|
|
|
- しなつ たかにし
- 5 years ago
- Views:
Transcription
1
2
3 I I I I I I I I I I I I AI BI CI III, IV III, IV III, IV I I II VII, VIII IX, X IX, X i
4 I VI Geisser, Thomas I I V Hesselholt, Lars I I I II II, III I III I Geisser, Thomas I I ,, I I NTT 4/15, 4/22, 4/27, 5/20, 5/27 5/6, 5/18, 6/1, 6/10, 6/17 6/24, 7/1, 7/8, 7/15, 7/22 II Geisser, Thomas II I ii
5 I II I II I III I III I IV I IV I IV I II I II I III Hesselholt, Lars I III I IV I II I ( ) I ( -,- ) I, IV III III V Garrigue, Jacques iii
6 II II II II II II II II II II II II II II AII BII CII CIII V, VI V, VI V, VI II II III I I I iv
7 II,, II RAID 10/7,10/14,11/4,11/18,11/25 10/21,10/28,12/2,12/16,1/20 11/30,12/7,12/14,12/21,1/18 II II IV IV II IV IV IV III III Jacques Garrigue IV II IV II I I v
8 II II II II II III II III II IV II IV II II II II II II II III Lars Hesselholt II III II IV II IV II ( )) II ( - ) II ( - ) ( ) ( ) vi
9 I ( ) ( )NTT ( ) ( )IIC NTT II UFJ ( ) II II ( ) ( )IIC I ( ) II vii
10 III III I I III Carleson II IV II II I viii
11 I ( p L p Birch and Swinnerton-Dyer IV ( III ( p II ( I ( I ( I ( Gromov-Witten I ( ix
12
13
14
15 I 2 I I 4 I III 1 I 2 3 III,IV I 4 I 1 BI II II CI 2 I 3 VII, VIII III 4 I 1 IX, X 2 3 AI 4 I 3
16 I II 3 I 4 1 I 2 3 VI I 4 V 1 II 2 II I 2 3 II 4 I 1 I 2 3 I 4 4
17 2011 I I yamagami/teaching/calculus/cal2011haru.pdf TA 1 () M1 M2 D ( ) ( ) (4/14) (4/21) (4/28) (5/12) (5/19) (5/26) 6/02 (6/09) (6/16) (6/23) (6/30) (7/07) (7/14) (7/21) 5 1 5
18 I x 4x + 20 S A B C F Web Web Web 2 1 6
19 2011 I I I II 30 TA 1 () M1 M2 D ( ) ( ) ) 2) 3) 7
20 I x = 0 lim f (x) x 0 8
21 2011 I I 2 1 0,,, 1992 I 2010 TA 1 () M1 M2 D ( ) ( )
22 I
23 2011 I 11
24 I 2011 I TA 1 () M1 M2 D ( ) ( )
25 2011 I
26 I 2011 I [1] [2] [3] 1 [4] 4 [5] 1 [6] [7] [8] [9] [10] TA 1 () M1 M2 D ( ) ( ) % I 14
27 2011 I II (1) 1 (2) 2 (3) 3 (4)
28 I S, A, B, C, F S 180 A B C140 1 S A B C F
29 2011 I I 2 1 0, TA 1 () M1 M2 D ( ) ( ) Part 1 Lect 1. (1., 2., 3. R n ) Lect 2 1., 2., 3. Lect 3 (1., 2. ) Lect 4 1., 2., 3. ) Lect 5 1., 2. ) Part 2 Lect 6 1., 2. ), 3. ) Lect 7 Im f Ker f 1. Im f Ker f, 2., 3. : Lect 8 rank 1. rank, 2. 1., Im f A, 4. Lect 9 1., 2. Part 3 17
30 I 2011 Lect 10 1., 2., 3. Lect 11 1., 2. (1), 3. (2) Lect 12 1., 2., 3. ) S 30 A 15 B 20 C 14 F 1 X 3 83 S 92 A 80 S S 18
31 2011 I I ,,, 1966 TA 1 () M1 M2 D ( ) ( )
32 I TA 20
33 2011 I I 2 1 0,, TA 1 () M1 M2 D ( ) ( ) ,.,..,,,,,,,,,,,,.,.,.,. 21
34 I ,.,. 22
35 2011 I I TA 1 () M1 M2 D ( ) ( ) : ; ; 4/18( ) : 4/25( ) : 1 5/2( ) : 2 5/9( ) : 5/16( ) : 5/23( ) : 5/30( ) : 23
36 I /6( ) : 6/13( ) : 6/20( ) : 6/27( ) : 7/4( ) : 7/11( ) : [] TA [] [ ] [ ] TA [ ] [] 10 (S) 24
37 2011 I [] [] [ ] [ ] TA [ ] [] 4 25
38 I 2011 I TA 1 () M1 M2 D ( ) ( ) : ; ; 4/18( ) : 4/25( ) : 1 5/2( ) : 2 5/9( ) : 5/16( ) : 5/23( ) : 5/30( ) : 26
39 2011 I 6/6( ) : 6/13( ) : 6/20( ) : 6/27( ) : 7/4( ) : 7/11( ) : [] TA [ ] TA [ ] 10 (S)
40 I 2011 [] [] [ ] [ ] 80 28
41 2011 I I TA 1 () M1 M2 D ( ) ( )
42 I
43 2011 I I TA 1 () M1 M2 D ( ) ( )
44 I ,.,..,.,,.,,.,.,,..,.,,, TA,,.. 32
45 2011 AI AI 4 1 TA 1 () M1 M2 D ( ) ( ) [ ] [] 33
46 AI
47 2011 BI BI 4 2 1,,, 2007 TA 1 () M1 M2 D ( ) ( )
48 BI M
49 2011 CI CI ,,, 1996,,, 1974 TA 1 () M1 M2 D ( ) ( ) , 50..,.. ε-δ, 180, ε-δ.,., 1,,,,. 6 36, 20, 50, 106., 60%. 37
50 CI , 3.,, M,,,,,.,,..,,. 3.,. 38
51 2011 III, IV III, IV TA 2 () M1 M2 D ( ) ( ) ,3 3,, (ε N ) (ε δ )
52 III, IV ,
53 2011 III, IV III, IV TA 1 () M1 M2 D ( ) ( )
54 III, IV 2011 TA ɛ δ 42
55 2011 III,IV III,IV TA 1 () M1 M2 D ( ) ( ) (1) 4 19 (2) 4 26 (3) 5 10 ε-n (4) 5 17 (1) (5) 5 24 (6) 5 31 ε-δ (7) 6 7 (8)
56 III,IV 2011 (9) 6 21 (10) 6 28 (2) (11) 7 5 (12) 7 12 (13) 7 19 (14) C 44
57 2011 I I () () () Barrett O Neill Elementry Differential Geometry (Academic Press) TA 1 () M1 M2 D ( ) ( ) () 4 R
58 I 2011 R 3 ( ) R 3 ( 1 2 ) (1, 2 1 ) ( ) 2 R (4 ) ( ) 46
59 2011 I 3 4 M
60 I 2011 I 6 3 1, (),, 2003,,, 1990,,, 1998 D. M. ( ),,, 1990 TA 1 () M1 M2 D ( ) ( )
61 2011 I Picard,, 3 4 M
62 II 2011 II 6 3 1,,,, TA 1 () M1 M2 D ( ) ( ) , L p 50
63 2011 II TA ?79 ABC 3 A3 B2 C M1 M R N 5 TA 51
64 VII,VIII 2011 VII,VIII TA () M1 M2 D ( ) ( ) VII, VIII itoken-3a
65 2011 VII,VIII or 53
66 IX,X 2011 IX,X TA () M1 M2 D ( ) ( ) [1] [2] [3] [4] [5] [1] [ 1 ].. [ 2 ] ( 1 2 )... 54
67 2011 IX,X [ 3 ] :,, 2 1,,,, sin 2 z, cot z, e,,,,,, 3 SO(3) : 4n ,.,. 55
68 IX,X 2011 IX,X TA () M1 M2 D ( ) ( )
69 2011 IX,X
70 IX,X
71 2011 I VI I VI Atiyah-MacDonald, Introduction to Commutative Algebra. Robin Hartshorne, Algebraic Geometry, Springer Graduate Text in Math. TA () M1 M2 D ( ) ( ) The avarage attendence was between 20 and 30 students throughout the semester. The goal of the class was to give an introduction into the concept of algebraic geometry and commutative algebra. I explained the notion of the spectrum of a ring, localization, the category of modules over a ring, I proved Hilbert s Nullstellensatz. I did not have time to cover normal rings and regular rings as I planed., becuause I had to go slower than planed. In the end, I spend two lecture on modules of differentials, after a request of students I motivated the notion of a spectrum of a ring as a generalization of the set of solution of several polynomial equations over an algebraically closed field. This naturally lead to the study of commutative rings. I encouraged students to participate in class with questions, and to submit solutions to homework problems. I lectured in Japanese, but I encouraged students to submit homework solutions in English, and I corrected the English language as well as the mathematics. 59
72 I VI 2011 I gave weekly homework, and eveluated the students based on the points in homework solutions. 4 M1 M The number of failed students is high because several students never submitted homework solutions. The lecture went according to my plan. I was pleased with the attendance, but participation of the students by questions was less than expected. I believe that the lecture was useful to many students in algebra. Weekly office hours were held, and I often asked students their opinion on my teaching of the class. 60
73 2011 I I 4 4 2,,, 1976, III,,, 2005,, 4, TA () M1 M2 D ( ) ( )
74 I , 7, M1 M
75 2011 I / V I / V [1] Ib Madsen and Jørgen Tornehave, From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes, Cambridge University Press, 1997 [2], larsh/teaching/s2011 G TA () M1 M2 D ( ) ( ) The course gave an introduction to algebraic topology through the definition and study of de Rham cohomology of open subsets of euclidean space. First, the alternating algebra were defined and its structure was studied in detail. Next, the de Rham cohomology of open subsets of euclidean space was defined and the Poincaré lemma and the Mayer-Vietoris sequence were proved. The technical heart of this part was the partition of unity which was proved in detail. Finally, de Rham cohomology was extended to homotopy invariant contravariant functor of all continuous maps between open subsets of euclidean spaces. The last two lectures were spent on a number of applications, including the Brouwer fixed point theorem. 63
76 I / V 2011 The course had one weekly lecture of 90 minutes which was given at the blackboard following lecture notes that were handed out at the beginning of each lecture and made available to students on the course homepage. Student were asked to hand in solutions to three sets of report problems. The evaluation of report problems. 4 M1 M
77 2011 I I 4/2 4 2,, 3 1 TA () M1 M2 D ( ) ( ) ,,,,,,,, 65
78 I
79 yamagami/teaching/functional/hilbert2011.pdf TA () M1 M2 D ( ) ( ) (4/14) (4/21) (4/28) (5/12) (5/19) (5/26) (6/2) (6/9) (6/16) (6/23) (6/30) (7/7) (7/14) (7/21) yamagami/ (Ries-Markov) 67
80 M1 M
81 2011 I I I I III Arnold, Mathematical Methods of Classical Mechanics, 2nd Edition, Springer-Verlag. TA () M1 M2 D ( ) ( )
82 I I
83 2011 II II II II 3 4 2,. TA () M1 M2 D ( ) ( ) ,.,.,.,.,,,. 2,, 2,,. 71
84 II II 2011, (1 + 1/n) n,,., arctan(x),,,.,., x (t) = f(t),,.,. Gauss-Jordan Gauss LU Jacobi Gauss-Seidel,.,,,,. 72
85 2011 II II QR,, Strume., QR LR.,,,.,.,.,,.,,,.,,,,,.,,..,.,,.,,., A, B, F,,. A,.,,.,, B.,, F.,,., 73
86 II II 2011.,,.,,,. 74
87 2011 III I() III I() Combinatorics and Representation Theory 2 related to Symmetric Groups 4 2 A. Kleshchev, Linear and projective representations of symmetric groups. Cambridge Tracts in Mathematics, 163. Cambridge University Press, Cambridge, xiv+277 pp. ISBN: TA () M1 M2 D ( ) ( ) , 8..,,. 2 3, ( 2),( 3). ( Hom.) 3,.,,.. ( Murphy.). (, degenerate.), Lie, Lie. Lie.,. 75
88 III I() 2011,....,,,,,, Hom,,, 2. 3, Young., Lascoux-Leclerc-Thibon. : , 1 ( ) ,.,,,.,. 4 M ,, ,.,..,. Cafe David,. 76
89 2011 III I(), Lie.,. 77
90 I 2011 I Introduction to coding theory San Ling and Chaoping Xing, Coding theory, A first course, Cambridge University Press Lekh R.Vermani, Elements of Algebraic Coding Theory, Chapman and Hall JH van Lint, Introduction to Coding theory, Springer GTM 86 TA () M1 M2 D ( ) ( ) The attendence was between around 5-8 students. The goal of this series of lectures was to give an introduction to the theory, and to explain how some of the coding methods work by giving many examples. Contrary to my expectation, most students in the class were already familiar with the concepts of finite fields and vector spaces, so that I could focus on concepts of coding theory. The main topics I covered were the definition of codes, linear codes, methods for their decoding and encoding, bounds in coding theory, and cyclic codes. I tried to give many practical examples of all the theorems I proved. For example, I introduced the Hamming codes and Goley codes, which where in fact used for the Voyager missions. I encouraged students to participate in class with questions, and to submit solutions to homework problems. 78
91 2011 I I gave weekly homework, and eveluated the students based on the points in homework solutions. 4 M1 M The lecture went according to my plan. I was pleased with the attendance, but participation of the students by questions was less than expected. I believe that the lecture was useful to many students in algebra. Weekly office hours were held, and I encouraged students their opinion on my teaching of the class. 79
92 I I 2011 I I 2 4 2,,, 2004 TA () M1 M2 D ( ) ( ) A4 80
93 2011 I I (S) (A) (B) (C) (D) 4 M1 M
94 I I 2011 I I () NTT 1/ TA () M1 M2 D ( ) ( )
95 2011 I I ( ) ( ) ( ) ( )
96 I I M1 M
97 2011 I I 1) I I 1) 1/ ,,,, IT-Text 4/15( ) 4/22( ) 4/27( ) 5/20( ) 5/27( ) TA () M1 M2 D ( ) ( ) ( ) ( ) ( ) ( ), 85
98 I I 1)2011 ( ), (15 ), ( ) 0 4 () 5 7 () 8 11 () () / ( ) A D( / / /) 86
99 2011 I I 1) 3 4 M1 M2 A B C D ( ) 87
100 I I 2011 I I / 2 5/6( ) 5/18( ) 6/1( ) 6/10( ) 6/17( ) TA () M1 M2 D ( ) ( )
101 2011 I I M1 M2 A B C D ( ) 89
102 I I
103 2011 I I I I 1/ /24( ) 7/1( ) 7/8( ) 7/15( ) 7/22( ) TA () M1 M2 D ( ) ( )
104 I I M1 M2 A B C D ( ) 92
105 2011 II II 2 3 J.Milne, Algebraic Number theory, at: jmilne.org : 1,2: Neukirch, J.: Class field theory. Springer Neukirch, J.:, Springer Artin, M; Tate, J.: Class field theory I did not use a specific textbook, but all the books mentioned above. TA () M1 M2 D ( ) ( ) The avarage attendence was around 10 students throughout the semester. Class field theory is a theory which was started more than 150 years ago in an attempt to prove Fermat s last theorem. My original goal was to prove the main theorem of class field theory. However, after noticing that the background of the students was not sufficient, I started with algebraic number theory. I discussed prime decomposition, valuation, local fields, and in the last three lectures explained the main theorem of local and global class field theory. 99
106 II 2011 I motivated class field theory as a classification of abelian extensions of number fields and local fields. It also answers questions regarding decomposition of prime ideals in abelian extensions of number fields. This can be viewed as a generalization of Gauss reciprocity law. I encouraged students to participate in class with questions, and to submit solutions to homework problems. I lectured in Japanese, but I encouraged students to submit homework solutions in English, and I corrected the English language as well as the mathematics. I gave weekly homework, and eveluated the students based on the points in homework solutions. M1 M The lecture went according to my plan. I was pleased with the attendance, but participation of the students by questions was less than expected. Weekly office hours were held, and I asked students to give their opinion on my teaching. 100
107 2011 II II N. Bourbaki, Groupes et Algebres de Lie, Chap. 4,5 et 6, Masson. 2. J. H. Conway, N.J.A. Sloane, Sphere Packings, Lattices, and Groups, Springer. 3. P. Griffiths, J. Harris, Principles of Algebraic Geometry, Wiley. 4. J.P. Serre, A course in arithmetic, Springer. TA () M1 M2 D ( ) ( )
108 II 2011 M1 M
109 2011 I I 2 3,,. O. Lehto. Univalent functions and Teichmüller spaces. Springer. O. Forster. Lectures on Riemann surfaces. Springer. C. McMullen, Riemann surfaces, dynamics and geometry: Course Notes, A. Douady and J. H. Hubbard. A proof of Thurston s topological characterization of rational maps. Acta Math. 171(1993), TA () M1 M2 D ( ) ( ) (2011/4/19) 2 (2011/4/26) 1 3 (2011/5/10) 2 4 (2011/5/17) 5 (2011/5/24) 6 (2011/5/31) 7 (2011/6/7) 103
110 I (2011/6/14) 9 (2011/6/21) 10 (2011/6/28) 11 (2011/7/5) 12 (2011/7/12) 13 (2011/7/26) 2 M1 M
111 II 2011 II 2 3 J.Milne, Algebraic Number theory, at: jmilne.org : 1,2: Neukirch, J.: Class field theory. Springer Neukirch, J.:, Springer Artin, M; Tate, J.: Class field theory I did not use a specific textbook, but all the books mentioned above. TA () M1 M2 D ( ) ( ) The avarage attendence was around 10 students throughout the semester. Class field theory is a theory which was started more than 150 years ago in an attempt to prove Fermat s last theorem. My original goal was to prove the main theorem of class field theory. However, after noticing that the background of the students was not sufficient, I started with algebraic number theory. I discussed prime decomposition, valuation, local fields, and in the last three lectures explained the main theorem of local and global class field theory. 106
112 2011 II I motivated class field theory as a classification of abelian extensions of number fields and local fields. It also answers questions regarding decomposition of prime ideals in abelian extensions of number fields. This can be viewed as a generalization of Gauss reciprocity law. I encouraged students to participate in class with questions, and to submit solutions to homework problems. I lectured in Japanese, but I encouraged students to submit homework solutions in English, and I corrected the English language as well as the mathematics. I gave weekly homework, and eveluated the students based on the points in homework solutions. M1 M The lecture went according to my plan. I was pleased with the attendance, but participation of the students by questions was less than expected. Weekly office hours were held, and I asked students to give their opinion on my teaching. 107
113 II 2011 II N. Bourbaki, Groupes et Algebres de Lie, Chap. 4,5 et 6, Masson. 2. J. H. Conway, N.J.A. Sloane, Sphere Packings, Lattices, and Groups, Springer. 3. P. Griffiths, J. Harris, Principles of Algebraic Geometry, Wiley. 4. J.P. Serre, A course in arithmetic, Springer. TA () M1 M2 D ( ) ( )
114 2011 II M1 M
115 I 2011 I 2 3,,. O. Lehto. Univalent functions and Teichmüller spaces. Springer. O. Forster. Lectures on Riemann surfaces. Springer. C. McMullen, Riemann surfaces, dynamics and geometry: Course Notes, A. Douady and J. H. Hubbard. A proof of Thurston s topological characterization of rational maps. Acta Math. 171(1993), TA () M1 M2 D ( ) ( ) (2011/4/19) 2 (2011/4/26) 1 3 (2011/5/10) 2 4 (2011/5/17) 5 (2011/5/24) 6 (2011/5/31) 7 (2011/6/7) 110
116 2011 I 8 (2011/6/14) 9 (2011/6/21) 10 (2011/6/28) 11 (2011/7/5) 12 (2011/7/12) 13 (2011/7/26) 2 M1 M
117 I( II ) 2011 I( II ) 2 1 0,,, 1992 TA 1 () M1 M2 D ( ) ( )
118 2011 I( II )
119 I ( II ) 2011 I ( II ) () () I () () () TA 1 () M1 M2 D ( ) ( ) ( ) () 114
120 2011 I ( II ) ( ) (4 )
121 I ( II )
122 2011 I ( III ) I ( III ) 2 1 0,,, 1992, I,, 1980 TA 1 () M1 M2 D ( ) ( ) ( ) 80 3 ε-δ ε-δ 5 117
123 I ( III ) 2011 (5 ) 100 2:2:6 ( ) S A B C 59 F S S S 3 10 S () S 10 ( 1 ) 118
124 2011 I ( III ) I ( III ) TA 1 () M1 M2 D ( ) ( ) % 1. : 2. : 3. : 9 TA 119
125 I ( III )
126 2011 I ( IV ) I ( IV ) 2 1 0,,,,,,, TA 1 () M1 M2 D ( ) ( ) (,, ), (,,, ), (,, ), (,,,, ), (,, ), (,,, ), (,,, ), (,, ), (,,, ), (,, ), (, ), (, ),, 121
127 I ( IV ) 2011,, (50 ),,,, 1 S A B C D F ,,,,, 122
128 2011 I IV I IV 2 / 1 0,, 2010, I II,, 1980, 1985, I II,, 2003,,, 1983 TA 1 () M1 M2 D ( ) ( )
129 I IV 2011 F F S A B C F
130 2011 I ( IV ) I ( IV ) TA 1 () M1 M2 D ( ) ( )
131 I ( IV ) 2011 S
132 2011 I ( II ) I ( II ) TA 1 () M1 M2 D ( ) ( )
133 I ( II ) ,
134 2011 I ( II ) I ( II ) TA 1 () M1 M2 D ( ) ( ) I TA 129
135 I ( II ) S A B C F
136 2011 I ( III ) I ( III ) 2 1 1, larsh/teaching/s2011 LA The greatest obstacle to teaching linear algebra and, indeed, mathematics in general is that students completely lack knowledge of basic set theory. In particular, it is a problem that students are unfamiliar with the notion of a map which is central to all mathematics. TA 1 () M1 M2 D ( ) ( ) This course is the first semester of a two-semester course in linear algebra. After a brief introduction to sets and maps, students are introduced to linear maps from one Euclidean space to another and the representation of such maps by matrices with respect to the standard bases. It is shown that composition of linear maps correspond to matrix multiplication. The course next treats systems of linear equations and their solution by Gaussian elimination. The final topic is the determinant of square matrices. The following fundamental theorem is proved: The determinant is the unique multi-linear alternating map from the set of real square matrices to the set of real numbers that takes the value 1 at the identity matrix. It is further shown how various properties of the determinant derives from this theorem. 131
137 I ( III ) 2011 The course had one weekly lecture of 90 minutes. In the first minutes, lecture was given at the blackboard following lecture notes that were handed out at the beginning of each lecture and made available to students on the course homepage. In the final minutes, the students were asked to solve practice problems at their seat assisted by lecturer and teaching assistant. The evaluation of the students was based on midterm and final exams S A B C F
138 2011 I ( III ) I ( III ) TA () M1 M2 D ( ) ( ) [ ] [] 133
139 I ( III )
140 2011 I IV I IV 2 1 0,, TA 1 () M1 M2 D ( ) ( )
141 I IV
142 2011 I II I II 2 / TA 1 () M1 M2 D ( ) ( )
143 I II
144 TA 1 () M1 M2 D ( ) ( ) calculus Home Work 1 TA 139
145 Home Work Home Work
146 2011 I ( - ) I ( - ) TA 1 () M1 M2 D ( ) ( ) ( ) ( ) ( ) 141
147 I ( - ) 2011 III ( 100 ) (20 ) III 142
148 ,, L.V. TA 1 () M1 M2 D ( ) ( ) (2011/4/14) 2 (2011/4/21) 3 (2011/4/28) 4 (2011/5/12) 5 (2011/5/19) 6 (2011/5/26) 7 (2011/6/9) 8 (2011/6/16) 9 (2011/6/23) 143
149 (2011/6/30) 11 (2011/7/7) 12 (2011/7/14) (2) 13 (2011/7/21) 1 Mathematica TA
150
151 TA 1 () M1 M2 D ( ) ( ) Home Work TA 146
152 2011 Home Work Home Work
153 , I II TA 1 () M1 M2 D ( ) ( ) / /28 148
154
155 ( I,IV ) 2011 ( I,IV ) TA 1 () M1 M2 D ( ) ( )
156 2011 ( I,IV )
157 ( III ) 2011 ( III ) 2 2 1,, TA 1 () M1 M2 D ( ) ( ) , (1). (2) (3), (4), (5) (6) 152
158 2011 ( III ),, ,,.,,,.. 153
159 ( III ) 2011 ( III ) 2 / 2,,, 1977 TA 1 () M1 M2 D ( ) ( ) TA 154
160 2011 ( III ) (S) (A) (B) (C) (D)
161 ( V ) 2011 ( V ) 2 / 2 TA 1 () M1 M2 D ( ) ( )
162 2011 ( V ) 1 30 (4 ) V
163 2011 Jacques Garrigue TA () M1 M2 D ( ) ( ) Turing Turing 4 URL kyouyou/
164 Turing 159
165
166 I () 2 II ( ) 3 IV ( ) 4 1 II 2 II ( ) 3 CIII ( ) 4 IV 1 AII ( ) 2 II ( 4 ) 3 Hesselholt I III (Garrigue) 4 1 ( ) III ( ) 2 II ( ) 3 II () 4 BII ( ) 1 V, VI () II ( ) 2 II ( ) 3 CII ( ) 4 II () 161
167 II 3 VI II ( ) I (Hershend) 3 II ( ) 4 II (Hesselholt) 1 III 2 Garrigue IV I 3 4 I 1 2 II 3 II 4 162
168 2011 II II I II TA 1 () M1 M2 D ( ) ( ) ) 2) 3) 163
169 II TA TA
170 2011 II( ) II( ) TA 1 () M1 M2 D ( ) ( ) ,
171 II( ) 2011 TA NUCT 90 S 1 80 A B C S 4 A( ) 18 B( ) 25 C( ) 13 F( ) F( ) 166
172 2011 II( ) 167
173 II( ) 2011 II( ) TA 1 () M1 M2 D ( ) ( ) TA 168
174 2011 II( ) = 50:30:20. (S) (A) (B) (C) (D)
175 II( ) 2011 II( ) yamagami/teaching/calculus/cal2011akib.pdf TA 1 () M1 M2 D ( ) ( ) (10/07) (10/14) (10/21) (10/28) (11/11 ) (11/18) (11/25) (12/02) (12/09) (12/16) (12/23) (01/20) (01/27) (02/03) web
176 2011 II( ) x 4x + 20 S A B C F
177 II 2011 II 2 1 0,, TA 1 () M1 M2 D ( ) ( )
178 2011 II S 9 A 22 B 22 C 18 F
179 II 2011 II [1] [2] [3] 1 [4] 4 [5] 1 [6] [7] [8] [9] [10] TA 1 () M1 M2 D ( ) ( ) % II I 174
180 2011 II (1) 1 (2) (3) 3 (4) II 175
181 II S, A, B, C, F S180 A B C140 1 S A B C F v 1, v 2, v 3 V 1 F : V V F (v 1 ), F (v 2 ), F (v 3 ) 1 β 1 F (v 1 ) + β 2 F (v 2 ) + β 3 F (v 3 ) = 0 β 1 = β 2 = β 3 = 0 176
182 2011 II II TA 1 () M1 M2 D ( ) ( )
183 II 2011 (S) (A) (B) (C) (D)
184 2011 II II TA 1 () M1 M2 D ( ) ( )
185 II
186 2011 II II TA 1 () M1 M2 D ( ) ( ) Lagrange Waring 181
187 II
188 2011 II II TA 1 () M1 M2 D ( ) ( ) TA 183
189 II 2011 S S 5 A 28 B 7 C
190 2011 II II TA 1 () M1 M2 D ( ) ( )
191 II ,.,..,.,,,.,,. TA 186
192 2011 II II TA 1 () M1 M2 D ( ) ( ) TA 187
193 II 2011 S S 2 A 26 B 9 C
194 2011 II II TA 1 () M1 M2 D ( ) ( )
195 II 2011 S 5 A 26 B 5 C
196 2011 II II TA 1 () M1 M2 D ( ) ( )
197 II TA 192
198 2011 A II A II 4 2 1,,, 2009 TA 1 () M1 M2 D ( ) ( ) L1 Ascoli-Arzela 193
199 A II M
200 2011 BII BII TA () M1 M2 D ( ) ( ) /6 10/13 10/20 10/27 11/3 11/10 195
201 BII /17 11/24 12/1 12/8 : 12/15 1: 12/22 2: 1/12 3: 1/19 1:, 1/26 2/
202 2011 CII CII 4 2 1, TA 1 () M1 M2 D ( ) ( ) ,., (1), (2),,.,, Taylor,,,,,.,. 197
203 CII 2011.,,, ,.,,. 198
204 2011 CIII CIII TA 1 () M1 M2 D ( ) ( )
205 CIII
206 2011 Mathematica 3 2 1, Mathematica Mathematica, Mathematica TA () M1 M2 D ( ) ( ) (2011/10/06) Mathematica 2 (2011/10/13) 3 (2011/10/20) 4 (2011/10/27) 5 (2011/11/10) 6 (2011/11/17) 1 ParametricPlot 7 (2011/11/24) Manipulate 8 (2011/12/1) 9 (2011/12/8) 10 (2011/12/15) 201
207 (2012/1/12) 13 (2012/1/19) M
208 2011 V VI V VI TA 1 () M1 M2 D ( ) ( ) ,,,., (1) ( ), (2), (3) ( ), (4), (5), (6) (), (7),.,., 2,.,,. 203
209 V VI 2011, 10:10:30:50.,, ,, 1/3.,.,,.,,,.,. 204
210 2011 V, VI V, VI TA 1 () M1 M2 D ( ) ( ) , ,. 10/7 10/14 (, 2 ) 10/21 (2 ) 205
211 V, VI /28 () ( ) 11/4 ( ) [ ] 11/11 11/18 () [ ] 11/25 ( ) 12/2 () 12/9 ( ) 12/16 [] 1/20 ( ) [ ] 1/27 ( ), ,, () ,, (12/9)..,,,. (. ). 206
212 2011 V, VI.,.,.,, 80, 70 80, 60 70, 60.,, (3 ) ,,,,.. w 2 = w w w = re iθ w = x + iy ( ) () 1 1 (2 ( ) 1.) ( 1 2 ) 1 () (.),
213 V, VI 2011, 1 208
214 2011 V VI V VI TA 1 () M1 M2 D ( ) ( ) , 1..,,,,,.,..,,,...,.,., ( ). 209
215 V VI , 50., 100, 150.,. 2, , 2,
216 2011 II II [1] [2] [3] [4] [5] [6] [7] [8] I II [9] [10] M. Artin, Algebra, Addison Wesley. [1], [2], [3] TA 1 () M1 M2 D ( ) ( )
217 II 2011 Jordan (1) (2) Noether I Jordan BII Euclid Z/nZ Euler Noether Eisenstein Gauss Jordan
218 2011 II /4 1/4 TA
219 II
220 2011 II II TA 1 () M1 M2 D ( ) ( ) II I (1). (2). (3). (4). van Kanpen 215
221 II 2011 TA
222 2011 IV VI IV VI TA () M1 M2 D ( ) ( ) Sobolev, Sobolev..,. 217
223 IV VI Sobolev.,. 218
224 TA () M1 M2 D ( ) ( )
225
226
227 I () 2011 I () M. Reid, Undergraduate Algebraic Geometry, London Math. Soc. TA () M1 M2 D ( ) ( )
228 2011 I ()
229 I () 2011 I () ,,, I,, 1996 = Fermat,, 2005,,, (),, 1971/72,, J.-P.,,, 1979, Lang, S., Algebraic Number theory, Springer, 1986, TA () M1 M2 D ( ) ( ) p (1) (2) p (3) p (4) (5) p 224
230 2011 I () p 225
231 I () 2011 I () 3 : [1], 30 () [2], () [3],,, () [4], () [5] M. Dunajski, Solitons, Instantons and Twistors (Oxford) TA () M1 M2 D ( ) ( ) , Korteweg-de Vries (KdV),,. ( ) 226
232 2011 I () 12/19KdV 12/26 KdV (Lax, ) [] 1/16, [] [] 1/23 τ 1/30 Yang-Mills [ ] ( 5.) ( 100 ) (.), 10, 70, 60 70, 50 60, 50.. (3.) 3, , 3 () (KP ) () 227
233 I () 2011 (3 ) ( ) ( 2 ) (3 ) (10 ) (9 ) 3 1 (6 ) (12 ) 12 (7 ) (5 ). 1 (5 ) (4 ). 1 (6 ) (3 )12. Yang-Mills quasideterminant () (, 5.)
234 2011 I I I I () 1/ TA () M1 M2 D ( ) ( )
235 I I 2011 ( ) ( ) ( ) ( )
236 2011 I I 3 4 M1 M
237 I I I I 1 1/ ( ) ( ) ( ) ( ) ( ) TA () M1 M2 D ( ) ( ) ( ) LSI LSI ( ) ( ) TCP/IP 232
238 2011 I I 1 ( ) http https( ) ( ) (RSA) 3 4 M1 M
239 I I I I / 2 ( ) ( ) ( ) ( ) PR ( ) TA () M1 M2 D ( ) ( )
240 2011 I I M1 M
241 I I I I 3 IT 1/ /30( ) 12/7( ) 12/14( ) 12/21( ) 1/18( ) TA () M1 M2 D ( ) ( )
242 2011 I I M1 M
243 II/ II 2011 II/ II 2 4 / 2 TA 1 () M1 M2 D ( ) ( ) Part 1. Lect. 1 Lie algebra (1. Definitions, 2. Examples, 3. Subalgebra, ideal,..., 4. Linear Lie algebras, 5. Lie Lie ) Lect. 2 (1. g-module, 2.. sl 2, 3. Lect. 3 sl 2 -weight (1. sl 2 -moudle, sl 2 -weight, 3., 4. character) Lect. 4 (1., 2., 3., 4. sl 2 -module Part 2. Lect. 5 sl 3 (1) (1. sl 3, 2. sl 3 -weight, 3. ) Lect. 6 sl 3 (2) (1. simple root, 2. Weyl, 3. highest weight module, 4. ) Lect. 7 Simple Lie algebras: simply laced type (1.Dynkin diagram Cartan, 2. ADE Lie algebra, 3. root weight, Exaple: type A n ) Lect. 8 Simple Lie algebra (1. root Weyl, 2. ) 238
244 2011 II/ II Lect. 9 Nonsimply laced case (1. Dynkin diagram Cartan, 2. nonsimply laced Lie algebras, 3. Example of rank 2, 4. type C n sp 2n, 5. ) Lect. 10 More about representations (1. Fundamental weight, 2. tensor, 3. character, 4. Example: A 2 ) Part 3. Lect. 11 Kac-Moody algebra (1. Generalized Cartan matrix, 2. Kac-Moody algebras, 3. Universal enveloping algebra, 4. Integrable module) Lect. 12 Affine Lie algebra (1. Affine type, 2. loop algebra realization) Lect. 13 quantum group (1. U q (sl 2 ), 2., 3. ) Part 1 exercise, Part 2 exercise, )
245 II VI 2011 II VI I. Chavel, Eigenvalues in Riemannian Geometry, Academic Press. INC, M. Taylor, Noncommutative Harmonic Analysis, Math. Surveys and Monographs, 22, AMS, 1986., 1992., TA () M1 M2 D ( ) ( )
246 2011 II VI M1 M , 3 241
247 III 2011 III TA 1 () M1 M2 D ( ) ( ) (Hilbert, Fourier, Fourier )... 5 TA. 242
248 2011 III
249 VI VI) 2011 VI VI) -Maxwell - 2 4, TA () M1 M2 D ( ) ( ) Maxwell 3. Maxwell 4. Maxwell Lorentz Maxwell 244
250 2011 VI VI) M1 M
251 III III 2011 III III Jacques Garrigue 4 2 OCaml-Nagoya OCaml 2007 Garrigue 1999 Coq URL AW/index.html TA () M1 M2 D ( ) ( ) OCaml Coq 246
252 2011 III III Coq 4 M1/M
253 IV II 2011 IV II TA () M1 M2 D ( ) ( ) Schubert Demazure 248
254 2011 IV II
255 IV II 2011 IV II Schur algebra J. A. Green, Polynomial representations of GL n, Springer (1980). S. Martin, Schur algebras and representation theory, Cambridge (1993). TA () M1 M2 D ( ) ( ) Schur algebra 0 Schur algebra Schur algebra Schur algebra Akin-Buchsbaum Schur algebra 250
256 2011 IV II A B C D D D S 4 M1 M D 251
257 I 2011 I 2 3 [1] W. Bruns and J.Herzog, Cohen-Macaulay rings, 1998, revised edition (10 ), Cambridge Univ. Press [2] C.Huneke, Tight closure and its application, CBMS 88, Lecture notes in Mathematics, AMS Providence. [3],, TA () M1 M2 D ( ) ( ) (Cohen-Macaulay, normality) Kunz, Colon-capturing. Briancon-Skoda, ( ) 252
258 2011 I 2 A 1 B M1 M
259 I 2011 I 2 3 I.G. Macdonald, Symmetric functions and Hall polynomials, 2nd ed., Oxford University Press, 1995 TA () M1 M2 D ( ) ( ) M2 M1 5 Macdonald Green GL n (F q) GL 2n (F q )/Sp 2n (F q ) 254
260 2011 I GL 2n (F q )/Sp 2n (F q ) H Macdonald GL n (F q ) H H Macdonald GL n (F q ) 255
261 II( II ) 2011 II( II ) 2 1,,, 1992 TA 1 () M1 M2 D ( ) ( )
262 2011 II( II )
263 II 2011 II 2 1 0,,, 2003,,, () () I () () () TA 1 () M1 M2 D ( ) ( ) (12/22) 64 (10/20) ,,, ( ),,,,,,,, 258
264 2011 II 7 8 TA 2 () ( ) ( ) (12 )
265 II
266 2011 II ( III ) II ( III ) 2 1 0,,, 1992, I,, 1980 TA 1 () M1 M2 D ( ) ( )
267 II ( III ) : 2 : F C B A 90 S S S
268 2011 II II 2 / 1 1 TA 1 () M1 M2 D ( ) ( ) % TA 263
269 II
270 2011 I I 2 1 0,,,,,, TA 1 () M1 M2 D ( ) ( ) ( )
271 I 2011 ( )
272 2011 II IV II IV 2 / , I II,, 1980, 1985, I II,, 2003,,, 1983 TA 1 () M1 M2 D ( ) ( )
273 II IV S A B C F
274 2011 II II II II 2 / TA 1 () M1 M2 D ( ) ( )
275 II II
276 2011 II II 2 1 0,,, 2006 TA 1 () M1 M2 D ( ) ( )
277 II * *
278 2011 II II TA 1 () M1 M2 D ( ) ( ) TA 273
279 II 2011 S, A, B, C, F 1 2 S A B C F S 274
280 2011 II II 2 1 1, larsh/teaching/f2011 LA The greatest obstacle to teaching linear algebra and, indeed, mathematics in general is that students completely lack knowledge of basic set theory. In particular, it is a problem that students are unfamiliar with the notion of a mapping, since this notion is central to all mathematics. TA 1 () M1 M2 D ( ) ( ) This course is the second semester of a two-semester course in linear algebra. The main subject is abstract real vector spaces. It is shown that every finite dimensional real vector space admits a basis. Linear maps between finite dimensional real vector spaces are introduced and it is shown that, after choices of ordered bases of the domain and target, every linear map is unique represented by a matrix. It is further shown that composition of linear maps corresponds to multiplication of the representing matrices; this is applied to coordinate change. Eigenvalues and eigenspaces of linear between finite dimensional real vector spaces are defined and it is shown how these may be evaluated. Finally, inner products, orthonormal bases, and orthogonal maps are defined. It is proved that every symmetric matrix can be diagonalized through conjugation by an orthogonal matrix. The theory is illustrated with numerous examples. 275
281 II 2011 The course had one weekly lecture of 90 minutes. In the first minutes, lecture was given at the blackboard following lecture notes that were handed out at the beginning of each lecture and made available to students on the course homepage. In the final minutes, the students were asked to solve practice problems at their seat assisted by lecturer and teaching assistant. The evaluation of the students was based on midterm and final exams S A B C F
2016 Course Description of Undergraduate Seminars (2015 12 16 ) 2016 12 16 ( ) 13:00 15:00 12 16 ( ) 1 21 ( ) 1 13 ( ) 17:00 1 14 ( ) 12:00 1 21 ( ) 15:00 1 27 ( ) 13:00 14:00 2 1 ( ) 17:00 2 3 ( ) 12
2010 ( )
2010 (2010 1 8 2010 1 13 ( 1 29 ( 17:00 2 3 ( e-mail (1 3 (2 (3 (1 (4 2010 1 2 3 4 5 6 7 8 9 10 11 Hesselholt, Lars 12 13 i 1 ( 2 3 Cohen-Macaulay Auslander-Reiten [1] [2] 5 [1], :,, 2002 [2] I Assem,
compact compact Hermann compact Hermite ( - ) Hermann Hermann ( ) compact Hermite Lagrange compact Hermite ( ) a, Σ a {0} a 3 1
014 5 4 compact compact Hermann compact Hermite ( - ) Hermann Hermann ( ) compact Hermite Lagrange compact Hermite ( ) 1 1.1. a, Σ a {0} a 3 1 (1) a = span(σ). () α, β Σ s α β := β α,β α α Σ. (3) α, β
Title < 論文 > 公立学校における在日韓国 朝鮮人教育の位置に関する社会学的考察 : 大阪と京都における 民族学級 の事例から Author(s) 金, 兌恩 Citation 京都社会学年報 : KJS = Kyoto journal of so 14: 21-41 Issue Date 2006-12-25 URL http://hdl.handle.net/2433/192679 Right
(check matrices and minimum distances) H : a check matrix of C the minimum distance d = (the minimum # of column vectors of H which are linearly depen
Hamming (Hamming codes) c 1 # of the lines in F q c through the origin n = qc 1 q 1 Choose a direction vector h i for each line. No two vectors are colinear. A linearly dependent system of h i s consists
i Version 1.1, (2012/02/22 24),.,..,.,,. R-space,, ( R- space),, Kahler (Kähler C-space)., R-space,., R-space, Hermite,.
R-space ( ) Version 1.1 (2012/02/29) i Version 1.1, (2012/02/22 24),.,..,.,,. R-space,, ( R- space),, Kahler (Kähler C-space)., R-space,., R-space, Hermite,. ii 1 Lie 1 1.1 Killing................................
II II,,,, AII BII CII
2012 Course Design of 2nd Semester (2012 9 24 ) 2012 1 II........................... 3 II,,,,.... 4 2 AII........................... 5 BII.......................... 6 CII.......................... 7 CIII...........................
1
1 Borel1956 Groupes linéaire algébriques, Ann. of Math. 64 (1956), 20 82. Chevalley1956/58 Sur la classification des groupes de Lie algébriques, Sém. Chevalley 1956/58, E.N.S., Paris. Tits1959 Sur la classification
0. I II I II (1) linear type: GL( ), Sp( ), O( ), (2) loop type: loop current Kac-Moody affine, hyperbolic (3) diffeo t
e-mail: koyama@math.keio.ac.jp 0. I II I II (1) linear type: GL( ), Sp( ), O( ), (2) loop type: loop current Kac-Moody affine, hyperbolic (3) diffeo type: diffeo universal Teichmuller modular I. I-. Weyl
. Mac Lane [ML98]. 1 2 (strict monoidal category) S 1 R 3 A S 1 [0, 1] C 2 C End C (1) C 4 1 U q (sl 2 ) Drinfeld double. 6 2
![. Mac Lane [ML98]. 1 2 (strict monoidal category) S 1 R 3 A S 1 [0, 1] C 2 C End C (1) C 4 1 U q (sl 2 ) Drinfeld double. 6 2](/thumbs/91/105488587.jpg ". Mac Lane [ML98]. 1 2 (strict monoidal category) S 1 R 3 A S 1 [0, 1] C 2 C End C (1) C 4 1 U q (sl 2 ) Drinfeld double. 6 2")
2014 6 30. 2014 3 1 6 (Hopf algebra) (group) Andruskiewitsch-Santos [AFS09] 1980 Drinfeld (quantum group) Lie Lie (ribbon Hopf algebra) (ribbon category) Turaev [Tur94] Kassel [Kas95] (PD) x12005i@math.nagoya-u.ac.jp
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
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.
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
駒田朋子.indd
2 2 44 6 6 6 6 2006 p. 5 2009 p. 6 49 12 2006 p. 6 2009 p. 9 2009 p. 6 2006 pp. 12 20 2005 2005 2 3 2005 An Integrated Approach to Intermediate Japanese 13 12 10 2005 8 p. 23 2005 2 50 p. 157 2 3 1 2010
- June 0 0
0 0 0 0 0 0 0 0 - June 0 0 0 - June 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 - June 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Yes 0 0 0 0 0 0 0 0 0 0 0 0 0 A 0
25 II :30 16:00 (1),. Do not open this problem booklet until the start of the examination is announced. (2) 3.. Answer the following 3 proble
25 II 25 2 6 13:30 16:00 (1),. Do not open this problem boolet until the start of the examination is announced. (2) 3.. Answer the following 3 problems. Use the designated answer sheet for each problem.
29 28 39 1936 Acquiring technique and forming character in physical education after 1936 Analysis of articles of Kenji Shinozaki FUJIKAWA Kazutoshi The United Graduate School of Education Tokyo Gakugei
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.
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
6 1Bulletin of Tokyo University and Graduate School of Social Welfarepp73-86 2015, 10 372-0831 2020-1 2015 5 29 2015 7 9 : : : 1 A B C D E 4 A B A B A B A ] AB C D E 4 8 73 17 2 22 750 1 2 26 2 16 17 32
WASEDA RILAS JOURNAL
27 200 WASEDA RILAS JOURNAL NO. 1 (2013. 10) WASEDA RILAS JOURNAL 28 199 29 198 WASEDA RILAS JOURNAL 30 197 31 196 WASEDA RILAS JOURNAL 32 195 1 3 12 6 23 No 1 3 0 13 3 4 3 2 7 0 5 1 6 6 3 12 0 47 23 12
篇 S-V / S-V-C / S-V-O / S-V-O-O / S-V-O-C IA 25 Mike Lawson 1 1 Students will improve their ability to use English in a professionally relevant manner by practicing a process of speech outline
Communicative English (1) Thomas Clancy, Roman Greco Communicative English (CE) I is an introductory course in Spoken English. The course provides freshmen students with the opportunity to express themselves
The Indirect Support to Faculty Advisers of die Individual Learning Support System for Underachieving Student The Indirect Support to Faculty Advisers of the Individual Learning Support System for Underachieving
Bull. of Nippon Sport Sci. Univ. 47 (1) Devising musical expression in teaching methods for elementary music An attempt at shared teaching
Bull. of Nippon Sport Sci. Univ. 47 (1) 45 70 2017 Devising musical expression in teaching methods for elementary music An attempt at shared teaching materials for singing and arrangements for piano accompaniment
B5 H1 H5 H2 H1 H1 H2 H4 H1 H2 H5 H1 H2 H4 S6 S1 S14 S5 S8 S4 S4 S2 S7 S7 S9 S11 S1 S14 S1 PC S9 S1 S2 S3 S4 S5 S5 S9 PC PC PC PC PC PC S6 S6 S7 S8 S9 S9 S5 S9 S9 PC PC PC S9 S10 S12 S13 S14 S11 S1 S2
The Key Questions about Today's "Experience Loss": Focusing on Provision Issues Gerald ARGENTON These last years, the educational discourse has been focusing on the "experience loss" problem and its consequences.
sequentially Cohen Macaulay Herzog Cohen Macaulay 5 unmixed semi-unmixed 2 Semi-unmixed Semi-unmixed G V V (G) V G V G e (G) G F(G) (G) F(G) G dim G G
Semi-unmixed 1 K S K n K[X 1,..., X n ] G G G 2 G V (G) E(G) S G V (G) = {1,..., n} I(G) G S square-free I(G) = (X i X j {i, j} E(G)) I(G) G (edge ideal) 1990 Villarreal [11] S/I(G) Cohen Macaulay G 2005
SAMA- SUKU-RU Contents p-adic families of Eisenstein series (modular form) Hecke Eisenstein Eisenstein p T
SAMA- SUKU-RU Contents 1. 1 2. 7.1. p-adic families of Eisenstein series 3 2.1. modular form Hecke 3 2.2. Eisenstein 5 2.3. Eisenstein p 7 3. 7.2. The projection to the ordinary part 9 3.1. The ordinary
平成 15 年度 ( 第 25 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 15 月年 78 日開催月 4 日 ) X 2 = 1 ( ) f 1 (X 1,..., X n ) = 0,..., f r (X 1,..., X n ) = 0 X = (
1 1.1 X 2 = 1 ( ) f 1 (X 1,..., X n ) = 0,..., f r (X 1,..., X n ) = 0 X = (X 1,..., X n ) ( ) X 1,..., X n f 1,..., f r A T X + XA XBR 1 B T X + C T QC = O X 1.2 X 1,..., X n X i X j X j X i = 0, P i
自分の天職をつかめ
Hiroshi Kawasaki / / 13 4 10 18 35 50 600 4 350 400 074 2011 autumn / No.389 5 5 I 1 4 1 11 90 20 22 22 352 325 27 81 9 3 7 370 2 400 377 23 83 12 3 2 410 3 415 391 24 82 9 3 6 470 4 389 362 27 78 9 5
Fig. 1 The district names and their locations A dotted line is the boundary of school-districts. The district in which 10 respondents and over live is indicated in italics. Fig. 2 A distribution of rank
CAPELLI (T\^o $\mathrm{r}\mathrm{u}$ UMEDA) MATHEMATICS, KYOTO UNIVERSITY DEPARTMENT $\mathrm{o}\mathrm{p}$ $0$:, Cape i,.,.,,,,.,,,.
1508 2006 1-11 1 CAPELLI (T\^o $\mathrm{r}\mathrm{u}$ UMEDA) MATHEMATICS KYOTO UNIVERSITY DEPARTMENT $\mathrm{o}\mathrm{p}$ $0$: Cape i Capelli 1991 ( ) (1994 ; 1998 ) 100 Capelli Capelli Capelli ( ) (
ブック 1.indb
Universitys Educational Challenge to Develop Leadership Skills of Women Through the Course of Business Leadership at Womens University Toru Anzai In Japan more women leaders are expected to play active
On Japanese empathy and interpretation IKEDA, Masatoshi In this paper I compared it with empathy as a manner of psychotherapist about interpretation a
On Japanese empathy and interpretation IKEDA, Masatoshi In this paper I compared it with empathy as a manner of psychotherapist about interpretation and discussed it. For words of English empathy, there
Virtual Window System Virtual Window System Virtual Window System Virtual Window System Virtual Window System Virtual Window System Social Networking
23 An attribute expression of the virtual window system communicators 1120265 2012 3 1 Virtual Window System Virtual Window System Virtual Window System Virtual Window System Virtual Window System Virtual
alternating current component and two transient components. Both transient components are direct currents at starting of the motor and are sinusoidal
Inrush Current of Induction Motor on Applying Electric Power by Takao Itoi Abstract The transient currents flow into the windings of the induction motors when electric sources are suddenly applied to the
1 2 1 2012 39 1964 1997 1 p. 65 1 88 2 1 2 2 1 2 5 3 2 1 89 1 2012 Frantzen & Magnan 2005 2010 6 N2 2014 3 3.1 2015 2009 1 2 3 2 90 2 3 2 B1 B1 1 2 1 2 1 2 1 3.2 1 2014 2015 2 2 2014 2015 9 4.1 91 1 2
,, 2024 2024 Web ,, ID ID. ID. ID. ID. must ID. ID. . ... BETWEENNo., - ESPNo. Works Impact of the Recruitment System of New Graduates as Temporary Staff on Transition from College to Work Naoyuki
2.1 H f 3, SL(2, Z) Γ k (1) f H (2) γ Γ f k γ = f (3) f Γ \H cusp γ SL(2, Z) f k γ Fourier f k γ = a γ (n)e 2πinz/N n=0 (3) γ SL(2, Z) a γ (0) = 0 f c
GL 2 1 Lie SL(2, R) GL(2, A) Gelbart [Ge] 1 3 [Ge] Jacquet-Langlands [JL] Bump [Bu] Borel([Bo]) ([Ko]) ([Mo]) [Mo] 2 2.1 H = {z C Im(z) > 0} Γ SL(2, Z) Γ N N Γ (N) = {γ SL(2, Z) γ = 1 2 mod N} g SL(2,
2018/10/04 IV/ IV 2/12. A, f, g A. (1) D(0 A ) =, D(1 A ) = Spec(A), D(f) D(g) = D(fg). (2) {f l A l Λ} A I D(I) = l Λ D(f l ). (3) I, J A D(I) D(J) =
2018/10/04 IV/ IV 1/12 2018 IV/ IV 10 04 * 1 : ( A 441 ) yanagida[at]math.nagoya-u.ac.jp https://www.math.nagoya-u.ac.jp/~yanagida 1 I: (ring)., A 0 A, 1 A. (ring homomorphism).. 1.1 A (ideal) I, ( ) I
(group A) (group B) PLE(Primary Leaving Examination) adobe Flash ipad 1 adobe Flash e-book ipad adobe Flash adobe Flash Pixton scratch PLE(Primary Lea
2012 Future University Hakodate 2012 System Information Science Practice Group Report Project Name Anime de Education Group Name Science Group /Project No. 1-B /Project Leader 1010071 Ayaka Saitou /Group
Studies of Foot Form for Footwear Design (Part 9) : Characteristics of the Foot Form of Young and Elder Women Based on their Sizes of Ball Joint Girth
Studies of Foot Form for Footwear Design (Part 9) : Characteristics of the Foot Form of Young and Elder Women Based on their Sizes of Ball Joint Girth and Foot Breadth Akiko Yamamoto Fukuoka Women's University,
1980年代半ば，米国中西部のモデル 理論，そして未来－モデル理論賛歌
2016 9 27 RIMS 1 2 3 1983 9-1989 6 University of Illinois at Chicago (UIC) John T Baldwin 1983 9-1989 6 University of Illinois at Chicago (UIC) John T Baldwin Y N Moschovakis, Descriptive Set Theory North
A pp CALL College Life CD-ROM Development of CD-ROM English Teaching Materials, College Life Series, for Improving English Communica
A CALL College Life CD-ROM Development of CD-ROM English Teaching Materials, College Life Series, for Improving English Communicative Skills of Japanese College Students The purpose of the present study
L3 Japanese (90570) 2008
90570-CDT-08-L3Japanese page 1 of 15 NCEA LEVEL 3: Japanese CD TRANSCRIPT 2008 90570: Listen to and understand complex spoken Japanese in less familiar contexts New Zealand Qualifications Authority: NCEA
Building a Culture of Self- Access Learning at a Japanese University An Action Research Project Clair Taylor Gerald Talandis Jr. Michael Stout Keiko Omura Problem Action Research English Central Spring,
Milnor 1 ( ), IX,. [KN].,. 2 : (1),. (2). 1 ; 1950, Milnor[M1, M2]. Milnor,,. ([Hil, HM, IO, St] ).,.,,, ( 2 5 )., Milnor ( 4.1)..,,., [CEGS],. Ω m, P
![Milnor 1 ( ), IX,. [KN].,. 2 : (1),. (2). 1 ; 1950, Milnor[M1, M2]. Milnor,,. ([Hil, HM, IO, St] ).,.,,, ( 2 5 )., Milnor ( 4.1)..,,., [CEGS],. Ω m, P](/thumbs/94/118231293.jpg "Milnor 1 ( ), IX,. [KN].,. 2 : (1),. (2). 1 ; 1950, Milnor[M1, M2]. Milnor,,. ([Hil, HM, IO, St] ).,.,,, ( 2 5 )., Milnor ( 4.1)..,,., [CEGS],. Ω m, P")
Milnor 1 ( ), IX,. [KN].,. 2 : (1),. (2). 1 ; 1950, Milnor[M1, M2]. Milnor,,. ([Hil, HM, IO, St] ).,.,,, ( 2 5 )., Milnor ( 4.1)..,,., [CEGS],. Ω m, PC ( 4 5 )., 5, Milnor Milnor., ( 6 )., (I) Z modulo
先端社会研究 ★５★号／４．山崎
71 72 5 1 2005 7 8 47 14 2,379 2,440 1 2 3 2 73 4 3 1 4 1 5 1 5 8 3 2002 79 232 2 1999 249 265 74 5 3 5. 1 1 3. 1 1 2004 4. 1 23 2 75 52 5,000 2 500 250 250 125 3 1995 1998 76 5 1 2 1 100 2004 4 100 200
1 4 1 ( ) ( ) ( ) ( ) () 1 4 2
7 1995, 2017 7 21 1 2 2 3 3 4 4 6 (1).................................... 6 (2)..................................... 6 (3) t................. 9 5 11 (1)......................................... 11 (2)
Mazur [Ma1] Schlessinger [Sch] [SL] [Ma1] [Ma1] [Ma2] Galois [] 17 R m R R R M End R M) M R ut R M) M R R G R[G] R G Sets 1 Λ Noether Λ k Λ m Λ k C Λ
![Mazur [Ma1] Schlessinger [Sch] [SL] [Ma1] [Ma1] [Ma2] Galois [] 17 R m R R R M End R M) M R ut R M) M R R G R[G] R G Sets 1 Λ Noether Λ k Λ m Λ k C Λ](/thumbs/78/78261740.jpg "Mazur [Ma1] Schlessinger [Sch] [SL] [Ma1] [Ma1] [Ma2] Galois [] 17 R m R R R M End R M) M R ut R M) M R R G R[G] R G Sets 1 Λ Noether Λ k Λ m Λ k C Λ")
Galois ) 0 1 1 2 2 4 3 10 4 12 5 14 16 0 Galois Galois Galois TaylorWiles Fermat [W][TW] Galois Galois Galois 1 Noether 2 1 Mazur [Ma1] Schlessinger [Sch] [SL] [Ma1] [Ma1] [Ma2] Galois [] 17 R m R R R
Pari-gp /7/5 1 Pari-gp 3 pq
Pari-gp 3 2007/7/5 1 Pari-gp 3 pq 3 2007 7 5 Pari-gp 3 2007/7/5 2 1. pq 3 2. Pari-gp 3. p p 4. p Abel 5. 6. 7. Pari-gp 3 2007/7/5 3 pq 3 Pari-gp 3 2007/7/5 4 p q 1 (mod 9) p q 3 (3, 3) Abel 3 Pari-gp 3
200708_LesHouches_02.ppt
Numerical Methods for Geodynamo Simulation Akira Kageyama Earth Simulator Center, JAMSTEC, Japan Part 2 Geodynamo Simulations in a Sphere or a Spherical Shell Outline 1. Various numerical methods used
評論・社会科学 ８４号（よこ）（Ｐ）／３．金子
1 1 1 23 2 3 3 4 3 5 CP 1 CP 3 1 1 6 2 CP OS Windows Mac Mac Windows SafariWindows Internet Explorer 3 1 1 CP 2 2. 1 1CP MacProMacOS 10.4.7. 9177 J/A 20 2 Epson GT X 900 Canon ip 4300 Fujifilm FinePix
<8ED089EF8B D312D30914F95742E696E6464>
* 1 The problem of privacy in the news of newspapers and weekly magazines The analysis of the articles on the child serial killing incidents in Kobe Akihiko SHIMAZAKI Kenzo SHIDA Toshihiko KATANO *2 1
) ,
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
専攻科シラバス 一般科目
(Practical English) () 12 2 2 TOEIC TEST TOEIC 1. TOEIC TEST 2. B () 2 Unit 1 Shopping 2 Unit 2 Entertaiment Weather 2 Unit 3 Eating out 2 Unit 4 Travel 2 Unit 5 Health 2 2 Unit 6 Housing Media 2 Unit
soturon.dvi
12 Exploration Method of Various Routes with Genetic Algorithm 1010369 2001 2 5 ( Genetic Algorithm: GA ) GA 2 3 Dijkstra Dijkstra i Abstract Exploration Method of Various Routes with Genetic Algorithm
untitled
総研大文化科学研究第 6 号 (2010) 65 ... 66 佐貫 丘浅次郎の 進化論講話 における変化の構造 67 68 佐貫丘浅次郎の 進化論講話 における変化の構造 69 E 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 70 佐貫 丘浅次郎の 進化論講話 における変化の構造 71 72 佐貫丘浅次郎の 進化論講話 における変化の構造 73 74 佐貫丘浅次郎の 進化論講話
A11 (1993,1994) 29 A12 (1994) 29 A13 Trefethen and Bau Numerical Linear Algebra (1997) 29 A14 (1999) 30 A15 (2003) 30 A16 (2004) 30 A17 (2007) 30 A18
2013 8 29y, 2016 10 29 1 2 2 Jordan 3 21 3 3 Jordan (1) 3 31 Jordan 4 32 Jordan 4 33 Jordan 6 34 Jordan 8 35 9 4 Jordan (2) 10 41 x 11 42 x 12 43 16 44 19 441 19 442 20 443 25 45 25 5 Jordan 26 A 26 A1
„h‹¤.05.07
Japanese Civilian Control in the Cold War Era Takeo MIYAMOTO In European and American democratic countries, the predominance of politics over military, i.e. civilian control, has been assumed as an axiom.
井手友里子.indd
I goal of movement Banno 1999 60 61 65 12 2006 1978 1979 2005 1 2004 8 7 10 2005 54 66 Around 40 Around 40 2008 4 6 45 11 2007 4 6 45 9 2 Around 40 A 30A B 30 K C 30 P D 30 S 50 2007 2004 1979 2005 100
A comparison of abdominal versus vaginal hysterectomy for leiomyoma and adenomyosis Kenji ARAHORI, Hisasi KATAYAMA, Suminori NIOKA Department of Obstetrics and Gnecology, National Maizuru Hospital,Kyoto,
sakigake1.dvi
(Zin ARAI) arai@cris.hokudai.ac.jp http://www.cris.hokudai.ac.jp/arai/ 1 dynamical systems ( mechanics ) dynamical systems 3 G X Ψ:G X X, (g, x) Ψ(g, x) =:Ψ g (x) Ψ id (x) =x, Ψ gh (x) =Ψ h (Ψ g (x)) (
840 Geographical Review of Japan 73A-12 835-854 2000 The Mechanism of Household Reproduction in the Fishing Community on Oro Island Masakazu YAMAUCHI (Graduate Student, Tokyo University) This
19 Systematization of Problem Solving Strategy in High School Mathematics for Improving Metacognitive Ability
19 Systematization of Problem Solving Strategy in High School Mathematics for Improving Metacognitive Ability 1105402 2008 2 4 2,, i Abstract Systematization of Problem Solving Strategy in High School
1 M = (M, g) m Riemann N = (N, h) n Riemann M N C f : M N f df : T M T N M T M f N T N M f 1 T N T M f 1 T N C X, Y Γ(T M) M C T M f 1 T N M Levi-Civi
1 Surveys in Geometry 1980 2 6, 7 Harmonic Map Plateau Eells-Sampson [5] Siu [19, 20] Kähler 6 Reports on Global Analysis [15] Sacks- Uhlenbeck [18] Siu-Yau [21] Frankel Siu Yau Frankel [13] 1 Surveys
L1 What Can You Blood Type Tell Us? Part 1 Can you guess/ my blood type? Well,/ you re very serious person/ so/ I think/ your blood type is A. Wow!/ G
L1 What Can You Blood Type Tell Us? Part 1 Can you guess/ my blood type? 当ててみて / 私の血液型を Well,/ you re very serious person/ so/ I think/ your blood type is A. えーと / あなたはとっても真面目な人 / だから / 私は ~ と思います / あなたの血液型は
(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
ON A FEW INFLUENCES OF THE DENTAL CARIES IN THE ELEMENTARY SCHOOL PUPIL BY Teruko KASAKURA, Naonobu IWAI, Sachio TAKADA Department of Hygiene, Nippon Dental College (Director: Prof. T. Niwa) The relationship
2 94
32 2008 pp. 93 106 1 Received October 30, 2008 The purpose of this study is to examine the effects of aerobics training class on weight loss for female students in HOKURIKU UNIVERSITY. Seventy four female
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
h education/educating teaching indoctrination reasonable teaching education teaching education teaching education teaching
P h education/educating teaching indoctrination reasonable teaching education teaching education teaching education teaching P Ÿ education É É É P É É É É Ÿ Ÿ i structure P logical necessity dispositional
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
main.dvi
SGC - 70 2, 3 23 ɛ-δ 2.12.8 3 2.92.13 4 2 3 1 2.1 2.102.12 [8][14] [1],[2] [4][7] 2 [4] 1 2009 8 1 1 1.1... 1 1.2... 4 1.3 1... 8 1.4 2... 9 1.5... 12 1.6 1... 16 1.7... 18 1.8... 21 1.9... 23 2 27 2.1
第5章 偏微分方程式の境界値問題
October 5, 2018 1 / 113 4 ( ) 2 / 113 Poisson 5.1 Poisson ( A.7.1) Poisson Poisson 1 (A.6 ) Γ p p N u D Γ D b 5.1.1: = Γ D Γ N 3 / 113 Poisson 5.1.1 d {2, 3} Lipschitz (A.5 ) Γ D Γ N = \ Γ D Γ p Γ N Γ
九州大学学術情報リポジトリ Kyushu University Institutional Repository 看護師の勤務体制による睡眠実態についての調査 岩下, 智香九州大学医学部保健学科看護学専攻 出版情報 : 九州大学医学部保健学
九州大学学術情報リポジトリ Kyushu University Institutional Repository 看護師の勤務体制による睡眠実態についての調査 岩下, 智香九州大学医学部保健学科看護学専攻 https://doi.org/10.15017/4055 出版情報 : 九州大学医学部保健学科紀要. 8, pp.59-68, 2007-03-12. 九州大学医学部保健学科バージョン : 権利関係
ñ{ï 01-65
191252005.2 19 *1 *2 *3 19562000 45 10 10 Abstract A review of annual change in leading rice varieties for the 45 years between 1956 and 2000 in Japan yielded 10 leading varieties of non-glutinous lowland
Bulletin of JSSAC(2014) Vol. 20, No. 2, pp (Received 2013/11/27 Revised 2014/3/27 Accepted 2014/5/26) It is known that some of number puzzles ca
Bulletin of JSSAC(2014) Vol. 20, No. 2, pp. 3-22 (Received 2013/11/27 Revised 2014/3/27 Accepted 2014/5/26) It is known that some of number puzzles can be solved by using Gröbner bases. In this paper,
地域共同体を基盤とした渇水管理システムの持続可能性
I 1994 1994 1994 1,176 1,377 1995, p.21; 1999 Kazuki Kagohashi / 10 1 1 1991 drought water bank 2013 466-8673 18 E-mail:kagohashi@gmail.com 1 355 10 2 Kondo 2013 136 2015 spring / No.403 2 1 1994 1995,
Visual Evaluation of Polka-dot Patterns Yoojin LEE and Nobuko NARUSE * Granduate School of Bunka Women's University, and * Faculty of Fashion Science,
Visual Evaluation of Polka-dot Patterns Yoojin LEE and Nobuko NARUSE * Granduate School of Bunka Women's University, and * Faculty of Fashion Science, Bunka Women's University, Shibuya-ku, Tokyo 151-8523
Macdonald, ,,, Macdonald. Macdonald,,,,,.,, Gauss,,.,, Lauricella A, B, C, D, Gelfand, A,., Heckman Opdam.,,,.,,., intersection,. Macdona
Macdonald, 2015.9.1 9.2.,,, Macdonald. Macdonald,,,,,.,, Gauss,,.,, Lauricella A, B, C, D, Gelfand, A,., Heckman Opdam.,,,.,,., intersection,. Macdonald,, q., Heckman Opdam q,, Macdonald., 1 ,,. Macdonald,
,,,,., 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
2.3. p(n)x n = n=0 i= x = i x x 2 x 3 x..,?. p(n)x n = + x + 2 x x 3 + x + 7 x + x + n=0, n p(n) x n, ( ). p(n) (mother function)., x i = + xi +
( ) : ( ) n, n., = 2+2+,, = 2 + 2 + = 2 + + 2 = + 2 + 2,,,. ( composition.), λ = (2, 2, )... n (partition), λ = (λ, λ 2,..., λ r ), λ λ 2 λ r > 0, r λ i = n i=. r λ, l(λ)., r λ i = n i=, λ, λ., n P n,
Vol. 48 No. 4 Apr LAN TCP/IP LAN TCP/IP 1 PC TCP/IP 1 PC User-mode Linux 12 Development of a System to Visualize Computer Network Behavior for L
Vol. 48 No. 4 Apr. 2007 LAN TCP/IP LAN TCP/IP 1 PC TCP/IP 1 PC User-mode Linux 12 Development of a System to Visualize Computer Network Behavior for Learning to Associate LAN Construction Skills with TCP/IP
関西福祉大学紀要 １２号（Ｐ）／１．太田
Social Work Practice and Methods for Scientific Progress Yoshihiro Ohta Abstract : Although theories and methods of social work have been progressing new ideas and ways that support social work practice
pla85900.tsp.eps
( ) 338 8570 255 Tel: 048 858 3577, Fax: 048 858 3716 Email: tohru@nls.ics.saitama-u.ac.jp URL: http://www.nls.ics.saitama-u.ac.jp/ tohru/ 2006.11.29 @ p.1/38 1. 1 2006.11.29 @ p.2/38 1. 1 2. (a) H16 (b)
:- Ofer Feldman,Feldman : -
- -- E-mail: nkawano@hiroshima-u.ac.jp : - :- Ofer Feldman,Feldman : - : : : Mueller : - Mueller :.. : ... :........ .. : : : - : Kawano & Matsuo: - : - : - : : No. Feldman, Ofer (), The Political
NO.80 2012.9.30 3
Fukuoka Women s University NO.80 2O12.9.30 CONTENTS 2 2 3 3 4 6 7 8 8 8 9 10 11 11 11 12 NO.80 2012.9.30 3 4 Fukuoka Women s University NO.80 2012.9.30 5 My Life in Japan Widchayapon SASISAKULPON (Ing)
在日外国人高齢者福祉給付金制度の創設とその課題
Establishment and Challenges of the Welfare Benefits System for Elderly Foreign Residents In the Case of Higashihiroshima City Naoe KAWAMOTO Graduate School of Integrated Arts and Sciences, Hiroshima University
-1- -2- -1- A -1- -2- -3- -1- -2- -1- -2- -1- http://www.unicef.or.jp/kenri.syouyaku.htm -2- 1 2 http://www.stat.go.jp/index.htm http://portal.stat.go.jp/ 1871.8.28 1.4 11.8 42.7 19.3
Page 1 of 6 B (The World of Mathematics) November 20, 2006 Final Exam 2006 Division: ID#: Name: 1. p, q, r (Let p, q, r are propositions. ) (10pts) (a
Page 1 of 6 B (The World of Mathematics) November 0, 006 Final Exam 006 Division: ID#: Name: 1. p, q, r (Let p, q, r are propositions. ) (a) (Decide whether the following holds by completing the truth
1 2 Japanese society and for implementation into its education system for the first time. Since then, there has been about 135 years of the history of
38 2017 3 1 2 1882 135 3 1 1930 1970 E 2 1970 2000 3 2000 1 2 1 2 1 2 The Development of Drama in English as a Foreign Language Education in Japan HIDA Norifumi Abstract In 1882, Sutematsu Yamagawa Oyama,
21(2009) I ( ) 21(2009) / 42
21(2009) 10 24 21(2009) 10 24 1 / 21(2009) 10 24 1. 2. 3.... 4. 5. 6. 7.... 8.... 2009 8 1 1 (1.1) z = x + iy x, y i R C i 2 = 1, i 2 + 1 = 0. 21(2009) 10 24 3 / 1 B.C. (N) 1, 2, 3,...; +,, (Z) 0, ±1,
Powered by TCPDF ( Title 初級レベルの授業報告 : 基幹コース3 科目を担当して Sub Title Author 中村, 愛 (Nakamura, Ai) Publisher 慶應義塾大学日本語 日本文化教育センター Publication 20
Powered by TCPDF (www.tcpdf.org) Title 初級レベルの授業報告 : 基幹コース3 科目を担当して Sub Title Author 中村, 愛 (Nakamura, Ai) Publisher 慶應義塾大学日本語 日本文化教育センター Publication 2016 year Jtitle 日本語と日本語教育 No.44 (2016. 3),p.85-101 Abstract
Core Ethics Vol.
Core Ethics Vol. < > Core Ethics Vol. ( ) ( ) < > < > < > < > < > < > ( ) < > ( ) < > - ( ) < > < > < > < > < > < > < > < > ( ) Core Ethics Vol. ( ) ( ) ( ) < > ( ) < > ( ) < > ( ) < >
ABSTRACT The "After War Phenomena" of the Japanese Literature after the War: Has It Really Come to an End? When we consider past theses concerning criticism and arguments about the theme of "Japanese Literature
' , 24 :,,,,, ( ) Cech Index theorem 22 5 Stability 44 6 compact 49 7 Donaldson 58 8 Symplectic structure 63 9 Wall crossing 66 1
1998 1998 7 20 26, 44. 400,,., (KEK), ( ) ( )..,.,,,. 1998 1 '98 7 23, 24 :,,,,, ( ) 1 3 2 Cech 6 3 13 4 Index theorem 22 5 Stability 44 6 compact 49 7 Donaldson 58 8 Symplectic structure 63 9 Wall crossing
, CH n. CH n, CP n,,,., CH n,,. RH n ( Cartan )., CH n., RH n CH n,,., RH n, CH n., RH n ( ), CH n ( 1.1 (v), (vi) )., RH n,, CH n,., CH n,. 1.2, CH n
( ), Jürgen Berndt,.,. 1, CH n.,,. 1.1 ([6]). CH n (n 2), : (i) CH k (k = 0,..., n 1) tube. (ii) RH n tube. (iii). (iv) ruled minimal, equidistant. (v) normally homogeneous submanifold F k tube. (vi) normally
149 (Newell [5]) Newell [5], [1], [1], [11] Li,Ryu, and Song [2], [11] Li,Ryu, and Song [2], [1] 1) 2) ( ) ( ) 3) T : 2 a : 3 a 1 :
![149 (Newell [5]) Newell [5], [1], [1], [11] Li,Ryu, and Song [2], [11] Li,Ryu, and Song [2], [1] 1) 2) ( ) ( ) 3) T : 2 a : 3 a 1 :](/thumbs/92/109497872.jpg "149 (Newell [5]) Newell [5], [1], [1], [11] Li,Ryu, and Song [2], [11] Li,Ryu, and Song [2], [1] 1) 2) ( ) ( ) 3) T : 2 a : 3 a 1 :")
Transactions of the Operations Research Society of Japan Vol. 58, 215, pp. 148 165 c ( 215 1 2 ; 215 9 3 ) 1) 2) :,,,,, 1. [9] 3 12 Darroch,Newell, and Morris [1] Mcneil [3] Miller [4] Newell [5, 6], [1]