ver.5.3web
|
|
|
- しょうこ しもとり
- 5 years ago
- Views:
Transcription
1 22 JSBi -1-
2
3 / AB AB 1 A B 2 B AB 3 A B AB 4 O A B AB -3-
4 6 A a AA aa 1 A a 2 Aa 3 AA RNA 2 3 TATA 4 RNA mrna UTR -4-
5 8 RNA (a) (d) (a) DNA (b) (c) RNA (c) (d) 1 (a) (b) mrna (c) (d) mrna 2 (a) (b) mrna (c) (d) mrna 3 (a) (b) trna (c) (d) 4 (a) (b) mrna (c) (d) trna -5-
6 10 RNA mrna mrna RNA RNA
7 N N- 2 3 O O G GTP 3 4 Na + K ras myc 2 Rb p
8 SNP DNA 2-8-
9 15 DNA 1 a, c 2 a, d 3 b, c 4 b, d 5-9-
10 16 LINE SINE 1 10% 2 30% 3 50% 4 70% 17 A B DNA PCR (a) A DNA B 5 -GAGTCAACGGATTTGGTCGT CGAGATCCCTCCAAAATCAA-3 3 -CTCAGTTGCCTAAACCAGCA GCTCTAGGGAGGTTTTAGTT-5 (a) 5 -GAGTCAACGGATTTGGTCGT CGAGATCCCTCCAAAATCAA GCTCTAGGGAGGTTTTAGTT AACTAAAACCTCCCTAGAGC TTGATTTTGGAGGGATCTCG-3-10-
11 18 SDS SDS-PAGE SDS-PAGE (a) (b) 1 (a) (b) 2 (a) (b) 3 (a) (b) 4 (a) (b)
12 20 X (AND) 2 110(2) AND 101(2) = 100(2) (n) n 6(10) = 110(2) x f(x) f(x) = x AND 101 (2) y, z f(y) = f(z) 1 y = 110(2) z = 100(2) 2 y = 101(2) z = 100(2) 3 y = 011(2) z = 101(2) 4 y = 000(2) z = 101(2) -12-
13 22 1 Perl 2 Ruby MySQL 3 JIT CISC (Complex Instruction Set Computer) RISC(Reduced Instruction Set Computer) CPU -13-
14 24 ( a ) ( d ) ( a ) ( b ) ( c ) ( d ) 1 (a) scp (b) ssh (c) telnet (d) ftp 2 (a) ftp (b) sftp (c) telnet (d) ssh 3 (a) telnet (b) ftp (c) scp (d) ssh 4 (a) telnet (b) ssh (c) ftp (d) sftp 25 O(n 2 ) 1 n 2 2 n 2 3 n > c n a n 2 a c 4 n > c n a n 2 a c -14-
15 26 ( a ) ( c ) ( a ) O(n 2 ) O(n log n) ( b ) O(n log n) ( c ) 1 (a) (b) (c) 2 (a) (b) (c) 3 (a) (b) (c) 4 (a) (b) (c) 27 AB * * A AB * * B AB * * 1 AA * B * * 2 AB * A * * 3 AB * B * * 4 AB * C * * -15-
16 28 2 S0, S1 S0 0 1 S0 S1 0 S1 S0 1 S0 S S S1 3 0 S0 4 1 S1 29 (index) 1 2 B- 3 B- 4 B
17 h(x) a, b h(a)+h(b) = h(a+b) 4-17-
18 31 SQL SELECT FROM WHERE = H1N1 AND > 1976 ; AAD17229 Human HA H1N1 USA 1918 ABD95350 Human HA H1N1 Russia 1977 ACF54400 Human HA H3N2 Hong Kong 1968 ACP41105 Human HA H1N1 USA 2009 ACU79959 Human HA H2N2 Japan 1957 AAF75994 Swine HA H1N2 USA 1999 AAB39851 Swine HA H1N1 USA 1976 AAD25304 Avian HA H1N1 Canada 1976 AAT65329 Avian HA H1N1 Canada
19 32 XML (extensible Markup Language) 1 XML 2 XML 3 XML 4 XML XML XML , 3, 3, 8, 9,
20 34 2 X, Y Pr(A, B ) A B E(A ) A Var(A ) A 1 X, Y XY E(XY ) E(X )E(Y ) 2 X, Y X, Y Pr(X, Y ) Pr(X )Pr(Y ) 3 X Var(X ) X X 2 Var(X ) = E(X 2 ) (E(X )) 2 4 Y X Pr(X Y ) Pr(X,Y )/Pr(Y ) 35 X Y N(0,1) N(0,1) X Y 1 X Y 2 X + Y 3 X + Y 2 4 2X 4-20-
21 p(x) p(x) < 0 x K- (K-means method) 2 UPGMA (Unweighted Pair Group Method with Arithmetic mean) 3 (Self-Organizing Map) 4 Fuzzy C-means -21-
22 38 10 X1, X2,, X y1, y2,,y10 X k- d(x, Xi ) 10 yi 10 d(x, Xi ) k- k- k k=1 k=3 2 k=1 k=3 3 k=1 k=3 4 k=1 k= n-fold 1/ n 2 n-fold n n = 2 3 LOO (leave-one-out)
23 40 TP = True Positive TN = True Negative FP = False Positive FN = False Negative 1 (recall) TP / (TP + FN) 2 (precision) TP / (TP + FP) 3 F (F-measure) 2TP / (TP+FN+TP+FP) 4 41 BLAST 1 DNA DNA 2 DNA 3 (low-complexity) (% identity) 4 PSI-BLAST (position-specific scoring matrix; PSSM) -23-
24 42 A B A B 1 B A 2 A B 3 B 4 A 43 ClustalW (progressive method)
25 44 BLAST (bit score) 1 BLOSUM45 BLOSUM s 10 S 45 BLAST = 0 Seq1 Seq2 GAGCAGCTAGATCGGATTGTTAGA CATGTGATAGACCGTATTAATGCA
26 46 Gene Ontology (GO term) A is_a B A B A part_of B A B A B GO term A is_a B A part_of B A B mitochondrion is_a cytoplasmic part A is_a B B is_a C A is_a C A part_of B B part_of C A part_of C A is_a B B part_of C A part_of C A part_of B B is_a C A part_of C 1 cytoplasmic part is_a intracellular part 2 cytoplasmic part part_of intracellular part 3 mitochondrion is_a organelle 4 intracellular organelle is_a intracellular -26-
27 47 RNA 1.((((...((.(((...)))))..)))). 2.((((..(((((((...))))))))))). 3 (((((..(((((((...)))))))))))) 4.(((...((..((...))))...))). -27-
28 48 A E A B C D E PAM BLOSUM PAM20 PAM70 PAM70 1 A B 2 B C 3 C D 4 D E 49 4 DNA position 1 position 2 position 3 position 4 A T G C GAGGTCT 1 AGGT 2 GAGG 3 GTCT 4 GGTC -28-
29 50 5 DNA 4 fj(a) j a p(a) a p(a) = p(t) = p(g) = p(c) = 0.25 = T A T A T 2 T A T T T 3 T A A G T 4 T A A C T 5 j f j (a) log 2 j =1 a {A,T,G,C} f (a) p(a)
30 51 C-X-X-C-x(5,7)-C-[FWY]-[LIV]-C X (-) ([ ]) 1 x(m,n) m n 1 CTGCGGCFVC 2 CTICGGENNRTCFVC 3 CLIHGGENDRTCWVC 4 CTMCGGEHNNRTCFVC 52 DNA (palindrome) DNA 1 5'-ATGGGCCGGCCCAT-3' 3'-TACCCGGCCGGGTA-5' 2 5'-ATGGGCCTTTAAAG-3' 3'-TACCCGGAAATTTC-5' 3 5'-ATGGGCCCCGGGTA-3' 3'-TACCCGGGGCCCAT-5' 4 5'-ATGGGCCATGGGCC-3' 3'-TACCCGGTACCCGG-5' -30-
31 53 (cis) (trans) C
32 55 2 L- D- L- Cα N C Cβ CαN CαC CαCβ L- 1 (CαN CαC) CαCβ > 0 2 (CαN CαC) CαCβ = 0 3 (CαN CαC) CαCβ < 0 4 (CαN CαC) CαCβ = Molecular Dynamics MD 2 Molecular Mechanics MM
33 57 PDB(Protein Data Bank) -33-
34 β 3 X TIM (Rossman) SCOP CATH 3 SCOP all all /
35 PDB(Protein Data Bank) BLAST 1 2 ab initio
36 62 5 A1~A5 B1~B5 2 C C RMSD(Root Mean Square Deviation) A1 B1 3.0 A2 B2 1.0 A3 B3 0.0 A4 B4 1.0 A5 B
37 63 DNA 1 B 2 (major groove)- (minor groove)
38 64 1 SCOP (space filling model) CNV 2 QTL 3 SNP 4 VNTR -38-
39 66 ABO 3 A B O AA AO BB BO AB OO 6 A A B B AB O A B AB O A B O 1 A 0.3 B 0.2 O A 0.1 B 0.5 O A 0.1 B 0.4 O A 0.3 B 0.3 O
40
41
42 70 (a) (b) (a) ML OTU Operational Taxonomic Unit; OTU 4 3 OTU 5 (b) OTU (a) NJ (b) 15 2 (a) NJ (b) 21 3 (a) MP (b) 15 4 (a) MP (b)
43 71 (Newick format) 1 ((a,b), c, (d, (e, f))) 2 (((a,b),c), d, (e,f)) 3 ((a, b), (c, d), (e, f)) 4 (c, ((e, f), d), (b, a)) -43-
44 72 (a) (b) (c) n x / d d p = ( 3/ 4) ( 3/ 4)e ( 4 d /3) L(d; x) (a) n! d x!(n x)! (a) (d; x) (b) d d (c) 1 (a) p x (1 p) (n x) (b) d (d; x) dd = 0 (c) 3 4 log x n 2 (a) p x (1 p) (n x) (b) d2 (d; x) = 0 dd 2 (c) 4 3 log x n 3 (a) ( 3/ 4) ( 3/ 4)e ( 4 d /3) (b) d (d; x) dd 4 (a) ( 3/ 4) ( 3/ 4)e ( 4 d /3) (b) d2 (d; x) = 0 (c) 3 4 log x n = 0 dd 2 (c) 4 3 log x n -44-
45 mrna 2 3 mrna 4-45-
46 75 A B X B A PCR X B Ct A Ct 2 1 X A B 2 2 X A B 4 3 X B A 2 4 X B A 4 76 X A B A B 1 2 X 2 2 X 3 2 X mrna 4 2 X -46-
47 77 v Y [Y] v = k K K +[Y] k K 1 v k 2 [Y] K 3 [Y] K v 4 Y 78 X k (>0) X 4 X -47-
48 79 y1, y2 1 1, 2 2 1, 2 3 1, 2 4 1, 2-48-
49 80 X Y Z Sx Z Z Sx Y Z -49-
50 22 JSBi
51 -51-
( )/2 hara/lectures/lectures-j.html 2, {H} {T } S = {H, T } {(H, H), (H, T )} {(H, T ), (T, T )} {(H, H), (T, T )} {1
( )/2 http://www2.math.kyushu-u.ac.jp/ hara/lectures/lectures-j.html 1 2011 ( )/2 2 2011 4 1 2 1.1 1 2 1 2 3 4 5 1.1.1 sample space S S = {H, T } H T T H S = {(H, H), (H, T ), (T, H), (T, T )} (T, H) S
A(6, 13) B(1, 1) 65 y C 2 A(2, 1) B( 3, 2) C 66 x + 2y 1 = 0 2 A(1, 1) B(3, 0) P 67 3 A(3, 3) B(1, 2) C(4, 0) (1) ABC G (2) 3 A B C P 6
1 1 1.1 64 A6, 1) B1, 1) 65 C A, 1) B, ) C 66 + 1 = 0 A1, 1) B, 0) P 67 A, ) B1, ) C4, 0) 1) ABC G ) A B C P 64 A 1, 1) B, ) AB AB = 1) + 1) A 1, 1) 1 B, ) 1 65 66 65 C0, k) 66 1 p, p) 1 1 A B AB A 67
08-02 生命の定義と遺伝.pptx
1 2 (1) (2) (3) (1) (2) DNA (3) (4) (ATP) Richard Dawkins () DNARNA () ( ) ( ) 1 2 2 1 heredity inheritance (Genetics) 1865 (1909 - - - DNA Molecular Genetics 1920 1953 ) 1. (P) (F1) (F2) 2. 1 2 3 web
untitled
18 12 10 40 H5N1 2005 11 WHO 2005 12 2006 6 (H5N1) 10 25 1,700 ( 1,300 2,500 ) 200 53 64 17 30% 3,785,000 291,200 3 14,100 4 30% 57,600 4,430 3 1,150 320 210 4 2% 0.56% () ) 1 10 2 3A (2B) 3B 4A5A 6A 4B
( )
18 10 01 ( ) 1 2018 4 1.1 2018............................... 4 1.2 2018......................... 5 2 2017 7 2.1 2017............................... 7 2.2 2017......................... 8 3 2016 9 3.1 2016...............................
4 4 4 a b c d a b A c d A a da ad bce O E O n A n O ad bc a d n A n O 5 {a n } S n a k n a n + k S n a a n+ S n n S n n log x x {xy } x, y x + y 7 fx
4 4 5 4 I II III A B C, 5 7 I II A B,, 8, 9 I II A B O A,, Bb, b, Cc, c, c b c b b c c c OA BC P BC OP BC P AP BC n f n x xn e x! e n! n f n x f n x f n x f k x k 4 e > f n x dx k k! fx sin x cos x tan
a n a n ( ) (1) a m a n = a m+n (2) (a m ) n = a mn (3) (ab) n = a n b n (4) a m a n = a m n ( m > n ) m n 4 ( ) 552
3 3.0 a n a n ( ) () a m a n = a m+n () (a m ) n = a mn (3) (ab) n = a n b n (4) a m a n = a m n ( m > n ) m n 4 ( ) 55 3. (n ) a n n a n a n 3 4 = 8 8 3 ( 3) 4 = 8 3 8 ( ) ( ) 3 = 8 8 ( ) 3 n n 4 n n
統計学のポイント整理
.. September 17, 2012 1 / 55 n! = n (n 1) (n 2) 1 0! = 1 10! = 10 9 8 1 = 3628800 n k np k np k = n! (n k)! (1) 5 3 5 P 3 = 5! = 5 4 3 = 60 (5 3)! n k n C k nc k = npk k! = n! k!(n k)! (2) 5 3 5C 3 = 5!
x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y)
x, y x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 1 1977 x 3 y xy 3 x 2 y + xy 2 x 3 + y 3 = 15 xy (x y) (x + y) xy (x y) (x y) ( x 2 + xy + y 2) = 15 (x y) ( x 2 y + xy 2 x 2 2xy y 2) = 15 (x y) (x + y) (xy
2
2 3 Page 4 5 6 A-1B-1 C0 D0 E0 F0 G0 A0 B0 C1 D1 E1 F1 G1 A1 B1 C2 D2 E2 F2 G2 A2 B2 C3 D3 E3 7 F3 G3 A3 B3 C4 D4 E4 F4 G4 A4 B4 C5 D5 E5 F5 G5 A5 B5 C6 D6 E6 F6 G6 A6 B6 C7 8 Page 9 1 2 3 1 2 10 1 11
計算機生命科学の基礎II_
Ⅱ 1.4 atsushi_doi@cell-innovator.com 812-8582 3-1-1 8 806 http://www.cell-innovator.com BioGPS Connectivity Map The Cancer Genome Atlas (TCGA); cbioportal GO DAVID, GSEA WCGNA BioGPS http://biogps.org/
Part () () Γ Part ,
Contents a 6 6 6 6 6 6 6 7 7. 8.. 8.. 8.3. 8 Part. 9. 9.. 9.. 3. 3.. 3.. 3 4. 5 4.. 5 4.. 9 4.3. 3 Part. 6 5. () 6 5.. () 7 5.. 9 5.3. Γ 3 6. 3 6.. 3 6.. 3 6.3. 33 Part 3. 34 7. 34 7.. 34 7.. 34 8. 35
BIT -2-
2004.3.31 10 11 12-1- BIT -2- -3-256 258 932 524 585 -4- -5- A B A B AB A B A B C AB A B AB AB AB AB -6- -7- A B -8- -9- -10- mm -11- fax -12- -13- -14- -15- s58.10.1 1255 4.2 30.10-16- -17- -18- -19-6.12.10
名古屋工業大の数学 2000 年 ~2015 年 大学入試数学動画解説サイト
名古屋工業大の数学 年 ~5 年 大学入試数学動画解説サイト http://mathroom.jugem.jp/ 68 i 4 3 III III 3 5 3 ii 5 6 45 99 5 4 3. () r \= S n = r + r + 3r 3 + + nr n () x > f n (x) = e x + e x + 3e 3x + + ne nx f(x) = lim f n(x) lim
(, Goo Ishikawa, Go-o Ishikawa) ( ) 1
(, Goo Ishikawa, Go-o Ishikawa) ( ) 1 ( ) ( ) ( ) G7( ) ( ) ( ) () ( ) BD = 1 DC CE EA AF FB 0 0 BD DC CE EA AF FB =1 ( ) 2 (geometry) ( ) ( ) 3 (?) (Topology) ( ) DNA ( ) 4 ( ) ( ) 5 ( ) H. 1 : 1+ 5 2
BD = a, EA = b, BH = a, BF = b 3 EF B, EOA, BOD EF B EOA BF : AO = BE : AE, b : = BE : b, AF = BF = b BE = bb. () EF = b AF = b b. (2) EF B BOD EF : B
2000 8 3.4 p q θ = 80 B E a H F b θ/2 O θ/2 D A B E BD = a, EA = b, BH = a, BF = b 3 EF B, EOA, BOD EF B EOA BF : AO = BE : AE, b : = BE : b, AF = BF = b BE = bb. () EF = b AF = b b. (2) EF B BOD EF :
D 24 D D D
5 Paper I.R. 2001 5 Paper HP Paper 5 3 5.1................................................... 3 5.2.................................................... 4 5.3.......................................... 6
OABC OA OC 4, OB, AOB BOC COA 60 OA a OB b OC c () AB AC () ABC D OD ABC OD OA + p AB + q AC p q () OABC 4 f(x) + x ( ), () y f(x) P l 4 () y f(x) l P
4 ( ) ( ) ( ) ( ) 4 5 5 II III A B (0 ) 4, 6, 7 II III A B (0 ) ( ),, 6, 8, 9 II III A B (0 ) ( [ ] ) 5, 0, II A B (90 ) log x x () (a) y x + x (b) y sin (x + ) () (a) (b) (c) (d) 0 e π 0 x x x + dx e
³ÎΨÏÀ
2017 12 12 Makoto Nakashima 2017 12 12 1 / 22 2.1. C, D π- C, D. A 1, A 2 C A 1 A 2 C A 3, A 4 D A 1 A 2 D Makoto Nakashima 2017 12 12 2 / 22 . (,, L p - ). Makoto Nakashima 2017 12 12 3 / 22 . (,, L p
(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
°ÌÁê¿ô³ØII
July 14, 2007 Brouwer f f(x) = x x f(z) = 0 2 f : S 2 R 2 f(x) = f( x) x S 2 3 3 2 - - - 1. X x X U(x) U(x) x U = {U(x) x X} X 1. U(x) A U(x) x 2. A U(x), A B B U(x) 3. A, B U(x) A B U(x) 4. A U(x),
ID POS F
01D8101011L 2005 3 ID POS 2 2 1 F 1... 1 2 ID POS... 2 3... 4 3.1...4 3.2...4 3.3...5 3.4 F...5 3.5...6 3.6 2...6 4... 8 4.1...8 4.2...8 4.3...8 4.4...9 4.5...10 5... 12 5.1...12 5.2...13 5.3...15 5.4...17
r 1 m A r/m i) t ii) m i) t B(t; m) ( B(t; m) = A 1 + r ) mt m ii) B(t; m) ( B(t; m) = A 1 + r ) mt m { ( = A 1 + r ) m } rt r m n = m r m n B
1 1.1 1 r 1 m A r/m i) t ii) m i) t Bt; m) Bt; m) = A 1 + r ) mt m ii) Bt; m) Bt; m) = A 1 + r ) mt m { = A 1 + r ) m } rt r m n = m r m n Bt; m) Aert e lim 1 + 1 n 1.1) n!1 n) e a 1, a 2, a 3,... {a n
入試の軌跡
4 y O x 4 Typed by L A TEX ε ) ) ) 6 4 ) 4 75 ) http://kumamoto.s.xrea.com/plan/.. PDF) Ctrl +L) Ctrl +) Ctrl + Ctrl + ) ) Alt + ) Alt + ) ESC. http://kumamoto.s.xrea.com/nyusi/kumadai kiseki ri i.pdf
5 Armitage x 1,, x n y i = 10x i + 3 y i = log x i {x i } {y i } 1.2 n i i x ij i j y ij, z ij i j 2 1 y = a x + b ( cm) x ij (i j )
5 Armitage. x,, x n y i = 0x i + 3 y i = log x i x i y i.2 n i i x ij i j y ij, z ij i j 2 y = a x + b 2 2. ( cm) x ij (i j ) (i) x, x 2 σ 2 x,, σ 2 x,2 σ x,, σ x,2 t t x * (ii) (i) m y ij = x ij /00 y
6.1 (P (P (P (P (P (P (, P (, P.
(011 30 7 0 ( ( 3 ( 010 1 (P.3 1 1.1 (P.4.................. 1 1. (P.4............... 1 (P.15.1 (P.16................. (P.0............3 (P.18 3.4 (P.3............... 4 3 (P.9 4 3.1 (P.30........... 4 3.
II R n k +1 v 0,, v k k v 1 v 0,, v k v v 0,, v k R n 1 a 0,, a k a 0 v 0 + a k v k v 0 v k k k v 0,, v k σ k σ dimσ = k 1.3. k
II 231017 1 1.1. R n k +1 v 0,, v k k v 1 v 0,, v k v 0 1.2. v 0,, v k R n 1 a 0,, a k a 0 v 0 + a k v k v 0 v k k k v 0,, v k σ kσ dimσ = k 1.3. k σ {v 0,...,v k } {v i0,...,v il } l σ τ < τ τ σ 1.4.
renshumondai-kaito.dvi
3 1 13 14 1.1 1 44.5 39.5 49.5 2 0.10 2 0.10 54.5 49.5 59.5 5 0.25 7 0.35 64.5 59.5 69.5 8 0.40 15 0.75 74.5 69.5 79.5 3 0.15 18 0.90 84.5 79.5 89.5 2 0.10 20 1.00 20 1.00 2 1.2 1 16.5 20.5 12.5 2 0.10
X G P G (X) G BG [X, BG] S 2 2 2 S 2 2 S 2 = { (x 1, x 2, x 3 ) R 3 x 2 1 + x 2 2 + x 2 3 = 1 } R 3 S 2 S 2 v x S 2 x x v(x) T x S 2 T x S 2 S 2 x T x S 2 = { ξ R 3 x ξ } R 3 T x S 2 S 2 x x T x S 2
熊本県数学問題正解
00 y O x Typed by L A TEX ε ( ) (00 ) 5 4 4 ( ) http://www.ocn.ne.jp/ oboetene/plan/. ( ) (009 ) ( ).. http://www.ocn.ne.jp/ oboetene/plan/eng.html 8 i i..................................... ( )0... (
SDS099-B1603OB_QuantStudio-3-and-5_PB_12.indd
QuantStudio 3 / QuantStudio 5 PCR PCR Applied Biosystems QuantStudio 3 QuantStudio 5 PCR Thermo Fisher Cloud 1 QuantStudio 3 and 5 Real-Time PCR Systems QuantStudio 3 and 5 Real-Time PCR Systems 2 Applied
i
i 3 4 4 7 5 6 3 ( ).. () 3 () (3) (4) /. 3. 4/3 7. /e 8. a > a, a = /, > a >. () a >, a =, > a > () a > b, a = b, a < b. c c n a n + b n + c n 3c n..... () /3 () + (3) / (4) /4 (5) m > n, a b >, m > n,
6.1 (P (P (P (P (P (P (, P (, P.101
(008 0 3 7 ( ( ( 00 1 (P.3 1 1.1 (P.3.................. 1 1. (P.4............... 1 (P.15.1 (P.15................. (P.18............3 (P.17......... 3.4 (P................ 4 3 (P.7 4 3.1 ( P.7...........
211 kotaro@math.titech.ac.jp 1 R *1 n n R n *2 R n = {(x 1,..., x n ) x 1,..., x n R}. R R 2 R 3 R n R n R n D D R n *3 ) (x 1,..., x n ) f(x 1,..., x n ) f D *4 n 2 n = 1 ( ) 1 f D R n f : D R 1.1. (x,
1 911 9001030 9:00 A B C D E F G H I J K L M 1A0900 1B0900 1C0900 1D0900 1E0900 1F0900 1G0900 1H0900 1I0900 1J0900 1K0900 1L0900 1M0900 9:15 1A0915 1B0915 1C0915 1D0915 1E0915 1F0915 1G0915 1H0915 1I0915
1. A0 A B A0 A : A1,...,A5 B : B1,...,B
1. A0 A B A0 A : A1,...,A5 B : B1,...,B12 2. 3. 4. 5. A0 A, B Z Z m, n Z m n m, n A m, n B m=n (1) A, B (2) A B = A B = Z/ π : Z Z/ (3) A B Z/ (4) Z/ A, B (5) f : Z Z f(n) = n f = g π g : Z/ Z A, B (6)
I L01( Wed) : Time-stamp: Wed 07:38 JST hig e, ( ) L01 I(2017) 1 / 19
I L01(2017-09-20 Wed) : Time-stamp: 2017-09-20 Wed 07:38 JST hig e, http://hig3.net ( ) L01 I(2017) 1 / 19 ? 1? 2? ( ) L01 I(2017) 2 / 19 ?,,.,., 1..,. 1,2,.,.,. ( ) L01 I(2017) 3 / 19 ? I. M (3 ) II,
PG1501-PJ7816-CO36363-QuantStudio-3-and-5-brochure-Global-J.indd
Applied Biosystems QuantStudio 3 / QuantStudio 5 PCR PCR Applied Biosystems QuantStudio 3 QuantStudio 5 PCR Thermo Fisher Cloud 1 QuantStudio 3 and 5 Real-Time PCR Systems QuantStudio 3 and 5 Real-Time
70 : 20 : A B (20 ) (30 ) 50 1
70 : 0 : A B (0 ) (30 ) 50 1 1 4 1.1................................................ 5 1. A............................................... 6 1.3 B............................................... 7 8.1 A...............................................
2012 A, N, Z, Q, R, C
2012 A, N, Z, Q, R, C 1 2009 9 2 2011 2 3 2012 9 1 2 2 5 3 11 4 16 5 22 6 25 7 29 8 32 1 1 1.1 3 1 1 1 1 1 1? 3 3 3 3 3 3 3 1 1, 1 1 + 1 1 1+1 2 2 1 2+1 3 2 N 1.2 N (i) 2 a b a 1 b a < b a b b a a b (ii)
B 02 Pocket Page Weekly 07 August 2015 No. 499
INDEX B 02 Pocket Page Weekly 07 August 2015 No. 499 Pocket Page Weekly 07 August 2015 No. 499 B 03 B 04 Pocket Page Weekly 07 August 2015 No. 499 B 06 Pocket Page Weekly 07 August 2015 No. 499 Pocket
特許侵害訴訟における無効の主張を認めた判決─半導体装置事件−
[*1847] 12 4 11 10 364 54 4 1368 1710 68 1032 120 X Y 6.8.31 29 3 875 X Y 9.9.10 29 3 819 Y 320275 391468 46 12 21 35 2 6 3513745 39 1 30 320249 1) 1 39 1 [*1848] 2) 3) Y 10 51 2 4 39 5 39 1 3 139 7 2
( 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
A b a B AaBb Ab ab 1 1 AB ab A-b a-b 2.Meiosis recombination Meiosis mitosis crossover recombination bivalent DNA 2
遺 伝 と 遺 伝 子 2007 年 度 参 考 問 題 リストの 解 答 例 xxax2002@yahoo.co.jp 2007 50 50 1. Mendel s second law of inheritance 2006 2006 A B A B Mendel s second law of inheritance principle of independent segregation P
..3. Ω, Ω F, P Ω, F, P ). ) F a) A, A,..., A i,... F A i F. b) A F A c F c) Ω F. ) A F A P A),. a) 0 P A) b) P Ω) c) [ ] A, A,..., A i,... F i j A i A
![..3. Ω, Ω F, P Ω, F, P ). ) F a) A, A,..., A i,... F A i F. b) A F A c F c) Ω F. ) A F A P A),. a) 0 P A) b) P Ω) c) [ ] A, A,..., A i,... F i j A i A](/thumbs/93/112175219.jpg "..3. Ω, Ω F, P Ω, F, P ). ) F a) A, A,..., A i,... F A i F. b) A F A c F c) Ω F. ) A F A P A),. a) 0 P A) b) P Ω) c) [ ] A, A,..., A i,... F i j A i A")
.. Laplace ). A... i),. ω i i ). {ω,..., ω } Ω,. ii) Ω. Ω. A ) r, A P A) P A) r... ).. Ω {,, 3, 4, 5, 6}. i i 6). A {, 4, 6} P A) P A) 3 6. ).. i, j i, j) ) Ω {i, j) i 6, j 6}., 36. A. A {i, j) i j }.
A B P (A B) = P (A)P (B) (3) A B A B P (B A) A B A B P (A B) = P (B A)P (A) (4) P (B A) = P (A B) P (A) (5) P (A B) P (B A) P (A B) A B P
1 1.1 (population) (sample) (event) (trial) Ω () 1 1 Ω 1.2 P 1. A A P (A) 0 1 0 P (A) 1 (1) 2. P 1 P 0 1 6 1 1 6 0 3. A B P (A B) = P (A) + P (B) (2) A B A B A 1 B 2 A B 1 2 1 2 1 1 2 2 3 1.3 A B P (A
untitled
17 5 13 1 2 1.1... 2 1.2... 2 1.3... 3 2 3 2.1... 3 2.2... 5 3 6 3.1... 6 3.2... 7 3.3 t... 7 3.4 BC a... 9 3.5... 10 4 11 1 1 θ n ˆθ. ˆθ, ˆθ, ˆθ.,, ˆθ.,.,,,. 1.1 ˆθ σ 2 = E(ˆθ E ˆθ) 2 b = E(ˆθ θ). Y 1,,Y
NDIS ( )
NDIS 3429 2010 8 25 () mail:ohnishi@jsndi.or.jp NDIS 3429:XXXX Method for Investigating Location of Reinforcing Bars in Concrete Structure by Radar 1 1) 1) 2 JIS A 0203 JIS G 3112 JIS G 3117 JIS Z 2300
情報理論 第5回 情報量とエントロピー
5 () ( ) ( ) ( ) p(a) a I(a) p(a) p(a) I(a) p(a) I(a) (2) (self information) p(a) = I(a) = 0 I(a) = 0 I(a) a I(a) = log 2 p(a) = log 2 p(a) bit 2 (log 2 ) (3) I(a) 7 6 5 4 3 2 0 0.5 p(a) p(a) = /2 I(a)
1990 IMO 1990/1/15 1:00-4:00 1 N N N 1, N 1 N 2, N 2 N 3 N 3 2 x x + 52 = 3 x x , A, B, C 3,, A B, C 2,,,, 7, A, B, C
0 9 (1990 1999 ) 10 (2000 ) 1900 1994 1995 1999 2 SAT ACT 1 1990 IMO 1990/1/15 1:00-4:00 1 N 1990 9 N N 1, N 1 N 2, N 2 N 3 N 3 2 x 2 + 25x + 52 = 3 x 2 + 25x + 80 3 2, 3 0 4 A, B, C 3,, A B, C 2,,,, 7,
(1.2) T D = 0 T = D = 30 kn 1.2 (1.4) 2F W = 0 F = W/2 = 300 kn/2 = 150 kn 1.3 (1.9) R = W 1 + W 2 = = 1100 N. (1.9) W 2 b W 1 a = 0
1 1 1.1 1.) T D = T = D = kn 1. 1.4) F W = F = W/ = kn/ = 15 kn 1. 1.9) R = W 1 + W = 6 + 5 = 11 N. 1.9) W b W 1 a = a = W /W 1 )b = 5/6) = 5 cm 1.4 AB AC P 1, P x, y x, y y x 1.4.) P sin 6 + P 1 sin 45
B's Recorderマニュアル_B's Recorderマニュアル
5 Part 6 - 8 9 - 0 5 A C B AB A B A B C 7-6 - 8 9-5 0 5 7 A D B C E F A B C D F E 6 9 8 0 Part - - 5 5 7 6 9-7 6 8 0 5 5-6 7 9 8 5-5 50 5 5 5 -6 5 55 5 57-7 56 59 8 7 6 58 0 8 9 6 6 7 6 5 60 7 5 6 6-8
B's Recorderマニュアル
2 3 4 5 Part 1 6 1-1 8 9 1-2 10 11 12 13 A B C A C B AB A B 14 15 17 1-4 2 1 16 1-3 18 19 1-5 2 1 20 21 22 23 24 25 A B C D E F A B C D E F 26 27 28 29 30 31 Part 2 32 2-1 2-2 1 2 34 35 5 37 4 3 36 6 2-3
18 ( ) I II III A B C(100 ) 1, 2, 3, 5 I II A B (100 ) 1, 2, 3 I II A B (80 ) 6 8 I II III A B C(80 ) 1 n (1 + x) n (1) n C 1 + n C
8 ( ) 8 5 4 I II III A B C( ),,, 5 I II A B ( ),, I II A B (8 ) 6 8 I II III A B C(8 ) n ( + x) n () n C + n C + + n C n = 7 n () 7 9 C : y = x x A(, 6) () A C () C P AP Q () () () 4 A(,, ) B(,, ) C(,,
2 1 Introduction
1 24 11 26 1 E-mail: toyoizumi@waseda.jp 2 1 Introduction 5 1.1...................... 7 2 8 2.1................ 8 2.2....................... 8 2.3............................ 9 3 10 3.1.........................
.1 A cos 2π 3 sin 2π 3 sin 2π 3 cos 2π 3 T ra 2 deta T ra 2 deta T ra 2 deta a + d 2 ad bc a 2 + d 2 + ad + bc A 3 a b a 2 + bc ba + d c d ca + d bc +
.1 n.1 1 A T ra A A a b c d A 2 a b a b c d c d a 2 + bc ab + bd ac + cd bc + d 2 a 2 + bc ba + d ca + d bc + d 2 A a + d b c T ra A T ra A 2 A 2 A A 2 A 2 A n A A n cos 2π sin 2π n n A k sin 2π cos 2π
Chapter16
16 Flat Clustering (cluster) 16.1 (unsupervised learning) 16.1 3 17 (13 237 ) (distance measure) 16.1 2 3 (flat clustering) (hierarchical clustering) 17 17 2 (hard) (soft) (Latent semantic indexing) (18
.3. (x, x = (, u = = 4 (, x x = 4 x, x 0 x = 0 x = 4 x.4. ( z + z = 8 z, z 0 (z, z = (0, 8, (,, (8, 0 3 (0, 8, (,, (8, 0 z = z 4 z (g f(x = g(
06 5.. ( y = x x y 5 y 5 = (x y = x + ( y = x + y = x y.. ( Y = C + I = 50 + 0.5Y + 50 r r = 00 0.5Y ( L = M Y r = 00 r = 0.5Y 50 (3 00 0.5Y = 0.5Y 50 Y = 50, r = 5 .3. (x, x = (, u = = 4 (, x x = 4 x,
p-sylow :
p-sylow :15114075 30 2 20 1 2 1.1................................... 2 1.2.................................. 2 1.3.................................. 3 2 3 2.1................................... 3 2.2................................
1. A0 A B A0 A : A1,...,A5 B : B1,...,B
1. A0 A B A0 A : A1,...,A5 B : B1,...,B12 2. 3. 4. 5. A0 A B f : A B 4 (i) f (ii) f (iii) C 2 g, h: C A f g = f h g = h (iv) C 2 g, h: B C g f = h f g = h 4 (1) (i) (iii) (2) (iii) (i) (3) (ii) (iv) (4)
IA 2013 : :10722 : 2 : :2 :761 :1 (23-27) : : ( / ) (1 /, ) / e.g. (Taylar ) e x = 1 + x + x xn n! +... sin x = x x3 6 + x5 x2n+1 + (
IA 2013 : :10722 : 2 : :2 :761 :1 23-27) : : 1 1.1 / ) 1 /, ) / e.g. Taylar ) e x = 1 + x + x2 2 +... + xn n! +... sin x = x x3 6 + x5 x2n+1 + 1)n 5! 2n + 1)! 2 2.1 = 1 e.g. 0 = 0.00..., π = 3.14..., 1
10:30 12:00 P.G. vs vs vs 2
1 10:30 12:00 P.G. vs vs vs 2 LOGIT PROBIT TOBIT mean median mode CV 3 4 5 0.5 1000 6 45 7 P(A B) = P(A) + P(B) - P(A B) P(B A)=P(A B)/P(A) P(A B)=P(B A) P(A) P(A B) P(A) P(B A) P(B) P(A B) P(A) P(B) P(B
9. 05 L x P(x) P(0) P(x) u(x) u(x) (0 < = x < = L) P(x) E(x) A(x) P(L) f ( d EA du ) = 0 (9.) dx dx u(0) = 0 (9.2) E(L)A(L) du (L) = f (9.3) dx (9.) P
9 (Finite Element Method; FEM) 9. 9. P(0) P(x) u(x) (a) P(L) f P(0) P(x) (b) 9. P(L) 9. 05 L x P(x) P(0) P(x) u(x) u(x) (0 < = x < = L) P(x) E(x) A(x) P(L) f ( d EA du ) = 0 (9.) dx dx u(0) = 0 (9.2) E(L)A(L)
() n C + n C + n C + + n C n n (3) n C + n C + n C 4 + n C + n C 3 + n C 5 + (5) (6 ) n C + nc + 3 nc n nc n (7 ) n C + nc + 3 nc n nc n (
3 n nc k+ k + 3 () n C r n C n r nc r C r + C r ( r n ) () n C + n C + n C + + n C n n (3) n C + n C + n C 4 + n C + n C 3 + n C 5 + (4) n C n n C + n C + n C + + n C n (5) k k n C k n C k (6) n C + nc
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
ORIGINAL TEXT I II A B 1 4 13 21 27 44 54 64 84 98 113 126 138 146 165 175 181 188 198 213 225 234 244 261 268 273 2 281 I II A B 292 3 I II A B c 1 1 (1) x 2 + 4xy + 4y 2 x 2y 2 (2) 8x 2 + 16xy + 6y 2
tokei01.dvi
2. :,,,. :.... Apr. - Jul., 26FY Dept. of Mechanical Engineering, Saga Univ., JAPAN 4 3. (probability),, 1. : : n, α A, A a/n. :, p, p Apr. - Jul., 26FY Dept. of Mechanical Engineering, Saga Univ., JAPAN
I, II 1, A = A 4 : 6 = max{ A, } A A 10 10%
1 2006.4.17. A 3-312 tel: 092-726-4774, e-mail: hara@math.kyushu-u.ac.jp, http://www.math.kyushu-u.ac.jp/ hara/lectures/lectures-j.html Office hours: B A I ɛ-δ ɛ-δ 1. 2. A 1. 1. 2. 3. 4. 5. 2. ɛ-δ 1. ɛ-n
2
1 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234 12123456789012345678901234
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..................................................
untitled
1 n m (ICA = independent component analysis) BSS (= blind source separation) : s(t) =(s 1 (t),...,s n (t)) R n : x(t) =(x 1 (t),...,x n (t)) R m 1 i s i (t) a ji R j 2 (A =(a ji )) x(t) =As(t) (1) n =
RM-P1000 (B)
RM-P1000 (B) HDR /HDR LST0502-001B A AB AB AB AB A B AB A B AB 2 _ _ 3 A B 4 J I H G F E D C B A HDR K L M N O P Q / HDR b a R STU V W X Y Z A A B B A AB C AB A : A B A D A : E A B A B F E G A A 5 J I
,, Poisson 3 3. t t y,, y n Nµ, σ 2 y i µ + ɛ i ɛ i N0, σ 2 E[y i ] µ * i y i x i y i α + βx i + ɛ i ɛ i N0, σ 2, α, β *3 y i E[y i ] α + βx i
![,, Poisson 3 3. t t y,, y n Nµ, σ 2 y i µ + ɛ i ɛ i N0, σ 2 E[y i ] µ * i y i x i y i α + βx i + ɛ i ɛ i N0, σ 2, α, β *3 y i E[y i ] α + βx i](/thumbs/87/95421301.jpg ",, Poisson 3 3. t t y,, y n Nµ, σ 2 y i µ + ɛ i ɛ i N0, σ 2 E[y i ] µ * i y i x i y i α + βx i + ɛ i ɛ i N0, σ 2, α, β *3 y i E[y i ] α + βx i")
Armitage.? SAS.2 µ, µ 2, µ 3 a, a 2, a 3 a µ + a 2 µ 2 + a 3 µ 3 µ, µ 2, µ 3 µ, µ 2, µ 3 log a, a 2, a 3 a µ + a 2 µ 2 + a 3 µ 3 µ, µ 2, µ 3 * 2 2. y t y y y Poisson y * ,, Poisson 3 3. t t y,, y n Nµ,
<4D F736F F D B B83578B6594BB2D834A836F815B82D082C88C60202E646F63>
電気電子数学入門 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/073471 このサンプルページの内容は, 初版 1 刷発行当時のものです. i 14 (tool) [ ] IT ( ) PC (EXCEL) HP() 1 1 4 15 3 010 9 ii 1... 1 1.1 1 1.
n ( (
1 2 27 6 1 1 m-mat@mathscihiroshima-uacjp 2 http://wwwmathscihiroshima-uacjp/~m-mat/teach/teachhtml 2 1 3 11 3 111 3 112 4 113 n 4 114 5 115 5 12 7 121 7 122 9 123 11 124 11 125 12 126 2 2 13 127 15 128
AJACS18_ ppt
1, 1, 1, 1, 1, 1,2, 1,2, 1 1 DDBJ 2 AJACS3 2010 6 414:20-15:20 2231 DDBJ DDBJ DDBJ DDBJ NCBI (GenBank) DDBJ EBI (EMBL-Bank) GEO DDBJ Omics ARchive(DOR) ArrayExpress DTA (DDBJ Trace Archive) DRA (DDBJ
D xy D (x, y) z = f(x, y) f D (2 ) (x, y, z) f R z = 1 x 2 y 2 {(x, y); x 2 +y 2 1} x 2 +y 2 +z 2 = 1 1 z (x, y) R 2 z = x 2 y
5 5. 2 D xy D (x, y z = f(x, y f D (2 (x, y, z f R 2 5.. z = x 2 y 2 {(x, y; x 2 +y 2 } x 2 +y 2 +z 2 = z 5.2. (x, y R 2 z = x 2 y + 3 (2,,, (, 3,, 3 (,, 5.3 (. (3 ( (a, b, c A : (x, y, z P : (x, y, x
0226_ぱどMD表1-ol前
No. MEDIA DATA 0 B O O K 00-090-0 0 000900 000 00 00 00 0000 0900 000900 AREA MAP 0,000 0,000 0,000 0,000 00,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 00,000 0,000
6. Euler x
...............................................................................3......................................... 4.4................................... 5.5......................................
() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi)
0. A A = 4 IC () det A () A () x + y + z = x y z X Y Z = A x y z ( 5) ( s5590) 0. a + b + c b c () a a + b + c c a b a + b + c 0 a b c () a 0 c b b c 0 a c b a 0 0. A A = 7 5 4 5 0 ( 5) ( s5590) () A ()
Solutions to Quiz 1 (April 20, 2007) 1. P, Q, R (P Q) R Q (P R) P Q R (P Q) R Q (P R) X T T T T T T T T T T F T F F F T T F T F T T T T T F F F T T F
Quiz 1 Due at 10:00 a.m. on April 20, 2007 Division: ID#: Name: 1. P, Q, R (P Q) R Q (P R) P Q R (P Q) R Q (P R) X T T T T T T F T T F T T T F F T F T T T F T F T F F T T F F F T 2. 1.1 (1) (7) p.44 (1)-(4)
ii 3.,. 4. F. ( ), ,,. 8.,. 1. (75% ) (25% ) =7 24, =7 25, =7 26 (. ). 1.,, ( ). 3.,...,.,.,.,.,. ( ) (1 2 )., ( ), 0., 1., 0,.
(1 C205) 4 10 (2 C206) 4 11 (2 B202) 4 12 25(2013) http://www.math.is.tohoku.ac.jp/~obata,.,,,..,,. 1. 2. 3. 4. 5. 6. 7. 8. 1., 2007 ( ).,. 2. P. G., 1995. 3. J. C., 1988. 1... 2.,,. ii 3.,. 4. F. ( ),..
卓球の試合への興味度に関する確率論的分析
17 i 1 1 1.1..................................... 1 1.2....................................... 1 1.3..................................... 2 2 5 2.1................................ 5 2.2 (1).........................
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
& 3 3 ' ' (., (Pixel), (Light Intensity) (Random Variable). (Joint Probability). V., V = {,,, V }. i x i x = (x, x,, x V ) T. x i i (State Variable),
.... Deeping and Expansion of Large-Scale Random Fields and Probabilistic Image Processing Kazuyuki Tanaka The mathematical frameworks of probabilistic image processing are formulated by means of Markov
( ) 2002 1 1 1 1.1....................................... 1 1.1.1................................. 1 1.1.2................................. 1 1.1.3................... 3 1.1.4......................................
Otsuma Nakano Senior High School Spring Seminar Mathematics B
Otsuma Nakano Senior High School Spring Seminar Mathematics B 2 a d a n = a + (n 1)d 1 2 ( ) {( ) + ( )} = n 2 {2a + (n 1)d} a r a n = ar n 1 a { r ( ) 1 } r 1 = a { 1 r ( )} 1 r (r 1) n 1 = n k=1 n k
2009 I 2 II III 14, 15, α β α β l 0 l l l l γ (1) γ = αβ (2) α β n n cos 2k n n π sin 2k n π k=1 k=1 3. a 0, a 1,..., a n α a
009 I II III 4, 5, 6 4 30. 0 α β α β l 0 l l l l γ ) γ αβ ) α β. n n cos k n n π sin k n π k k 3. a 0, a,..., a n α a 0 + a x + a x + + a n x n 0 ᾱ 4. [a, b] f y fx) y x 5. ) Arcsin 4) Arccos ) ) Arcsin
(4) P θ P 3 P O O = θ OP = a n P n OP n = a n {a n } a = θ, a n = a n (n ) {a n } θ a n = ( ) n θ P n O = a a + a 3 + ( ) n a n a a + a 3 + ( ) n a n
3 () 3,,C = a, C = a, C = b, C = θ(0 < θ < π) cos θ = a + (a) b (a) = 5a b 4a b = 5a 4a cos θ b = a 5 4 cos θ a ( b > 0) C C l = a + a + a 5 4 cos θ = a(3 + 5 4 cos θ) C a l = 3 + 5 4 cos θ < cos θ < 4
y π π O π x 9 s94.5 y dy dx. y = x + 3 y = x logx + 9 s9.6 z z x, z y. z = xy + y 3 z = sinx y 9 s x dx π x cos xdx 9 s93.8 a, fx = e x ax,. a =
[ ] 9 IC. dx = 3x 4y dt dy dt = x y u xt = expλt u yt λ u u t = u u u + u = xt yt 6 3. u = x, y, z = x + y + z u u 9 s9 grad u ux, y, z = c c : grad u = u x i + u y j + u k i, j, k z x, y, z grad u v =
浜松医科大学紀要
On the Statistical Bias Found in the Horse Racing Data (1) Akio NODA Mathematics Abstract: The purpose of the present paper is to report what type of statistical bias the author has found in the horse
5 n P j j (P i,, P k, j 1) 1 n n ) φ(n) = n (1 1Pj [ ] φ φ P j j P j j = = = = = n = φ(p j j ) (P j j P j 1 j ) P j j ( 1 1 P j ) P j j ) (1 1Pj (1 1P
![5 n P j j (P i,, P k, j 1) 1 n n ) φ(n) = n (1 1Pj [ ] φ φ P j j P j j = = = = = n = φ(p j j ) (P j j P j 1 j ) P j j ( 1 1 P j ) P j j ) (1 1Pj (1 1P](/thumbs/90/103736623.jpg "5 n P j j (P i,, P k, j 1) 1 n n ) φ(n) = n (1 1Pj [ ] φ φ P j j P j j = = = = = n = φ(p j j ) (P j j P j 1 j ) P j j ( 1 1 P j ) P j j ) (1 1Pj (1 1P")
p P 1 n n n 1 φ(n) φ φ(1) = 1 1 n φ(n), n φ(n) = φ()φ(n) [ ] n 1 n 1 1 n 1 φ(n) φ() φ(n) 1 3 4 5 6 7 8 9 1 3 4 5 6 7 8 9 1 4 5 7 8 1 4 5 7 8 10 11 1 13 14 15 16 17 18 19 0 1 3 4 5 6 7 19 0 1 3 4 5 6 7
newmain.dvi
数論 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/008142 このサンプルページの内容は, 第 2 版 1 刷発行当時のものです. Daniel DUVERNEY: THÉORIE DES NOMBRES c Dunod, Paris, 1998, This book is published
1 1 3 ABCD ABD AC BD E E BD 1 : 2 (1) AB = AD =, AB AD = (2) AE = AB + (3) A F AD AE 2 = AF = AB + AD AF AE = t AC = t AE AC FC = t = (4) ABD ABCD 1 1
ABCD ABD AC BD E E BD : () AB = AD =, AB AD = () AE = AB + () A F AD AE = AF = AB + AD AF AE = t AC = t AE AC FC = t = (4) ABD ABCD AB + AD AB + 7 9 AD AB + AD AB + 9 7 4 9 AD () AB sin π = AB = ABD AD
DVIOUT
A. A. A-- [ ] f(x) x = f 00 (x) f 0 () =0 f 00 () > 0= f(x) x = f 00 () < 0= f(x) x = A--2 [ ] f(x) D f 00 (x) > 0= y = f(x) f 00 (x) < 0= y = f(x) P (, f()) f 00 () =0 A--3 [ ] y = f(x) [, b] x = f (y)