9 8 7 23456 108 25 1 2016 3 78 9 II. III. IV. 1. 24 4 A 114 2. 24 5 6 3. 4. 5. 3 42 5 16 6 22 5 4 4 4 3 6.

More information

( ) ( ) 1729 (, 2016:17) = = (1) 1 1

( ) ( ) 1729 (, 2016:17) = = (1) 1 1 1729 1 2016 10 28 1 1729 1111 1111 1729 (1887 1920) (1877 1947) 1729 (, 2016:17) 12 3 1728 9 3 729 1729 = 12 3 + 1 3 = 10 3 + 9 3 (1) 1 1 2 1729 1729 19 13 7 = 1729 = 12 3 + 1 3 = 10 3 + 9 3 13 7 = 91

More information

T75 T55 T45 T67 T54 D81 D71 D51 D61 D41 T95 V83 V73 V63 L93 D81 D71 D51 D61 D41 T95 RX82 V83 V73 V63 L93

T75 T55 T45 T67 T54 D81 D71 D51 D61 D41 T95 V83 V73 V63 L93 D81 D71 D51 D61 D41 T95 RX82 V83 V73 V63 L93 T75 T55 T45 T67 T54 D81 D71 D51 D61 D41 T95 V83 V73 V63 L93 D81 D71 D51 D61 D41 T95 RX82 V83 V73 V63 L93 T95 T95T75 T75T5 T55T4 T45T6 T67T54 T54 L93 L93V83 V83V73 V73V63 V63 RX82 RX82N72 N72N61 N61N51

More information

+ + + + n S (n) = + + + + n S (n) S (n) S 0 (n) S (n) 6 4 S (n) S (n) 7 S (n) S 4 (n) 8 6 S k (n) 0 7 (k + )S k (n) 8 S 6 (n), S 7 (n), S 8 (n), S 9 (

+ + + + n S (n) = + + + + n S (n) S (n) S 0 (n) S (n) 6 4 S (n) S (n) 7 S (n) S 4 (n) 8 6 S k (n) 0 7 (k + )S k (n) 8 S 6 (n), S 7 (n), S 8 (n), S 9 ( k k + k + k + + n k 006.7. + + + + n S (n) = + + + + n S (n) S (n) S 0 (n) S (n) 6 4 S (n) S (n) 7 S (n) S 4 (n) 8 6 S k (n) 0 7 (k + )S k (n) 8 S 6 (n), S 7 (n), S 8 (n), S 9 (n), S 0 (n) 9 S (n) S 4

More information

漸化式のすべてのパターンを解説しましたー高校数学の達人・河見賢司のサイト

漸化式のすべてのパターンを解説しましたー高校数学の達人・河見賢司のサイト https://www.hmg-gen.com/tuusin.html https://www.hmg-gen.com/tuusin1.html 1 2 OK 3 4 {a n } (1) a 1 = 1, a n+1 a n = 2 (2) a 1 = 3, a n+1 a n = 2n a n a n+1 a n = ( ) a n+1 a n = ( ) a n+1 a n {a n } 1,

More information

さくらの個別指導 ( さくら教育研究所 ) a a n n A m n 1 a m a n = a m+n 2 (a m ) n = a mn 3 (ab) n = a n b n a n n = = 3 2, = 3 2+

さくらの個別指導 ( さくら教育研究所 ) a a n n A m n 1 a m a n = a m+n 2 (a m ) n = a mn 3 (ab) n = a n b n a n n = = 3 2, = 3 2+ 5 5. 5.. a a n n A m n a m a n = a m+n (a m ) n = a mn 3 (ab) n = a n b n a n n 0 3 3 0 = 3 +0 = 3, 3 3 = 3 +( ) = 3 0 3 0 3 3 0 = 3 3 =, 3 = 30 3 = 3 0 a 0 a`n a 0 n a 0 = a`n = a n a` = a 83 84 5 5.

More information

59 1 2 3 6 7 8 10 12 13 14 15 16 17 18 19 20 21 23 24 25 26 46 49 30 33 36 38 39 40 42 44 41 45 56 43 52 2 3 4 5 6 7 8 9 q w e r t y u i o!0!1!2!3!4!5!6!7!8!9 @0 @1 @2 @3 @4 10 @5 J @6 @7 @8 @9 #0 #1 #2

More information

untitled

untitled 1 1 1. 2. 3. 2 2 1 (5/6) 4 =0.517... 5/6 (5/6) 4 1 (5/6) 4 1 (35/36) 24 =0.491... 0.5 2.7 3 1 n =rand() 0 1 = rand() () rand 6 0,1,2,3,4,5 1 1 6 6 *6 int() integer 1 6 = int(rand()*6)+1 1 4 3 500 260 52%

More information

N72 T95 T75 T55 T45 T67 T54 N72 RX82 N40 L93 V83 V73 RX73 N51 S90 S80 D81 D51

N72 T95 T75 T55 T45 T67 T54 N72 RX82 N40 L93 V83 V73 RX73 N51 S90 S80 D81 D51 N72 T75 S80 D81 N72 T95 T75 T55 T45 T67 T54 N72 RX82 N40 L93 V83 V73 RX73 N51 S90 S80 D81 D51 N72 RX82 L93 S90 S80 S90 S80 N72 RX82 L93 N40 N29 N72 RX82 N72 RX82 N72 RX82 T95 T75 T55 T45 T67 T54 RX73 L93

More information

untitled

untitled 20073-1- 3 4 5 9 12 14 17-2- 3,700ha 30,000t -3- 1t 70 50 40 C/N -4- 20011228 C/N 13 2001 2cm 1t 60 70 60-5- 70 1t -6- 2003131 ph EC T-C T-N C/N P2O5 K2O CaO MgO HO 2 ms % % % % % % % 8.52 0.64 74.9 44.9

More information

31 33

31 33 17 3 31 33 36 38 42 45 47 50 52 54 57 60 74 80 82 88 89 92 98 101 104 106 94 1 252 37 1 2 2 1 252 38 1 15 3 16 6 24 17 2 10 252 29 15 21 20 15 4 15 467,555 14 11 25 15 1 6 15 5 ( ) 41 2 634 640 1 5 252

More information

( )

( ) 5 60 2 1 54 ( ) 0.8 2 37 3 180 4 1 9 123654789 1 2 3 4 5 6 7 8 9 5 32 4 9 3 8 2 5 6 0 7 30 36 24 8 8 6 450 3 9 26 5 2 2016 2013-2015 14 10 ABC 24DEF BCADAB BEF A F E B D C 11 4 4 1 5 5 2 6 6 3 12 54 24

More information

1 + 1 + 1 + 1 + 1 + 1 + 1 = 0? 1 2003 10 8 1 10 8, 2004 1, 2003 10 2003 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 ( )?, 1, 8, 15, 22, 29?, 1 7, 1, 8, 15, 22,

More information

09-12-15_1203new

09-12-15_1203new 12 15 12/15 1/14 E _ GC DC Y FB GA BF Y 2 g g a f Y b b d b b c c b b g a c e b f b - Y b b c a c C A C C Y f g a b c d e - g a b c d c ab ab b g bb fbbd 3 4 1 F B 1 DF C A A A 6 G F A B 5 GA 6 E BF G

More information

203 x, y, z (x, y, z) x 6 + y 6 + z 6 = 3xyz ( 203 5) a 0, b 0, c 0 a3 + b 3 + c 3 abc 3 a = b = c 3xyz = x 6 + y 6 + z 6 = (x 2 ) 3 + (y 2 ) 3

203 x, y, z (x, y, z) x 6 + y 6 + z 6 = 3xyz ( 203 5) a 0, b 0, c 0 a3 + b 3 + c 3 abc 3 a = b = c 3xyz = x 6 + y 6 + z 6 = (x 2 ) 3 + (y 2 ) 3 203 24 203 x, y, z (x, y, z) x 6 + y 6 + z 6 = 3xyz ( 203 5) 202 20 a 0, b 0, c 0 a3 + b 3 + c 3 abc 3 a = b = c 3xyz = x 6 + y 6 + z 6 = (x 2 ) 3 + (y 2 ) 3 + (z 2 ) 3 3x 2 y 2 z 2 ( ) 3xyz 3(xyz) 2.

More information

CAT. No. 1102k 2011 E-3 B206-B243

CAT. No. 1102k 2011 E-3 B206-B243 0 00mm B20 B2 0 60mm B24 B27 0 90mm B28 B22 5 20mm B224 B227 60 500mm B228 B2 B24 B24 2 2 5 52 52 52U 5 5 5U 54 54 54U 522 542 542U 52 54 54U 524 544 544U 500 552X 5200 526X 505 56X 5405 548X 5200 526X

More information

n 2 + π2 6 x [10 n x] x = lim n 10 n n 10 k x 1.1. a 1, a 2,, a n, (a n ) n=1 {a n } n=1 1.2 ( ). {a n } n=1 Q ε > 0 N N m, n N a m

n 2 + π2 6 x [10 n x] x = lim n 10 n n 10 k x 1.1. a 1, a 2,, a n, (a n ) n=1 {a n } n=1 1.2 ( ). {a n } n=1 Q ε > 0 N N m, n N a m 1 1 1 + 1 4 + + 1 n 2 + π2 6 x [10 n x] x = lim n 10 n n 10 k x 1.1. a 1, a 2,, a n, (a n ) n=1 {a n } n=1 1.2 ( ). {a n } n=1 Q ε > 0 N N m, n N a m a n < ε 1 1. ε = 10 1 N m, n N a m a n < ε = 10 1 N

More information

~!f' 美 しい 女 (.j: ff, ~ 同 麟 豆 ) 中 野 重 t~fì 論 -tjffi 辰 雄 との 文 学 史 的 統 一 保 を Il lh( ~ 至 17 5 ~ なの~ .... -

More information

CG38.PDF

CG38.PDF ............3...3...6....6....8.....8.....4...9 3....9 3.... 3.3...4 3.4...36...39 4....39 4.....39 4.....4 4....49 4.....5 4.....57...64 5....64 5....66 5.3...68 5.4...7 5.5...77...8 6....8 6.....8 6.....83

More information

DC0 MC OFF THR ON MC AX AX MC SD AX AX SRD THR TH MC MC MC MC MC MC MC MC MC MC 9 0 9

DC0 MC OFF THR ON MC AX AX MC SD AX AX SRD THR TH MC MC MC MC MC MC MC MC MC MC 9 0 9 SDN0 SD-N(CX) MSOD-N(CX) SD-N(CX) MSOD-N(CX) SD-N(CX) MSOD-N(CX) SD-N(CX) MSOD-N(CX) SD-N0 MSOD-N0 SD-N MSOD-N SD-N0 MSOD-N0 SD-N9 MSOD-N9 SD-N MSOD-N SD-N MSOD-N SD-N0 MSOD-N0 SD-N00 MSOD-N00 SD-N00 MSOD-N00

More information

INDEX p01-02 p03-04 p05-07 p08 p09-10 p011 p12-16 p17-18 Audio Philosophy Integrated Amplifier Introduction A-30/A-10 Super Audio CD Player Introducti

INDEX p01-02 p03-04 p05-07 p08 p09-10 p011 p12-16 p17-18 Audio Philosophy Integrated Amplifier Introduction A-30/A-10 Super Audio CD Player Introducti 2012 INDEX p01-02 p03-04 p05-07 p08 p09-10 p011 p12-16 p17-18 Audio Philosophy Integrated Amplifier Introduction A-30/A-10 Super Audio CD Player Introduction / Network Audio Player Introduction N-50/N-30

More information

Chap9.dvi

Chap9.dvi .,. f(),, f(),,.,. () lim 2 +3 2 9 (2) lim 3 3 2 9 (4) lim ( ) 2 3 +3 (5) lim 2 9 (6) lim + (7) lim (8) lim (9) lim (0) lim 2 3 + 3 9 2 2 +3 () lim sin 2 sin 2 (2) lim +3 () lim 2 2 9 = 5 5 = 3 (2) lim

More information

(1) 3 A B E e AE = e AB OE = OA + e AB = (1 35 e ) e OE z 1 1 e E xy e = 0 e = 5 OE = ( 2 0 0) E ( 2 0 0) (2) 3 E P Q k EQ = k EP E y 0

(1) 3 A B E e AE = e AB OE = OA + e AB = (1 35 e ) e OE z 1 1 e E xy e = 0 e = 5 OE = ( 2 0 0) E ( 2 0 0) (2) 3 E P Q k EQ = k EP E y 0 (1) 3 A B E e AE = e AB OE = OA + e AB = (1 35 e 0 1 15 ) e OE z 1 1 e E xy 5 1 1 5 e = 0 e = 5 OE = ( 2 0 0) E ( 2 0 0) (2) 3 E P Q k EQ = k EP E y 0 Q y P y k 2 M N M( 1 0 0) N(1 0 0) 4 P Q M N C EP

More information

main

main 14 1. 12 5 main 1.23 3 1.230000 3 1.860867 1 2. 1988 1925 1911 1867 void JPcalendar(int x) 1987 1 64 1 1 1 while(1) Ctrl C void JPcalendar(int x){ if (x > 1988) printf(" %d %d \n", x, x-1988); else if(x

More information

0 (18) /12/13 (19) n Z (n Z ) 5 30 (5 30 ) (mod 5) (20) ( ) (12, 8) = 4

0   (18) /12/13 (19) n Z (n Z ) 5 30 (5 30 ) (mod 5) (20) ( ) (12, 8) = 4 0 http://homepage3.nifty.com/yakuikei (18) 1 99 3 2014/12/13 (19) 1 100 3 n Z (n Z ) 5 30 (5 30 ) 37 22 (mod 5) (20) 201 300 3 (37 22 5 ) (12, 8) = 4 (21) 16! 2 (12 8 4) (22) (3 n )! 3 (23) 100! 0 1 (1)

More information

3 3.3. I 3.3.2. [ ] N(µ, σ 2 ) σ 2 (X 1,..., X n ) X := 1 n (X 1 + + X n ): µ X N(µ, σ 2 /n) 1.8.4 Z = X µ σ/ n N(, 1) 1.8.2 < α < 1/2 Φ(z) =.5 α z α

3 3.3. I 3.3.2. [ ] N(µ, σ 2 ) σ 2 (X 1,..., X n ) X := 1 n (X 1 + + X n ): µ X N(µ, σ 2 /n) 1.8.4 Z = X µ σ/ n N(, 1) 1.8.2 < α < 1/2 Φ(z) =.5 α z α 2 2.1. : : 2 : ( ): : ( ): : : : ( ) ( ) ( ) : ( pp.53 6 2.3 2.4 ) : 2.2. ( ). i X i (i = 1, 2,..., n) X 1, X 2,..., X n X i (X 1, X 2,..., X n ) ( ) n (x 1, x 2,..., x n ) (X 1, X 2,..., X n ) : X 1,

More information

68 A mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1

68 A mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1 67 A Section A.1 0 1 0 1 Balmer 7 9 1 0.1 0.01 1 9 3 10:09 6 A.1: A.1 1 10 9 68 A 10 9 10 9 1 10 9 10 1 mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1 A.1. 69 5 1 10 15 3 40 0 0 ¾ ¾ É f Á ½ j 30 A.3: A.4: 1/10

More information

SC- SC-RM SC-/G SC-/SE SC-/V SC-/VG SC-/VS SC-/U SC-C SC-LG SW- SW-RM SW-/G SW-/SE SW-/U SW-/3H SW-/2L SW-/3Q SW-/2E SW-C SW-RMC SW-C/U SW-P SW-LG SW-

SC- SC-RM SC-/G SC-/SE SC-/V SC-/VG SC-/VS SC-/U SC-C SC-LG SW- SW-RM SW-/G SW-/SE SW-/U SW-/3H SW-/2L SW-/3Q SW-/2E SW-C SW-RMC SW-C/U SW-P SW-LG SW- SC- SC-RM SC-/G SC-/SE SC-/V SC-/VG SC-/VS SC-/U SC-C SC-LG SW- SW-RM SW-/G SW-/SE SW-/U SW-/3H SW-/2L SW-/3Q SW-/2E SW-C SW-RMC SW-C/U SW-P SW-LG SW-C/3H SW-C/2E SW RM C / N10 S C 2 5 A B - A 2 2 2 T

More information

66 σ σ (8.1) σ = 0 0 σd = 0 (8.2) (8.2) (8.1) E ρ d = 0... d = 0 (8.3) d 1 NN K K 8.1 d σd σd M = σd = E 2 d (8.4) ρ 2 d = I M = EI ρ 1 ρ = M EI ρ EI

66 σ σ (8.1) σ = 0 0 σd = 0 (8.2) (8.2) (8.1) E ρ d = 0... d = 0 (8.3) d 1 NN K K 8.1 d σd σd M = σd = E 2 d (8.4) ρ 2 d = I M = EI ρ 1 ρ = M EI ρ EI 65 8. K 8 8 7 8 K 6 7 8 K 6 M Q σ (6.4) M O ρ dθ D N d N 1 P Q B C (1 + ε)d M N N h 2 h 1 ( ) B (+) M 8.1: σ = E ρ (E, 1/ρ ) (8.1) 66 σ σ (8.1) σ = 0 0 σd = 0 (8.2) (8.2) (8.1) E ρ d = 0... d = 0 (8.3)

More information

2 A B A B A A B Ea 1 51 Ea 1 A B A B B A B B A Ea 2 A B Ea 1 ( )k 1 Ea 1 Ea 2 Arrhenius 53 Ea R T k 1 = χe 1 Ea RT k 2 = χe 2 Ea RT 53 A B A B

2 A B A B A A B Ea 1 51 Ea 1 A B A B B A B B A Ea 2 A B Ea 1 ( )k 1 Ea 1 Ea 2 Arrhenius 53 Ea R T k 1 = χe 1 Ea RT k 2 = χe 2 Ea RT 53 A B A B 5. A B B A B A B B A A B A B 2 A [A] B [B] 51 v = k[a][b] 51 A B 3 0 273.16 A B A B A B A A [A] 52 v= k[a] 52 A B 55 2 A B A B A A B Ea 1 51 Ea 1 A B A B B A B B A Ea 2 A B Ea 1 ( )k 1 Ea 1 Ea 2 Arrhenius

More information

untitled

untitled Study 6 Watch Experiment & Experience Experiment & Experience 2007 8/21() JAEA 2007 10/3() JAEA JAEA 2007 12/3 () JAEA JAEA 2007 8/28()30() 8/28 NSRR (JAEA) FCA (JAEA) 8/29 JRR-4(JAEA) 8/30 2007 9/10()14()

More information

KZ3N Series ø, ø U94V0 1 New New New New New 39% 15 Rc KZ3N KZ2N New New KZ3N KZ2N New 1

KZ3N Series ø, ø U94V0 1 New New New New New 39% 15 Rc KZ3N KZ2N New New KZ3N KZ2N New 1 ø, ø 39% 39% New KZ3N-135T 4.36kg 7.16kg New KZ2N-135T 15 15 KZ3N Series KZ3 Series KZ3T Series T.S20-202 KZ3N Series ø, ø U94V0 1 New New New New New 39% 15 Rc KZ3N KZ2N New New KZ3N KZ2N New 1 KZ3T Series

More information

(1) (2) (3) (4) HB B ( ) (5) (6) (7) 40 (8) (9) (10)

(1) (2) (3) (4) HB B ( ) (5) (6) (7) 40 (8) (9) (10) 2017 12 9 4 1 30 4 10 3 1 30 3 30 2 1 30 2 50 1 1 30 2 10 (1) (2) (3) (4) HB B ( ) (5) (6) (7) 40 (8) (9) (10) (1) i 23 c 23 0 1 2 3 4 5 6 7 8 9 a b d e f g h i (2) 23 23 (3) 23 ( 23 ) 23 x 1 x 2 23 x

More information

(1) (2) (1) (2) 2 3 {a n } a 2 + a 4 + a a n S n S n = n = S n

(1) (2) (1) (2) 2 3 {a n } a 2 + a 4 + a a n S n S n = n = S n . 99 () 0 0 0 () 0 00 0 350 300 () 5 0 () 3 {a n } a + a 4 + a 6 + + a 40 30 53 47 77 95 30 83 4 n S n S n = n = S n 303 9 k d 9 45 k =, d = 99 a d n a n d n a n = a + (n )d a n a n S n S n = n(a + a n

More information

Chapter9 9 LDPC sum-product LDPC 9.1 ( ) 9.2 c 1, c 2, {0, 1, } SUM, PROD : {0, 1, } {0, 1, } SUM(c 1, c 2,, c n ) := { c1 + + c n (c n0 (1 n

Chapter9 9 LDPC sum-product LDPC 9.1 ( ) 9.2 c 1, c 2, {0, 1, } SUM, PROD : {0, 1, } {0, 1, } SUM(c 1, c 2,, c n ) := { c1 + + c n (c n0 (1 n 9 LDPC sum-product 9.1 9.2 LDPC 9.1 ( ) 9.2 c 1, c 2, {0, 1, } SUM, PROD : {0, 1, } {0, 1, } SUM(c 1, c 2,, c n ) := { c1 + + c n (c n0 (1 n 0 n)) ( ) 0 (N(0 c) > N(1 c)) PROD(c 1, c 2,, c n ) := 1 (N(0

More information

( ) 2.1. C. (1) x 4 dx = 1 5 x5 + C 1 (2) x dx = x 2 dx = x 1 + C = 1 2 x + C xdx (3) = x dx = 3 x C (4) (x + 1) 3 dx = (x 3 + 3x 2 + 3x +

( ) 2.1. C. (1) x 4 dx = 1 5 x5 + C 1 (2) x dx = x 2 dx = x 1 + C = 1 2 x + C xdx (3) = x dx = 3 x C (4) (x + 1) 3 dx = (x 3 + 3x 2 + 3x + (.. C. ( d 5 5 + C ( d d + C + C d ( d + C ( ( + d ( + + + d + + + + C (5 9 + d + d tan + C cos (sin (6 sin d d log sin + C sin + (7 + + d ( + + + + d log( + + + C ( (8 d 7 6 d + 6 + C ( (9 ( d 6 + 8 d

More information

() ( ) ( )

() ( ) ( ) () ( ) ( ) C10-14 LAS LAS C12-15 AE AE DHTDMAC DHTDMAC DHTDMAC N,N- N- AO AO C10-14 LAS LAS 1 2 3 4 5 MBAS(mg/L) 1.2 1 0.8 0.6 0.4 0.2 0 BODMBAS 1998 0 5 10 15 BOD(mg/L) MBASNH 4 -N 1998 1.2 MBAS(mg/L)

More information

ÄêÀÑʬ¤ÎÄêµÁ¤Ë¤Ä¤¤¤Æ

ÄêÀÑʬ¤ÎÄêµÁ¤Ë¤Ä¤¤¤Æ http://www.math.sci.hokudai.ac.jp/~yano/biseki2_2014/ 2014 II ( : ) 紀元前 3000 年 紀元前 300 年 17 世紀 18 世紀 19 世紀 積分 古代エジプト 古代ギリシャ積分法の起源 微分 フェルマー デカルト 微分積分学の黎明期 ニュートンライプニッツ コーシー 微分積分学の誕 厳密化と発展 リーマン : : ( 287?

More information

NTN すべり軸受標準品シリーズ NTN すべり軸受標準品シリーズ 10

NTN すべり軸受標準品シリーズ NTN すべり軸受標準品シリーズ 10 3 3. R-ARE35 3 +.2 +. +.9 +. 5 -.2.3 3 R-ARE +.2 +. 7 +.9 +. -.2.3 R-ARE5 5 +.2 +. 8 +.9 +. -.2.3 5 R-ARE8 +.2 +. 9 +.9 +. 8 -.2.3 R-ARE78 7 +.23 +. +. +.5 8 -.2.5 7 R-ARE88 8 +.23 +. +. +.5 8 -.2.5 8

More information

Ultrason® E, S, P – グレード一覧

Ultrason® E, S, P – グレード一覧 E, S, P PESU, PSU, PPSU : www.plasticsportalasia.basf.com/ultrason E, S, P PESU PSU PPSU E, S, P E, S, P 04 04 06 06 08 10 4 E, S, P E, S, P E, S, P 5 E 1010 E 2010 E 2020 P E 3010 E 6020 P S 2010 S 3010

More information

2001 年度 『数学基礎 IV』 講義録

2001 年度 『数学基礎 IV』 講義録 4 A 95 96 4 1 n {1, 2,,n} n n σ ( ) 1 2 n σ(1) σ(2) σ(n) σ σ 2 1 n 1 2 {1, 2,,n} n n! n S n σ, τ S n {1, 2,,n} τ σ {1, 2,,n} n τ σ σ, τ τσ σ n σ 1 n σ 1 ( σ σ ) 1 σ = σσ 1 = ι 1 2 n ι 1 2 n 4.1. 4 σ =

More information

, x R, f (x),, df dx : R R,, f : R R, f(x) ( ).,, f (a) d f dx (a), f (a) d3 f dx 3 (a),, f (n) (a) dn f dx n (a), f d f dx, f d3 f dx 3,, f (n) dn f

, x R, f (x),, df dx : R R,, f : R R, f(x) ( ).,, f (a) d f dx (a), f (a) d3 f dx 3 (a),, f (n) (a) dn f dx n (a), f d f dx, f d3 f dx 3,, f (n) dn f ,,,,.,,,. R f : R R R a R, f(a + ) f(a) lim 0 (), df dx (a) f (a), f(x) x a, f (a), f(x) x a ( ). y f(a + ) y f(x) f(a+) f(a) f(a + ) f(a) f(a) x a 0 a a + x 0 a a + x y y f(x) 0 : 0, f(a+) f(a)., f(x)

More information

Microsoft Word - 計算力学2007有限要素法.doc

Microsoft Word - 計算力学2007有限要素法.doc 95 2 x y yz = zx = yz = zx = { } T = { x y z xy } () {} T { } T = { x y z xy } = u u x y u z u x x y z y + u y (2) x u x u y x y x y z xy E( ) = ( + )( 2) 2 2( ) x y z xy (3) E x y z z = z = (3) z x y

More information

7. 1 max max min f g h h(x) = max{f(x), g(x)} f g h l(x) l(x) = min{f(x), g(x)} f g 1 f g h(x) = max{f(x), g(x)} l(x) = min{f(x), g(x)} h(x) = 1 (f(x)

7. 1 max max min f g h h(x) = max{f(x), g(x)} f g h l(x) l(x) = min{f(x), g(x)} f g 1 f g h(x) = max{f(x), g(x)} l(x) = min{f(x), g(x)} h(x) = 1 (f(x) 7. 1 ma ma min f g h h() = ma{f(), g()} f g h l() l() = min{f(), g()} f g 1 f g h() = ma{f(), g()} l() = min{f(), g()} h() = 1 (f() + g() + f() g() ) 2 1 1 l() = 1 (f() + g() f() g() ) 2 2 1 45 = 2 e 1

More information