19 Systematization of Problem Solving Strategy in High School Mathematics for Improving Metacognitive Ability

Size: px
Start display at page:

Download "19 Systematization of Problem Solving Strategy in High School Mathematics for Improving Metacognitive Ability"

Transcription

1 19 Systematization of Problem Solving Strategy in High School Mathematics for Improving Metacognitive Ability

2 2,, i

3 Abstract Systematization of Problem Solving Strategy in High School Mathematics for Improving Metacognitive Ability Shinichirou KAWASHIMA The purpose of mathematics education is to raise students ability to solve unknown problems using their known formulas and solution patterns. In order to realize this purpose, it is important for students to solve problems heuristically. Because it is not easy for students themselves to solve problems heuristically, appropriate support is necessary. Problem solving is promoted by appropriate hints based on problem solving strategy. The problem solving strategy consists of the strategy of problem solving independent of subject domain, and the strategy of problem solving depending on subject domain and the knowledge about subject domain. In this research, in order to aim at improvement in metacognitive ability paying attention to metacognition, the model of problem solving is proposed first and problem solving strategy is systematized. Next, the trial production system which generates a hint from systematized problem solving strategy for the quadratic function of high school mathematics is described. key words Metacognition, The strategy of problem solving, Ontology ii

4 iii

5 MathML iv

6 MathML v

7 vi

8 1 [1]

9 [2] 2 2

10 [3] 2.2 [3] Thorndike,E.L. 3

11 Köhler,W. Wertheimer,M (1) (2) (3) (4) problem space problem representation search 4

12 2.3 [3] 2.3 metacognition A. Brown J. H. Flavell 1970 meta-cognitive knowledge metacognitive activity 3 2 awareness feeling prediction checking goal setting planning revision [4] 5

13

14

15 [5] 1. Understanding the Problem UP 2. Devising a Plan DP 3. Carrying out the Plan CP 4. Looking Back LB [3]

16

17 ( 3, 0) (2, 0) (1, 12)

18 y = ax 2 + bx + c y = a(x p) 2 + q 2 2 y = a(x p) 2 + q y = ax 2 + bx + c 3 a b c a b c a b c y = ax 2 + bx + c ( 3, 0) 1 y = ax 2 + bx + c ( 3, 0) 0 9a 3b + c

19

20 [2]

21

22

23 4 4.1 [6] (Conceptualization) / [7] 16

24 4.1 ( ) 17

25 (1) (2) (3) y = ax

26 a < b a + c < b + c, a c < b c 2. a < b, m > 0 ma < mb, 3. a < b, m < 0 ma > mb, a m < b m a m > b m x 2 = k k > x 2 = k x = ± k ax 2 + bx + c = 0 D = b 2 4ac D 0 x = b ± b 2 4ac 2a D x 2 + kx = (x + k 2 )2 k2 4 y = ax 2 + bx + c y = ax 2 + bx + c y = ax 2 x = b b ( 2a 2a, b2 4ac ) 4a 0 0 D = b 2 4ac 19

27 ax = b a y = ax 2 + bx + c 1 2 y = a(x p) 2 + q 2 y = ax 2 + bx + c 1 2 y = a(x p) 2 + q y = ax 2 + bx + c x ax 2 + bx + c =

28 ,12,13,24 4 UP P (x, y) x, y 4. 21

29 a, b, c y dy dx 6. DP 7. (a + b + c)(bc + ca + ab) abc x, y x + y xy

30 sin θ cos θ P (x, y) CP LB

31 s2: 2 3 ( 3, 0) (2, 0) (1, 12) 2 s1 : s2 : s5 : y x f y = f(x) 2 s6 : s11: 2 y = ax 2 + bx + c y = a(x p) 2 + q y = a(x p) 2 + q s8 : y = f(x) (1) (a, b) x = a, y = b (1) b = f(a) 24

32 4.4 s12: y = ax 2 +bx+c ( 3, 0) y = ax 2 +bx+c ( 3, 0) 0 = 9a 3b + c 9a 3b + c = 0 (2, 0) 4a + 2b + c = 0 (1, 12) a + b + c = 12 s23: s24: s25: s26: 2 ( 3, 0) (2, 0) 2 (α, 0), (β, 0) 2 y = a(x α)(x β) 2 y = a(x + 3)(x 2) (1, 12) a s27: (1) a b + c = 7, c = 2, a + b + c = 5 a = 3, b = 6, c = 2 (2) a + b + c = 4, 9a + 3b + c = 6, 4a 2b + c = 16 a = 1, b = 3, c = 6 25

33 MathML MathML[8] MathML XML W3C MathML2.0 MathML 2 MathML XML MathML XHTML Web XML 26

34 SVG XHTML+MathML+SVG MathML Mathematica XHTML Web (Mozilla/Netscape 7 )[9] Web PHP Java JavaScript Web PC MathML

35 MathML MathML 28

36

37

38 (1) (2) 31

39 6.4 (3) (4) (1) 2 1 (2) (3)

40 6.5 (1) 1 (2) (3) 33

41 7 2 34

42

43 [1] [2],, ( (C)(1)) ; [3] [4], [5].,,,1975. [6],,, Vol.12, No.4, pp ,1997. [7], [8] W3C Math Home [9] IT e-words 36

> > <., vs. > x 2 x y = ax 2 + bx + c y = 0 2 ax 2 + bx + c = 0 y = 0 x ( x ) y = ax 2 + bx + c D = b 2 4ac (1) D > 0 x (2) D = 0 x (3

> > <., vs. > x 2 x y = ax 2 + bx + c y = 0 2 ax 2 + bx + c = 0 y = 0 x ( x ) y = ax 2 + bx + c D = b 2 4ac (1) D > 0 x (2) D = 0 x (3 13 2 13.0 2 ( ) ( ) 2 13.1 ( ) ax 2 + bx + c > 0 ( a, b, c ) ( ) 275 > > 2 2 13.3 x 2 x y = ax 2 + bx + c y = 0 2 ax 2 + bx + c = 0 y = 0 x ( x ) y = ax 2 + bx + c D = b 2 4ac (1) D >

More information

6 2 2 x y x y t P P = P t P = I P P P ( ) ( ) ,, ( ) ( ) cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ y x θ x θ P

6 2 2 x y x y t P P = P t P = I P P P ( ) ( ) ,, ( ) ( ) cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ y x θ x θ P 6 x x 6.1 t P P = P t P = I P P P 1 0 1 0,, 0 1 0 1 cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ x θ x θ P x P x, P ) = t P x)p ) = t x t P P ) = t x = x, ) 6.1) x = Figure 6.1 Px = x, P=, θ = θ P

More information

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

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(,,

More information

SOM SOM(Self-Organizing Maps) SOM SOM SOM SOM SOM SOM i

SOM SOM(Self-Organizing Maps) SOM SOM SOM SOM SOM SOM i 20 SOM Development of Syllabus Vsualization System using Spherical Self-Organizing Maps 1090366 2009 3 5 SOM SOM(Self-Organizing Maps) SOM SOM SOM SOM SOM SOM i Abstract Development of Syllabus Vsualization

More information

Web Web Web Web Web, i

Web Web Web Web Web, i 22 Web Research of a Web search support system based on individual sensitivity 1135117 2011 2 14 Web Web Web Web Web, i Abstract Research of a Web search support system based on individual sensitivity

More information

,,,,., C Java,,.,,.,., ,,.,, i

,,,,., C Java,,.,,.,., ,,.,, i 24 Development of the programming s learning tool for children be derived from maze 1130353 2013 3 1 ,,,,., C Java,,.,,.,., 1 6 1 2.,,.,, i Abstract Development of the programming s learning tool for children

More information

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

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

More information

Web Web Web Web i

Web Web Web Web i 28 Research of password manager using pattern lock and user certificate 1170369 2017 2 28 Web Web Web Web i Abstract Research of password manager using pattern lock and user certificate Takuya Mimoto In

More information

() 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)

() 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 ()

More information

26 Development of Learning Support System for Fixation of Basketball Shoot Form

26 Development of Learning Support System for Fixation of Basketball Shoot Form 26 Development of Learning Support System for Fixation of Basketball Shoot Form 1175094 ,.,,.,,.,,.,,,.,,,,.,,,.,,,,, Kinect i Abstract Development of Learning Support System for Fixation of Basketball

More information

1 12 ( )150 ( ( ) ) x M x 0 1 M 2 5x 2 + 4x + 3 x 2 1 M x M 2 1 M x (x + 1) 2 (1) x 2 + x + 1 M (2) 1 3 M (3) x 4 +

1 12 ( )150 ( ( ) ) x M x 0 1 M 2 5x 2 + 4x + 3 x 2 1 M x M 2 1 M x (x + 1) 2 (1) x 2 + x + 1 M (2) 1 3 M (3) x 4 + ( )5 ( ( ) ) 4 6 7 9 M M 5 + 4 + M + M M + ( + ) () + + M () M () 4 + + M a b y = a + b a > () a b () y V a () V a b V n f() = n k= k k () < f() = log( ) t dt log () n+ (i) dt t (n + ) (ii) < t dt n+ n

More information

) ,

) , Vol. 2, 1 17, 2013 1986 A study about the development of the basic policy in the field of reform of China s sports system 1986 HaoWen Wu Abstract: This study focuses on the development of the basic policy

More information

function2.pdf

function2.pdf 2... 1 2009, http://c-faculty.chuo-u.ac.jp/ nishioka/ 2 11 38 : 5) i) [], : 84 85 86 87 88 89 1000 ) 13 22 33 56 92 147 140 120 100 80 60 40 20 1 2 3 4 5 7.1 7 7.1 1. *1 e = 2.7182 ) fx) e x, x R : 7.1)

More information

1 (1) ( i ) 60 (ii) 75 (iii) 315 (2) π ( i ) (ii) π (iii) 7 12 π ( (3) r, AOB = θ 0 < θ < π ) OAB A 2 OB P ( AB ) < ( AP ) (4) 0 < θ < π 2 sin θ

1 (1) ( i ) 60 (ii) 75 (iii) 315 (2) π ( i ) (ii) π (iii) 7 12 π ( (3) r, AOB = θ 0 < θ < π ) OAB A 2 OB P ( AB ) < ( AP ) (4) 0 < θ < π 2 sin θ 1 (1) ( i ) 60 (ii) 75 (iii) 15 () ( i ) (ii) 4 (iii) 7 1 ( () r, AOB = θ 0 < θ < ) OAB A OB P ( AB ) < ( AP ) (4) 0 < θ < sin θ < θ < tan θ 0 x, 0 y (1) sin x = sin y (x, y) () cos x cos y (x, y) 1 c

More information

20 Method for Recognizing Expression Considering Fuzzy Based on Optical Flow

20 Method for Recognizing Expression Considering Fuzzy Based on Optical Flow 20 Method for Recognizing Expression Considering Fuzzy Based on Optical Flow 1115084 2009 3 5 3.,,,.., HCI(Human Computer Interaction),.,,.,,.,.,,..,. i Abstract Method for Recognizing Expression Considering

More information

IT,, i

IT,, i 22 Retrieval support system using bookmarks that are shared in an organization 1110250 2011 3 17 IT,, i Abstract Retrieval support system using bookmarks that are shared in an organization Yoshihiko Komaki

More information

x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x

x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x [ ] IC. f(x) = e x () f(x) f (x) () lim f(x) lim f(x) x + x (3) lim f(x) lim f(x) x + x (4) y = f(x) ( ) ( s46). < a < () a () lim a log xdx a log xdx ( ) n (3) lim log k log n n n k=.3 z = log(x + y ),

More information

udc-2.dvi

udc-2.dvi 13 0.5 2 0.5 2 1 15 2001 16 2009 12 18 14 No.39, 2010 8 2009b 2009a Web Web Q&A 2006 2007a20082009 2007b200720082009 20072008 2009 2009 15 1 2 2 2.1 18 21 1 4 2 3 1(a) 1(b) 1(c) 1(d) 1) 18 16 17 21 10

More information

Web Basic Web SAS-2 Web SAS-2 i

Web Basic Web SAS-2 Web SAS-2 i 19 Development of moving image delivery system for elementary school 1080337 2008 3 10 Web Basic Web SAS-2 Web SAS-2 i Abstract Development of moving image delivery system for elementary school Ayuko INOUE

More information

1 29 ( ) I II III A B (120 ) 2 5 I II III A B (120 ) 1, 6 8 I II A B (120 ) 1, 6, 7 I II A B (100 ) 1 OAB A B OA = 2 OA OB = 3 OB A B 2 :

1 29 ( ) I II III A B (120 ) 2 5 I II III A B (120 ) 1, 6 8 I II A B (120 ) 1, 6, 7 I II A B (100 ) 1 OAB A B OA = 2 OA OB = 3 OB A B 2 : 9 ( ) 9 5 I II III A B (0 ) 5 I II III A B (0 ), 6 8 I II A B (0 ), 6, 7 I II A B (00 ) OAB A B OA = OA OB = OB A B : P OP AB Q OA = a OB = b () OP a b () OP OQ () a = 5 b = OP AB OAB PAB a f(x) = (log

More information

n 2 n (Dynamic Programming : DP) (Genetic Algorithm : GA) 2 i

n 2 n (Dynamic Programming : DP) (Genetic Algorithm : GA) 2 i 15 Comparison and Evaluation of Dynamic Programming and Genetic Algorithm for a Knapsack Problem 1040277 2004 2 25 n 2 n (Dynamic Programming : DP) (Genetic Algorithm : GA) 2 i Abstract Comparison and

More information

kut-paper-template.dvi

kut-paper-template.dvi 26 Discrimination of abnormal breath sound by using the features of breath sound 1150313 ,,,,,,,,,,,,, i Abstract Discrimination of abnormal breath sound by using the features of breath sound SATO Ryo

More information

23 Study on Generation of Sudoku Problems with Fewer Clues

23 Study on Generation of Sudoku Problems with Fewer Clues 23 Study on Generation of Sudoku Problems with Fewer Clues 1120254 2012 3 1 9 9 21 18 i Abstract Study on Generation of Sudoku Problems with Fewer Clues Norimasa NASU Sudoku is puzzle a kind of pencil

More information

untitled

untitled yoshi@image.med.osaka-u.ac.jp http://www.image.med.osaka-u.ac.jp/member/yoshi/ II Excel, Mathematica Mathematica Osaka Electro-Communication University (2007 Apr) 09849-31503-64015-30704-18799-390 http://www.image.med.osaka-u.ac.jp/member/yoshi/

More information

JFE.dvi

JFE.dvi ,, Department of Civil Engineering, Chuo University Kasuga 1-13-27, Bunkyo-ku, Tokyo 112 8551, JAPAN E-mail : atsu1005@kc.chuo-u.ac.jp E-mail : kawa@civil.chuo-u.ac.jp SATO KOGYO CO., LTD. 12-20, Nihonbashi-Honcho

More information

i

i 14 i ii iii iv v vi 14 13 86 13 12 28 14 16 14 15 31 (1) 13 12 28 20 (2) (3) 2 (4) (5) 14 14 50 48 3 11 11 22 14 15 10 14 20 21 20 (1) 14 (2) 14 4 (3) (4) (5) 12 12 (6) 14 15 5 6 7 8 9 10 7

More information

06’ÓŠ¹/ŒØŒì

06’ÓŠ¹/ŒØŒì FD. FD FD FD FD FD FD / Plan-Do-See FD FD FD FD FD FD FD FD FD FD FD FD FD FD JABEE FD A. C. A B .. AV .. B Communication Space A FD FD ES FD FD The approach of the lesson improvement in Osaka City University

More information

WebRTC P2P Web Proxy P2P Web Proxy WebRTC WebRTC Web, HTTP, WebRTC, P2P i

WebRTC P2P Web Proxy P2P Web Proxy WebRTC WebRTC Web, HTTP, WebRTC, P2P i 26 WebRTC The data distribution system using browser cache sharing and WebRTC 1150361 2015/02/27 WebRTC P2P Web Proxy P2P Web Proxy WebRTC WebRTC Web, HTTP, WebRTC, P2P i Abstract The data distribution

More information

x = a 1 f (a r, a + r) f(a) r a f f(a) 2 2. (a, b) 2 f (a, b) r f(a, b) r (a, b) f f(a, b)

x = a 1 f (a r, a + r) f(a) r a f f(a) 2 2. (a, b) 2 f (a, b) r f(a, b) r (a, b) f f(a, b) 2011 I 2 II III 17, 18, 19 7 7 1 2 2 2 1 2 1 1 1.1.............................. 2 1.2 : 1.................... 4 1.2.1 2............................... 5 1.3 : 2.................... 5 1.3.1 2.....................................

More information

2 2 1 2 1 2 1 2 2 Web Web Web Web 1 1,,,,,, Web, Web - i -

2 2 1 2 1 2 1 2 2 Web Web Web Web 1 1,,,,,, Web, Web - i - 2015 Future University Hakodate 2015 System Information Science Practice Group Report Project Name Improvement of Environment for Learning Mathematics at FUN C (PR ) Group Name GroupC (PR) /Project No.

More information

zz + 3i(z z) + 5 = 0 + i z + i = z 2i z z z y zz + 3i (z z) + 5 = 0 (z 3i) (z + 3i) = 9 5 = 4 z 3i = 2 (3i) zz i (z z) + 1 = a 2 {

zz + 3i(z z) + 5 = 0 + i z + i = z 2i z z z y zz + 3i (z z) + 5 = 0 (z 3i) (z + 3i) = 9 5 = 4 z 3i = 2 (3i) zz i (z z) + 1 = a 2 { 04 zz + iz z) + 5 = 0 + i z + i = z i z z z 970 0 y zz + i z z) + 5 = 0 z i) z + i) = 9 5 = 4 z i = i) zz i z z) + = a {zz + i z z) + 4} a ) zz + a + ) z z) + 4a = 0 4a a = 5 a = x i) i) : c Darumafactory

More information

25 Removal of the fricative sounds that occur in the electronic stethoscope

25 Removal of the fricative sounds that occur in the electronic stethoscope 25 Removal of the fricative sounds that occur in the electronic stethoscope 1140311 2014 3 7 ,.,.,.,.,.,.,.,,.,.,.,.,,. i Abstract Removal of the fricative sounds that occur in the electronic stethoscope

More information

熊本県数学問題正解

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... (

More information

(ii) (iii) z a = z a =2 z a =6 sin z z a dz. cosh z z a dz. e z dz. (, a b > 6.) (z a)(z b) 52.. (a) dz, ( a = /6.), (b) z =6 az (c) z a =2 53. f n (z

(ii) (iii) z a = z a =2 z a =6 sin z z a dz. cosh z z a dz. e z dz. (, a b > 6.) (z a)(z b) 52.. (a) dz, ( a = /6.), (b) z =6 az (c) z a =2 53. f n (z B 4 24 7 9 ( ) :,..,,.,. 4 4. f(z): D C: D a C, 2πi C f(z) dz = f(a). z a a C, ( ). (ii), a D, a U a,r D f. f(z) = A n (z a) n, z U a,r, n= A n := 2πi C f(ζ) dζ, n =,,..., (ζ a) n+, C a D. (iii) U a,r

More information

A S- hara/lectures/lectures-j.html r A = A 5 : 5 = max{ A, } A A A A B A, B A A A %

A S-   hara/lectures/lectures-j.html r A = A 5 : 5 = max{ A, } A A A A B A, B A A A % A S- http://www.math.kyushu-u.ac.jp/ hara/lectures/lectures-j.html r A S- 3.4.5. 9 phone: 9-8-444, e-mail: hara@math.kyushu-u.ac.jp, http://www.math.kyushu-u.ac.jp/ hara/lectures/lectures-j.html Office

More information

SURF,,., 55%,.,., SURF(Speeded Up Robust Features), 4 (,,, ), SURF.,, 84%, 96%, 28%, 32%.,,,. SURF, i

SURF,,., 55%,.,., SURF(Speeded Up Robust Features), 4 (,,, ), SURF.,, 84%, 96%, 28%, 32%.,,,. SURF, i 24 SURF Recognition of Facial Expression Based on SURF 1130402 2013 3 1 SURF,,., 55%,.,., SURF(Speeded Up Robust Features), 4 (,,, ), SURF.,, 84%, 96%, 28%, 32%.,,,. SURF, i Abstract Recognition of Facial

More information

4 4 θ X θ P θ 4. 0, 405 P 0 X 405 X P 4. () 60 () 45 () 40 (4) 765 (5) 40 B 60 0 P = 90, = ( ) = X

4 4 θ X θ P θ 4. 0, 405 P 0 X 405 X P 4. () 60 () 45 () 40 (4) 765 (5) 40 B 60 0 P = 90, = ( ) = X 4 4. 4.. 5 5 0 A P P P X X X X +45 45 0 45 60 70 X 60 X 0 P P 4 4 θ X θ P θ 4. 0, 405 P 0 X 405 X P 4. () 60 () 45 () 40 (4) 765 (5) 40 B 60 0 P 0 0 + 60 = 90, 0 + 60 = 750 0 + 60 ( ) = 0 90 750 0 90 0

More information

2016 Future University Hakodate 2016 System Information Science Practice Group Report Project Name Designing Learning Environment for Mathematics at F

2016 Future University Hakodate 2016 System Information Science Practice Group Report Project Name Designing Learning Environment for Mathematics at F 2016 Future University Hakodate 2016 System Information Science Practice Group Report Project Name Group Name Mathematical Group /Project No. 2-B /Project Leader 1014216 Kaito Kawakatsu /Group Leader 1014249

More information

1 No.1 5 C 1 I III F 1 F 2 F 1 F 2 2 Φ 2 (t) = Φ 1 (t) Φ 1 (t t). = Φ 1(t) t = ( 1.5e 0.5t 2.4e 4t 2e 10t ) τ < 0 t > τ Φ 2 (t) < 0 lim t Φ 2 (t) = 0

1 No.1 5 C 1 I III F 1 F 2 F 1 F 2 2 Φ 2 (t) = Φ 1 (t) Φ 1 (t t). = Φ 1(t) t = ( 1.5e 0.5t 2.4e 4t 2e 10t ) τ < 0 t > τ Φ 2 (t) < 0 lim t Φ 2 (t) = 0 1 No.1 5 C 1 I III F 1 F 2 F 1 F 2 2 Φ 2 (t) = Φ 1 (t) Φ 1 (t t). = Φ 1(t) t = ( 1.5e 0.5t 2.4e 4t 2e 10t ) τ < 0 t > τ Φ 2 (t) < 0 lim t Φ 2 (t) = 0 0 < t < τ I II 0 No.2 2 C x y x y > 0 x 0 x > b a dx

More information

SNS ( ) SNS(Social Networking Service) SNS SNS i

SNS ( ) SNS(Social Networking Service) SNS SNS i 22 SNS Job-Hunting Activities situation Understanding Support System Using SNS 1110252 2011 03 01 SNS ( ) SNS(Social Networking Service) SNS SNS i Abstract Job-Hunting Activities situation Understanding

More information

1 Web Web 1,,,, Web, Web : - i -

1 Web Web 1,,,, Web, Web : - i - 2015 Future University Hakodate 2015 System Information Science Practice Group Report Project Name Improvement of Environment for Learning Mathematics at FUN A ( ) Group Name GroupA (System) /Project No.

More information

n ( (

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

More information

16_.....E...._.I.v2006

16_.....E...._.I.v2006 55 1 18 Bull. Nara Univ. Educ., Vol. 55, No.1 (Cult. & Soc.), 2006 165 2002 * 18 Collaboration Between a School Athletic Club and a Community Sports Club A Case Study of SOLESTRELLA NARA 2002 Rie TAKAMURA

More information

(1) i NGO ii (2) 112

(1) i NGO ii (2) 112 MEMOIRS OF SHONAN INSTITUTE OF TECHNOLOGY Vol. 41, No. 1, 2007 * * 2 * 3 * 4 * 5 * 6 * 7 * 8 Service Learning for Engineering Students Satsuki TASAKA*, Mitsutoshi ISHIMURA* 2, Hikaru MIZUTANI* 3, Naoyuki

More information

A B C B C ICT ICT ITC ICT

A B C B C ICT ICT ITC ICT ICT Development of curriculum for improving of teachers ICT based on evaluation standards. Kazuhiko ISHIHARA Abstract Ministry of Education and Science announced Checklist of teacher s ICT in March,. All

More information

28 Horizontal angle correction using straight line detection in an equirectangular image

28 Horizontal angle correction using straight line detection in an equirectangular image 28 Horizontal angle correction using straight line detection in an equirectangular image 1170283 2017 3 1 2 i Abstract Horizontal angle correction using straight line detection in an equirectangular image

More information

1 1 tf-idf tf-idf i

1 1 tf-idf tf-idf i 14 A Method of Article Retrieval Utilizing Characteristics in Newspaper Articles 1055104 2003 1 31 1 1 tf-idf tf-idf i Abstract A Method of Article Retrieval Utilizing Characteristics in Newspaper Articles

More information

7,, i

7,, i 23 Research of the authentication method on the two dimensional code 1145111 2012 2 13 7,, i Abstract Research of the authentication method on the two dimensional code Karita Koichiro Recently, the two

More information

II

II II 16 16.0 2 1 15 x α 16 x n 1 17 (x α) 2 16.1 16.1.1 2 x P (x) P (x) = 3x 3 4x + 4 369 Q(x) = x 4 ax + b ( ) 1 P (x) x Q(x) x P (x) x P (x) x = a P (a) P (x) = x 3 7x + 4 P (2) = 2 3 7 2 + 4 = 8 14 +

More information

i

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,

More information

さくらの個別指導 ( さくら教育研究所 ) A 2 P Q 3 R S T R S T P Q ( ) ( ) m n m n m n n n

さくらの個別指導 ( さくら教育研究所 ) A 2 P Q 3 R S T R S T P Q ( ) ( ) m n m n m n n n 1 1.1 1.1.1 A 2 P Q 3 R S T R S T P 80 50 60 Q 90 40 70 80 50 60 90 40 70 8 5 6 1 1 2 9 4 7 2 1 2 3 1 2 m n m n m n n n n 1.1 8 5 6 9 4 7 2 6 0 8 2 3 2 2 2 1 2 1 1.1 2 4 7 1 1 3 7 5 2 3 5 0 3 4 1 6 9 1

More information

,,.,.,,.,.,.,.,,.,..,,,, i

,,.,.,,.,.,.,.,,.,..,,,, i 22 A person recognition using color information 1110372 2011 2 13 ,,.,.,,.,.,.,.,,.,..,,,, i Abstract A person recognition using color information Tatsumo HOJI Recently, for the purpose of collection of

More information

t θ, τ, α, β S(, 0 P sin(θ P θ S x cos(θ SP = θ P (cos(θ, sin(θ sin(θ P t tan(θ θ 0 cos(θ tan(θ = sin(θ cos(θ ( 0t tan(θ

t θ, τ, α, β S(, 0 P sin(θ P θ S x cos(θ SP = θ P (cos(θ, sin(θ sin(θ P t tan(θ θ 0 cos(θ tan(θ = sin(θ cos(θ ( 0t tan(θ 4 5 ( 5 3 9 4 0 5 ( 4 6 7 7 ( 0 8 3 9 ( 8 t θ, τ, α, β S(, 0 P sin(θ P θ S x cos(θ SP = θ P (cos(θ, sin(θ sin(θ P t tan(θ θ 0 cos(θ tan(θ = sin(θ cos(θ ( 0t tan(θ S θ > 0 θ < 0 ( P S(, 0 θ > 0 ( 60 θ

More information

( )

( ) 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...............................

More information

1996. Vol. 16, No. 2, pp The Learning Process in "Tanoshii-Taiiku" Theory through the Spectrum of Teaching Styles Abstract In recent years, the

1996. Vol. 16, No. 2, pp The Learning Process in Tanoshii-Taiiku Theory through the Spectrum of Teaching Styles Abstract In recent years, the 1996. Vol. 16, No. 2, pp. 83-93 The Learning Process in "Tanoshii-Taiiku" Theory through the Spectrum of Teaching Styles Abstract In recent years, the concept of "teaching style", especially Mosston's

More information

2 7 V 7 {fx fx 3 } 8 P 3 {fx fx 3 } 9 V 9 {fx fx f x 2fx } V {fx fx f x 2fx + } V {{a n } {a n } a n+2 a n+ + a n n } 2 V 2 {{a n } {a n } a n+2 a n+

2 7 V 7 {fx fx 3 } 8 P 3 {fx fx 3 } 9 V 9 {fx fx f x 2fx } V {fx fx f x 2fx + } V {{a n } {a n } a n+2 a n+ + a n n } 2 V 2 {{a n } {a n } a n+2 a n+ R 3 R n C n V??,?? k, l K x, y, z K n, i x + y + z x + y + z iv x V, x + x o x V v kx + y kx + ky vi k + lx kx + lx vii klx klx viii x x ii x + y y + x, V iii o K n, x K n, x + o x iv x K n, x + x o x

More information

微分積分 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. このサンプルページの内容は, 初版 1 刷発行時のものです.

微分積分 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.   このサンプルページの内容は, 初版 1 刷発行時のものです. 微分積分 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. ttp://www.morikita.co.jp/books/mid/00571 このサンプルページの内容は, 初版 1 刷発行時のものです. i ii 014 10 iii [note] 1 3 iv 4 5 3 6 4 x 0 sin x x 1 5 6 z = f(x, y) 1 y = f(x)

More information

1 [1, 2, 3, 4, 5, 8, 9, 10, 12, 15] The Boston Public Schools system, BPS (Deferred Acceptance system, DA) (Top Trading Cycles system, TTC) cf. [13] [

1 [1, 2, 3, 4, 5, 8, 9, 10, 12, 15] The Boston Public Schools system, BPS (Deferred Acceptance system, DA) (Top Trading Cycles system, TTC) cf. [13] [ Vol.2, No.x, April 2015, pp.xx-xx ISSN xxxx-xxxx 2015 4 30 2015 5 25 253-8550 1100 Tel 0467-53-2111( ) Fax 0467-54-3734 http://www.bunkyo.ac.jp/faculty/business/ 1 [1, 2, 3, 4, 5, 8, 9, 10, 12, 15] The

More information

mugensho.dvi

mugensho.dvi 1 1 f (t) lim t a f (t) = 0 f (t) t a 1.1 (1) lim(t 1) 2 = 0 t 1 (t 1) 2 t 1 (2) lim(t 1) 3 = 0 t 1 (t 1) 3 t 1 2 f (t), g(t) t a lim t a f (t) g(t) g(t) f (t) = o(g(t)) (t a) = 0 f (t) (t 1) 3 1.2 lim

More information

I A A441 : April 15, 2013 Version : 1.1 I Kawahira, Tomoki TA (Shigehiro, Yoshida )

I A A441 : April 15, 2013 Version : 1.1 I   Kawahira, Tomoki TA (Shigehiro, Yoshida ) I013 00-1 : April 15, 013 Version : 1.1 I Kawahira, Tomoki TA (Shigehiro, Yoshida) http://www.math.nagoya-u.ac.jp/~kawahira/courses/13s-tenbou.html pdf * 4 15 4 5 13 e πi = 1 5 0 5 7 3 4 6 3 6 10 6 17

More information

本文(横)  ※リュウミンL・カンマ使用/大扉●還暦記念論集用

本文(横)  ※リュウミンL・カンマ使用/大扉●還暦記念論集用 47 48 a 49 J.Piagetreflective thinkingr.skemp reflective intelligence A.H.SchoenfeldF.K.Lester J.Garofalo J.H.FlavellA.L.Brown 50 51 52 53 a b 54 SQSShared Questionnaire System PC G.Polya Schoenfild Polya

More information

<4D F736F F D B B83578B6594BB2D834A836F815B82D082C88C60202E646F63>

<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.

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

学習内容と日常生活との関連性の研究-第2部-第6章

学習内容と日常生活との関連性の研究-第2部-第6章 378 379 10% 10%10% 10% 100% 380 381 2000 BSE CJD 5700 18 1996 2001 100 CJD 1 310-7 10-12 10-6 CJD 100 1 10 100 100 1 1 100 1 10-6 1 1 10-6 382 2002 14 5 1014 10 10.4 1014 100 110-6 1 383 384 385 2002 4

More information

WebRTC P2P,. Web,. WebRTC. WebRTC, P2P, i

WebRTC P2P,. Web,. WebRTC. WebRTC, P2P, i 28 WebRTC Design of multi-platform file sharing system using WebRTC 1170336 2017 2 28 WebRTC P2P,. Web,. WebRTC. WebRTC, P2P, i Abstract Design of multi-platform file sharing system using WebRTC Harumi

More information

1

1 1 1 7 1.1.................................. 11 2 13 2.1............................ 13 2.2............................ 17 2.3.................................. 19 3 21 3.1.............................

More information

() 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 (

() 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

More information

1 Abstract 2 3 n a ax 2 + bx + c = 0 (a 0) (1) ( x + b ) 2 = b2 4ac 2a 4a 2 D = b 2 4ac > 0 (1) 2 D = 0 D < 0 x + b 2a = ± b2 4ac 2a b ± b 2

1 Abstract 2 3 n a ax 2 + bx + c = 0 (a 0) (1) ( x + b ) 2 = b2 4ac 2a 4a 2 D = b 2 4ac > 0 (1) 2 D = 0 D < 0 x + b 2a = ± b2 4ac 2a b ± b 2 1 Abstract n 1 1.1 a ax + bx + c = 0 (a 0) (1) ( x + b ) = b 4ac a 4a D = b 4ac > 0 (1) D = 0 D < 0 x + b a = ± b 4ac a b ± b 4ac a b a b ± 4ac b i a D (1) ax + bx + c D 0 () () (015 8 1 ) 1. D = b 4ac

More information

1 θ i (1) A B θ ( ) A = B = sin 3θ = sin θ (A B sin 2 θ) ( ) 1 2 π 3 < = θ < = 2 π 3 Ax Bx3 = 1 2 θ = π sin θ (2) a b c θ sin 5θ = sin θ f(sin 2 θ) 2

1 θ i (1) A B θ ( ) A = B = sin 3θ = sin θ (A B sin 2 θ) ( ) 1 2 π 3 < = θ < = 2 π 3 Ax Bx3 = 1 2 θ = π sin θ (2) a b c θ sin 5θ = sin θ f(sin 2 θ) 2 θ i ) AB θ ) A = B = sin θ = sin θ A B sin θ) ) < = θ < = Ax Bx = θ = sin θ ) abc θ sin 5θ = sin θ fsin θ) fx) = ax bx c ) cos 5 i sin 5 ) 5 ) αβ α iβ) 5 α 4 β α β β 5 ) a = b = c = ) fx) = 0 x x = x =

More information

橡最新卒論

橡最新卒論 Research of improving of recognition ability in Face recognition system Abstract The age when baiometrics was used as a password came today. Because various baiometrics such as a voice, a fingerprint,

More information

卒業論文2.dvi

卒業論文2.dvi 15 GUI A study on the system to transfer a GUI sub-picture to the enlarging viewer for operational support 1040270 2004 2 27 GUI PC PC GUI Graphical User Interface PC GUI GUI PC GUI PC PC GUI i Abstract

More information

, (GPS: Global Positioning Systemg),.,, (LBS: Local Based Services).. GPS,.,. RFID LAN,.,.,.,,,.,..,.,.,,, i

, (GPS: Global Positioning Systemg),.,, (LBS: Local Based Services).. GPS,.,. RFID LAN,.,.,.,,,.,..,.,.,,, i 25 Estimation scheme of indoor positioning using difference of times which chirp signals arrive 114348 214 3 6 , (GPS: Global Positioning Systemg),.,, (LBS: Local Based Services).. GPS,.,. RFID LAN,.,.,.,,,.,..,.,.,,,

More information

) ] [ h m x + y + + V x) φ = Eφ 1) z E = i h t 13) x << 1) N n n= = N N + 1) 14) N n n= = N N + 1)N + 1) 6 15) N n 3 n= = 1 4 N N + 1) 16) N n 4

) ] [ h m x + y + + V x) φ = Eφ 1) z E = i h t 13) x << 1) N n n= = N N + 1) 14) N n n= = N N + 1)N + 1) 6 15) N n 3 n= = 1 4 N N + 1) 16) N n 4 1. k λ ν ω T v p v g k = π λ ω = πν = π T v p = λν = ω k v g = dω dk 1) ) 3) 4). p = hk = h λ 5) E = hν = hω 6) h = h π 7) h =6.6618 1 34 J sec) hc=197.3 MeV fm = 197.3 kev pm= 197.3 ev nm = 1.97 1 3 ev

More information

本文.indd

本文.indd Bull. of Yamagata Univ., Educ. Sci., Vol. 14 No. 3, February McCrindle Christensen ( ) Oxford( ) Flavell Brown Flavell F w F w F w F w F / / / / w F w F / w F w F w F w F / w F w F / w F wf w F w F w

More information

II A A441 : October 02, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka )

II A A441 : October 02, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka ) II 214-1 : October 2, 214 Version : 1.1 Kawahira, Tomoki TA (Kondo, Hirotaka ) http://www.math.nagoya-u.ac.jp/~kawahira/courses/14w-biseki.html pdf 1 2 1 9 1 16 1 23 1 3 11 6 11 13 11 2 11 27 12 4 12 11

More information

°ÌÁê¿ô³ØII

°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),

More information

ax 2 + bx + c = n 8 (n ) a n x n + a n 1 x n a 1 x + a 0 = 0 ( a n, a n 1,, a 1, a 0 a n 0) n n ( ) ( ) ax 3 + bx 2 + cx + d = 0 4

ax 2 + bx + c = n 8 (n ) a n x n + a n 1 x n a 1 x + a 0 = 0 ( a n, a n 1,, a 1, a 0 a n 0) n n ( ) ( ) ax 3 + bx 2 + cx + d = 0 4 20 20.0 ( ) 8 y = ax 2 + bx + c 443 ax 2 + bx + c = 0 20.1 20.1.1 n 8 (n ) a n x n + a n 1 x n 1 + + a 1 x + a 0 = 0 ( a n, a n 1,, a 1, a 0 a n 0) n n ( ) ( ) ax 3 + bx 2 + cx + d = 0 444 ( a, b, c, d

More information

1 1 sin cos P (primary) S (secondly) 2 P S A sin(ω2πt + α) A ω 1 ω α V T m T m 1 100Hz m 2 36km 500Hz. 36km 1

1 1 sin cos P (primary) S (secondly) 2 P S A sin(ω2πt + α) A ω 1 ω α V T m T m 1 100Hz m 2 36km 500Hz. 36km 1 sin cos P (primary) S (secondly) 2 P S A sin(ω2πt + α) A ω ω α 3 3 2 2V 3 33+.6T m T 5 34m Hz. 34 3.4m 2 36km 5Hz. 36km m 34 m 5 34 + m 5 33 5 =.66m 34m 34 x =.66 55Hz, 35 5 =.7 485.7Hz 2 V 5Hz.5V.5V V

More information

2 2 MATHEMATICS.PDF 200-2-0 3 2 (p n ), ( ) 7 3 4 6 5 20 6 GL 2 (Z) SL 2 (Z) 27 7 29 8 SL 2 (Z) 35 9 2 40 0 2 46 48 2 2 5 3 2 2 58 4 2 6 5 2 65 6 2 67 7 2 69 2 , a 0 + a + a 2 +... b b 2 b 3 () + b n a

More information

.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(

.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,

More information

i ii iii iv v vi vii ( ー ー ) ( ) ( ) ( ) ( ) ー ( ) ( ) ー ー ( ) ( ) ( ) ( ) ( ) 13 202 24122783 3622316 (1) (2) (3) (4) 2483 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) 11 11 2483 13

More information

Web Web ID Web 16 Web Web i

Web Web ID Web 16 Web Web i 24 Web Proposal of Web Application Password Operations Management System 1130343 2013 3 1 Web Web ID Web 16 Web Web i Abstract Proposal of Web Application Password Operations Management System Tatsuro

More information

..,,,, , ( ) 3.,., 3.,., 500, 233.,, 3,,.,, i

..,,,, , ( ) 3.,., 3.,., 500, 233.,, 3,,.,, i 25 Feature Selection for Prediction of Stock Price Time Series 1140357 2014 2 28 ..,,,,. 2013 1 1 12 31, ( ) 3.,., 3.,., 500, 233.,, 3,,.,, i Abstract Feature Selection for Prediction of Stock Price Time

More information

,,.,,., II,,,.,,.,.,,,.,,,.,, II i

,,.,,., II,,,.,,.,.,,,.,,,.,, II i 12 Load Dispersion Methods in Thin Client Systems 1010405 2001 2 5 ,,.,,., II,,,.,,.,.,,,.,,,.,, II i Abstract Load Dispersion Methods in Thin Client Systems Noritaka TAKEUCHI Server Based Computing by

More information

o 2o 3o 3 1. I o 3. 1o 2o 31. I 3o PDF Adobe Reader 4o 2 1o I 2o 3o 4o 5o 6o 7o 2197/ o 1o 1 1o

o 2o 3o 3 1. I o 3. 1o 2o 31. I 3o PDF Adobe Reader 4o 2 1o I 2o 3o 4o 5o 6o 7o 2197/ o 1o 1 1o 78 2 78... 2 22201011... 4... 9... 7... 29 1 1214 2 7 1 8 2 2 3 1 2 1o 2o 3o 3 1. I 1124 4o 3. 1o 2o 31. I 3o PDF Adobe Reader 4o 2 1o 72 1. I 2o 3o 4o 5o 6o 7o 2197/6 9. 9 8o 1o 1 1o 2o / 3o 4o 5o 6o

More information

07_伊藤由香_様.indd

07_伊藤由香_様.indd A 1 A A 4 1 85 14 A 2 2006 A B 2 A 3 4 86 3 4 2 1 87 14 1 1 A 2010 2010 3 5 2 1 15 1 15 20 2010 88 2 3 5 2 1 2010 14 2011 15 4 1 3 1 3 15 3 16 3 1 6 COP10 89 14 4 1 7 1 2 3 4 5 1 2 3 3 5 90 4 1 3 300 5

More information

25 About what prevent spoofing of misusing a session information

25 About what prevent spoofing of misusing a session information 25 About what prevent spoofing of misusing a session information 1140349 2014 2 28 Web Web [1]. [2] SAS-2(Simple And Secure password authentication protocol, ver.2)[3] SAS-2 i Abstract About what prevent

More information

262014 3 1 1 6 3 2 198810 2/ 198810 2 1 3 4 http://www.pref.hiroshima.lg.jp/site/monjokan/ 1... 1... 1... 2... 2... 4... 5... 9... 9... 10... 10... 10... 10... 13 2... 13 3... 15... 15... 15... 16 4...

More information

1W II K =25 A (1) office(a439) (2) A4 etc. 12:00-13:30 Cafe David 1 2 TA appointment Cafe D

1W II K =25 A (1) office(a439) (2) A4 etc. 12:00-13:30 Cafe David 1 2 TA  appointment Cafe D 1W II K200 : October 6, 2004 Version : 1.2, kawahira@math.nagoa-u.ac.jp, http://www.math.nagoa-u.ac.jp/~kawahira/courses.htm TA M1, m0418c@math.nagoa-u.ac.jp TA Talor Jacobian 4 45 25 30 20 K2-1W04-00

More information

Kansai University of Welfare Sciences Practical research on the effectiveness of the validation for the elderly with dementia Naoko Tsumura, Tomoko Mi

Kansai University of Welfare Sciences Practical research on the effectiveness of the validation for the elderly with dementia Naoko Tsumura, Tomoko Mi Practical research on the effectiveness of the validation for the elderly with dementia Naoko Tsumura, Tomoko Mitamura and Takeshi Hashino 2 1 Abstract : The present conditions to surround the elderly

More information

Vol. 48 No. 3 Mar PM PM PMBOK PM PM PM PM PM A Proposal and Its Demonstration of Developing System for Project Managers through University-Indus

Vol. 48 No. 3 Mar PM PM PMBOK PM PM PM PM PM A Proposal and Its Demonstration of Developing System for Project Managers through University-Indus Vol. 48 No. 3 Mar. 2007 PM PM PMBOK PM PM PM PM PM A Proposal and Its Demonstration of Developing System for Project Managers through University-Industry Collaboration Yoshiaki Matsuzawa and Hajime Ohiwa

More information

, IT.,.,..,.. i

, IT.,.,..,.. i 25 To construct the system that promote a interactive method as a knowledge acquisition 1140317 2014 2 28 , IT.,.,..,.. i Abstract To construct the system that promote a interactive method as a knowledge

More information

1.2 y + P (x)y + Q(x)y = 0 (1) y 1 (x), y 2 (x) y 1 (x), y 2 (x) (1) y(x) c 1, c 2 y(x) = c 1 y 1 (x) + c 2 y 2 (x) 3 y 1 (x) y 1 (x) e R P (x)dx y 2

1.2 y + P (x)y + Q(x)y = 0 (1) y 1 (x), y 2 (x) y 1 (x), y 2 (x) (1) y(x) c 1, c 2 y(x) = c 1 y 1 (x) + c 2 y 2 (x) 3 y 1 (x) y 1 (x) e R P (x)dx y 2 1 1.1 R(x) = 0 y + P (x)y + Q(x)y = R(x)...(1) y + P (x)y + Q(x)y = 0...(2) 1 2 u(x) v(x) c 1 u(x)+ c 2 v(x) = 0 c 1 = c 2 = 0 c 1 = c 2 = 0 2 0 2 u(x) v(x) u(x) u (x) W (u, v)(x) = v(x) v (x) 0 1 1.2

More information

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

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

More information

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

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

More information

E MathML W3C MathJax 1.3 MathJax MathJax[5] TEX MathML JavaScript TEX MathML [8] [9] MathSciNet[10] MathJax MathJax MathJax MathJax MathJax MathJax We

E MathML W3C MathJax 1.3 MathJax MathJax[5] TEX MathML JavaScript TEX MathML [8] [9] MathSciNet[10] MathJax MathJax MathJax MathJax MathJax MathJax We MathML TEX 1,a) 1,b) MathML TEX JavaScript MathJax TEX GUI MathML TEX MathJax Prototype of e-learning and Communication Systems to Support Displaying Math Equations with MathML and TEX Nobuo Yamashita

More information