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


 しょうこ ふじした
 6 months ago
 Views:
Transcription
1 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 table below. And write your conclusion with reason.) p (q r) (p ( r)) q. p q r p (q r) (p ( r)) q T T T T T F T F T T F F F T T F T F F F T F F F [ (Conclusion and reason)] (b) p (q r) (Express p (q r) using, and parentheses. Do not use or.) Points
2 Page of 6. (Find the following and explain your reasoning.) (a) 50 (50 teams are in a tournament. If there is no draw, how many games are required to decide the winner of the touranment? Why?) (b) 1000 A, B, C, D, E n C m (How many ways are there to make 1000 paper cranes by five people, A, B, C, D, E, if each one makes at least 100? Use n C m to express your answer.) 3. 1 (Find the minimum cost of a connected network using the diagram below. Draw your network on the right as well by connecting corresponding points.) (Total)
3 Page 3 of (An 8 8 chess board has checkered pattern in black and white.) (a) 1 (Show that it is impossible to cover all squares of the board except the top right and the bottom left corners by 1 rectangular plates without overlapping.) (b) 4 1 (Show the following. If we choose two white squares and two black squares properly, it is impossible to cover the rest of the board by 1 rectangular plates without overlapping.) 5. K 3,3 (Show that K 3,3 below is not a planar graph.)
4 Page 4 of 6 6. A A 0 A (Ms. A attended a party. There were 0 people including Ms. A. After some period, Ms. A asked the attendants how many people they shook hands with. All of them answered different numbers, and none of them shook hands with all. ) (a) A (Explain that Ms. A shook hands with at least one of them.) (b) (Explain that there is a person who shook hands with exactly two persons, and they are the ones who shook hands with exactly 18 and 17 people.) 7. (Show that the graph below is not a Hamilton graph.)
5 Page 5 of 6 8. Γ = (X, E) v e (Let Γ = (X, E) be a tree with v vertices and e edges.) (a) v 1 (Show that if v, there is a vertex of degree 1.) (b) e = v 1 (Show by Mathematical Induction that e = v 1.) m v e f (Γ is a connected plane graph such that each vertex is of degree 3 and each face is surrounded by either four edges or six edges. Suppose there are m faces surrounded by four edges, and Γ has v vertices, e edges and f faces.) (a) 3f = e + m (Show that 3f = e + m.) (b) m (Determine m. Show work!)
6 Page 6 of B (Mr. B played games 77 consecutive days. Suppose he played at least one game each day but the total number of games is at most 13. Show that there is a certain consecutive period he played exactly 77 games. By a certain consecutive period, we mean for example, from the 3rd day to the 57th day.) If you wish, write Do Not Post. 1.. (a) (b) (c) 3.
7 Page 1 of 6 B (The World of Mathematics) November 0, 006 Solutions to Final Exam p, q, r (Let p, q, r are propositions. ) (a) (Decide whether the following holds by completing the truth table below. And write your conclusion with reason.) p (q r) (p ( r)) q. p q r p (q r) (p ( r)) q T T T T T F T T T F T T T T T F T T T F T T F F F F T F F T T T T F T F T F T T F T F F T T T F T F F F T F F T [ (Conclusion and reason)] (b) p (q r) (Express p (q r) using, and parentheses. Do not use or.) p (q r) (p ( r)) q (p ( r)) q ((p ( r)) ( q)). F T T F T p T, q F, r F (p ( q) ( r))
8 Page of 6. (Find the following and explain your reasoning.) (a) 50 (50 teams are in a tournament. If there is no draw, how many games are required to decide the winner of the touranment? Why?) (b) 1000 A, B, C, D, E n C m (How many ways are there to make 1000 paper cranes by five people, A, B, C, D, E, if each one makes at least 100? Use n C m to express your answer.) = C (Find the minimum cost of a connected network using the diagram below. Draw your network on the right as well by connecting corresponding points.) (Total) 1 ( )
9 Page 3 of (An 8 8 chess board has checkered pattern in black and white.) (a) 1 (Show that it is impossible to cover all squares of the board except the top right and the bottom left corners by 1 rectangular plates without overlapping.) (b) 4 1 (Show the following. If we choose two white squares and two black squares properly, it is impossible to cover the rest of the board by 1 rectangular plates without overlapping.) 5. K 3,3 (Show that K 3,3 below is not a planar graph.) v = 6 e = 9 v e + f = f = e v + = = 5 5 n 1, n, n 3, n 4, n 5 3 n 1 4, n 4, n 3 4, n 4 4, n 5 4 Proposition 8. (ii) 18 = e = n 1 + n + n 3 + n 4 + n = 0.
10 Page 4 of 6 6. A A 0 A (Ms. A attended a party. There were 0 people including Ms. A. After some period, Ms. A asked the attendants how many people they shook hands with. All of them answered different numbers, and none of them shook hands with all. ) (a) A (Explain that Ms. A shook hands with at least one of them.) A 19 A A A A A (b) (Explain that there is a person who shook hands with exactly two persons, and they are the ones who shook hands with exactly 18 and 17 people.) A A A 17 A 7. (Show that the graph below is not a Hamilton graph.) Theorem Bipartite
11 Page 5 of 6 8. Γ = (X, E) v e (Let Γ = (X, E) be a tree with v vertices and e edges.) (a) v 1 (Show that if v, there is a vertex of degree 1.) x 1 x x 3 x 1 x 3, x x 4,... 1 (b) e = v 1 (Show by Mathematical Induction that e = v 1.) v v = 1 e = 0 e = v 1 v = k v 1 v = k + 1 v (a) 1 v 1 = k e e 1 Γ Γ k e 1 k 1 e = k = v 1 v = k + 1 v v v m v e f (Γ is a connected plane graph such that each vertex is of degree 3 and each face is surrounded by either four edges or six edges. Suppose there are m faces surrounded by four edges, and Γ has v vertices, e edges and f faces.) (a) 3f = e + m (Show that 3f = e + m.) 4 m 6 f m Proposition 8. (ii) 3f = e + m 4m + 6(f m) = e. (b) m (Determine m. Show work!) Proposition 8. (i) 3 v = e (a) 3f = e + m Theorem = 3v 3e + 3f = e 3e + e + m = m m = 6
12 Page 6 of B (Mr. B played games 77 consecutive days. Suppose he played at least one game each day but the total number of games is at most 13. Show that there is a certain consecutive period he played exactly 77 games. By a certain consecutive period, we mean for example, from the 3rd day to the 57th day.) b 1 b... b b 1 < b < < b Case 1. b 1, b,..., b b i 1 b i b i = 77 i 77 Case. b 1, b,..., b b 1 b p 1 p 77 r 1 r 77 b 1 = 77p 1 + r 1,..., b 77 = 77p 77 + r r 1 76,... 1 r b i, b j b i > b j b i = 77p i + r i, b j = 77p j + r j r i = r j b i b j = 77(p i p j ) b i b j b i b j = 77 i j j + 1 i 77 77
Quiz 1 ID#: Name: 1. p, q, r (Let p, q and r be propositions. Determine whether the following equation holds or not by completing the truth table belo
Quiz 1 ID#: Name: 1. p, q, r (Let p, q and r be propositions. Determine whether the following equation holds or not by completing the truth table below.) (p q) r p ( q r). p q r (p q) r p ( q r) x T T
More information25 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.
More informationAtCoder Regular Contest 073 Editorial Kohei Morita(yosupo) A: Shiritori if python3 a, b, c = input().split() if a[len(a)1] == b[0] and b[len(
AtCoder Regular Contest 073 Editorial Kohei Morita(yosupo) 29 4 29 A: Shiritori if python3 a, b, c = input().split() if a[len(a)1] == b[0] and b[len(b)1] == c[0]: print( YES ) else: print( NO ) 1 B:
More information2
2011 8 6 2011 5 7 [1] 1 2 i ii iii i 3 [2] 4 5 ii 6 7 iii 8 [3] 9 10 11 cf. Abstracts in English In terms of democracy, the patience and the kindness Tohoku people have shown will be dealt with as an exception.
More informationelemmay09.pub
Elementary Activity Bank Activity Bank Activity Bank Activity Bank Activity Bank Activity Bank Activity Bank Activity Bank Activity Bank Activity Bank Activity Bank Activity Bank Number Challenge Time:
More informationL1 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
More information1 ( 8:12) Eccles. 1:8 2 2
1 http://www.hyuki.com/imit/ 1 1 ( 8:12) Eccles. 1:8 2 2 3 He to whom it becomes everything, who traces all things to it and who sees all things in it, may ease his heart and remain at peace with God.
More information外国語科 ( 英語 Ⅱ) 学習指導案 A TOUR OF THE BRAIN ( 高等学校第 2 学年 ) 神奈川県立総合教育センター 平成 20 年度研究指定校共同研究事業 ( 高等学校 ) 授業改善の組織的な取組に向けて 平成 21 年 3 月 平成 20 年度研究指定校である光陵高等学校において 授業改善に向けた組織的な取組として授業実践を行った学習指導案です 生徒主体の活動を多く取り入れ 生徒の学習活動に変化をもたせるとともに
More informationKyushu Communication Studies 第２号
Kyushu Communication Studies. 2004. 2:111 2004 How College Students Use and Perceive Pictographs in Cell Phone Email Messages IGARASHI Noriko (Niigata University of Health and Welfare) ITOI Emi (Bunkyo
More information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.5968, 20070312. 九州大学医学部保健学科バージョン : 権利関係
More informationT rank A max{rank Q[R Q, J] trank T [R T, C \ J] J C} 2 ([1, p.138, Theorem 4.2.5]) A = ( ) Q rank A = min{ρ(j) γ(j) J J C} C, (5) ρ(j) = rank Q[R Q,
(ver. 4:. 20050727) 1 1.1 (mixed matrix) (layered mixed matrix, LMmatrix) m n A = Q T (2m) (m n) ( ) ( ) Q I m Q Ã = = (1) T diag [t 1,, t m ] T rank Ã = m rank A (2) 1.2 [ ] B rank [B C] rank B rank
More information1 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
More informationS1Šû‘KŒâ‚è
are you? I m thirteen years old. do you study at home every day? I study after dinner. is your cat? It s under the table. I leave for school at seven in Monday. I leave for school at seven on Monday. I
More information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
More information10 2000 11 11 48 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) CUSeeMe NetMeeting Phoenix mini SeeMe Integrated Services Digital Network 64kbps 16kbps 128kbps 384kbps
More informationMicrosoft Word  j201drills27.doc
Drill 1: Giving and Receiving (Part 1) [Due date: ] Directions: Describe each picture using the verb of giving and the verb of receiving. E.g.) (1) (2) (3) (4) 1 (5) (6) Drill 2: Giving and Receiving (Part
More informationMicrosoft Word  j201drills27.doc
Drill 1: Giving and Receiving (Part 1) Directions: Describe each picture using the verb of giving and the verb of receiving. (1) (2) (3) (4) 1 (5) (6) Drill 2: Giving and Receiving (Part 1) Directions:
More informationALT : Hello. May I help you? Student : Yes, please. I m looking for a white Tshirt. ALT : How about this one? Student : Well, this size is good. But do you have a cheaper one? ALT : All right. How about
More information1 3 19 J.S. 7 1 2 1 1 1 3 1 1960 1928 2 3 10 1
2006 4 2 47 3 1 3 3 25 26 2 1 3 19 J.S. 7 1 2 1 1 1 3 1 1960 1928 2 3 10 1 26 27... and when they have to answer opponents, only endeavour, by such arguments as they can command, to support the opposite
More information扉日59
,, ,,,,, fluent pause filler H,. ,, fluent, pause, filler A B A B,,,, fluent, pause, filler, A B filler A filler A B pause fluent,, filler fluent ms pause filler ms Praat A B B ,, fluent, pause, filler...,.,.
More informationII
No. 19 January 19 2013 19 Regionalism at the 19 th National Assembly Elections Focusing on the Yeongnam and Honam Region Yasurou Mori As the biggest issue of contemporary politics at South Korea, there
More information日本語教育紀要 ７／ｐｄｆ用 表紙
JF JF NC JF JF NC peer JF Cando JF JF http : // jfstandard.jpjf CandoCommon European Framework of Reference for Languages : learning, teaching,assessment CEFR AABBCC CEFR ABB A A B B B B Cando CEFR
More informationA Contrastive Study of Japanese and Korean by Analyzing Mistranslation from Japanese into Korean Yukitoshi YUTANI Japanese, Korean, contrastive study, mistranslation, JapaneseKorean dictionary It is already
More informationMicrosoft Word  PCM TLEd.4.4(特定電気用品適合性検査申込のご案内)
(2017.04 29 36 234 9 1 1. (1) 3 (2) 9 1 2 2. (1) 9 1 1 2 1 2 (2) 1 2 ( PSERE101/205/306/405 2 PSERE201 PSERE301 PSERE401 PSERE302 PSERE202 PSERE303 PSERE402 PSERE203 PSERE304 PSERE403
More information鹿大広報149号
No.149 Feb/1999 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Learned From Japanese Life and Experiences in Kagoshima When I first came to Japan I was really surprised by almost everything, the weather,
More information2015 8 65 87. J. Osaka Aoyama University. 2015, vol. 8, 6587. 20 * Recollections of the Pacific War in the eyes of a school kid Hisao NAGAOKA Osaka Aoyama Gakuen Summary Seventy years have passed since
More information~ ユリシーズ における語りのレベル Synopsis Who Is the Man in Macintosh?  Narrative Levels in Ulysses Wataru TAKAHASHI Who is the man in macintosh? This is a famous enigma in Ulysses. He comes out of the blue on the
More information137. Tenancy specific information (a) Amount of deposit paid. (insert amount of deposit paid; in the case of a joint tenancy it should be the total am
13Fast Fair Secure PRESCRIBED INFORMATION RELATING TO TENANCY DEPOSITS* The Letting Protection Service Northern Ireland NOTE: The landlord must supply the tenant with the Prescribed Information regarding
More information2 ( ) i
25 Study on Rating System in Multiplayer Games with Imperfect Information 1165069 2014 2 28 2 ( ) i ii Abstract Study on Rating System in Multiplayer Games with Imperfect Information Shigehiko MORITA
More informationWebster's New World Dictionary of the American Language, College Edition. N. Y. : The World Publishing Co., 1966. [WNWD) Webster 's Third New International Dictionary of the English LanguageUnabridged.
More informationTitle 社 会 化 教 育 における 公 民 的 資 質 : 法 教 育 における 憲 法 的 価 値 原 理 ( fulltext ) Author(s) 中 平, 一 義 Citation 学 校 教 育 学 研 究 論 集 (21): 113126 Issue Date 201003 URL http://hdl.handle.net/2309/107543 Publisher 東 京
More informationON 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
More information16_.....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 informationThe social image of Muay Thai in Thailand Hishida yoshifumi Abstract Muay Thai is a martial art which is a root of Japanese Kick Boxing and K1. It has become a famous sport among Thai as a martial art.
More informationLevel 3 Japanese (90570) 2011
90570 905700 3SUPERVISOR S Level 3 Japanese, 2011 90570 Listen to and understand complex spoken Japanese in less familiar contexts 2.00 pm riday Friday 1 November 2011 Credits: Six Check that the National
More informationTitle < 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: 2141 Issue Date 20061225 URL http://hdl.handle.net/2433/192679 Right
More information10 11 12 33.4 1 open / window / I / shall / the? 79.3 2 something / want / drink / I / to. 43.5 3 the way / you / tell / the library / would / to / me
1 10 11 12 33.4 1 open / window / I / shall / the? 79.3 2 something / want / drink / I / to. 43.5 3 the way / you / tell / the library / would / to / me? 28.7 4 Miyazaki / you / will / in / long / stay
More information840 Geographical Review of Japan 73A12 835854 2000 The Mechanism of Household Reproduction in the Fishing Community on Oro Island Masakazu YAMAUCHI (Graduate Student, Tokyo University) This
More information０
Speedy & Simple Kenji, Yoshio, and Goro are good at English. They have their ways of learning. Kenji often listens to English songs and tries to remember all the words. Yoshio reads one English book every
More informationTo the Conference of District 2652 It is physically impossile for Mary Jane and me to attend the District Conferences around the world. As a result, we must use representatives for that purpose. I have
More information<4D6963726F736F667420506F776572506F696E74202D2089708CEA8D758DC0814091E396BC8E8C8145914F92758E8C81458C6097658E8C81458F9593AE8E8C>
英 語 特 別 講 座 代 名 詞 前 置 詞 形 容 詞 助 動 詞 #1 英 語 特 別 講 座 2010 代 名 詞 前 置 詞 形 容 詞 助 動 詞 英 語 特 別 講 座 代 名 詞 前 置 詞 形 容 詞 助 動 詞 #2 代 名 詞 日 本 語 私 あなた 彼 のうしろに は の を に のもの をつけて 使 う どこに 置 くかは 比 較 的 自 由 私 はジャスコに 行 った ジャスコに
More informationThis paper is going to take up the "Cultural history of dishes" as a part of the "Ancient pulley and the Korean people series II". In the ancient times the pulley was used to make basically dishes for
More informationuntitled
SATO Kentaro Milk and its byproducts are naturally nutritious food, and people in ancient Japan enjoyed tasting them as foods, drinks, or medicines. On the other hand, milk and its byproducts were closely
More informationキャリアワークショップ教師用
iii v vi vii viii ix x xi xii 1 2 3 4 1.1 CYCLE OF SELFRELIANCE GOALS SUCCESS INTERACTION RESOURCES 5 6 7 8 9 10 11 12 13 14 15 16 17 18 2.1 MY RESOURCES FOR THE EARTH IS FULL, AND THERE IS ENOUGH AND
More informationClustering in Time and Periodicity of Strong Earthquakes in Tokyo Masami OKADA Kobe Marine Observatory (Received on March 30, 1977) The clustering in time and periodicity of earthquake occurrence are investigated
More information123099_Y05…X…`…‘…“†[…h…•
1. 2 1993 2001 2 1 2 1 2 1 99 2009. 1982 250 251 1991 112 115 1988 75 2004 132 2006 73 3 100 3 4 1. 2. 3. 4. 5. 6.. 3.1 1991 2002 2004 3 4 101 2009 3 4 4 5 1 5 6 1 102 5 6 3.2 2 7 8 2 X Y Z Z X 103 2009
More informationh23w1.dvi
24 I 24 2 8 10:00 12:30 1),. Do not open this problem booklet until the start of the examination is announced. 2) 3.. Answer the following 3 problems. Use the designated answer sheet for each problem.
More information[2] 1. 2. 2 2. 1, [3] 2. 2 [4] 2. 3 BABOK BABOK(Business Analysis Body of Knowledge) BABOK IIBA(International Institute of Business Analysis) BABOK 7
32 (2015 ) [2] Projects of the short term increase at present. In order to let projects complete without rework and delays, it is important that request for proposals (RFP) are written by reflecting precisely
More information千葉県における温泉地の地域的展開
1) 1999 11 50 1948 23) 2 2519 9 3) 2006 4) 151 47 37 1.2 l 40 3.6 15 240 21 9.2 l 7. 210 1972 5) 1.9 l 5 1 0.2 l 6 1 1972 1.9 0.4 210 4017 292006 34 6 l/min.42 6) 2006 1 1 2006 42 60% 5060 4050 3040
More information™…
Review The Secret to Healthy Long Life Decrease in Oxidative and Mental Stress My motto is Health is not all. But nothing can be done without health. Health is the most important requisite for all human
More informationはじめに
IT 1 NPO (IPEC) 55.7 29.5 Web TOEIC Nice to meet you. How are you doing? 1 type (2002 5 )66 15 1 IT Java (IZUMA, Tsuyuki) James Robinson James James James Oh, YOU are Tsuyuki! Finally, huh? What's going
More information,,,, :  i 
2017 Future University Hakodate 2017 System Information Science Practice Group Report Project Name Manga engineering Group Name Literacy Manga /Project No. 19 /Project Leader 1015131 Kiyomasa Murakami
More informationDOUSHISYAsports_R12339(高解像度).pdf
Doshisha Journal of Health & Sports Science, 4, 4150 2012 41 A Case Study of the Comprehensive community sports clubs that People with Disability Participate in. Motoaki Fujita In this study, the interview
More informationJJRM5005／04.短報.責了.indd
Jpn J Rehabil Med 2013 ; : 319.327 1 2 3 4 5 6 Survey of the Electronic Medical Recoding System Used in Kaifukuki Rehabilitation Wards Hidekazu SUGAWARA, 1 Tetsutaro YAHATA, 2 Hideto OKAZAKI, 3 Mitsuhiro
More informationA 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,
More informationCain & Abel
Cain & Abel: False Religion vs. The Gospel Now Adam knew Eve his wife, and she conceived and bore Cain, saying, I have gotten a man with the help of the LORD. And again, she bore his brother Abel. Now
More information1 1 tfidf tfidf i
14 A Method of Article Retrieval Utilizing Characteristics in Newspaper Articles 1055104 2003 1 31 1 1 tfidf tfidf i Abstract A Method of Article Retrieval Utilizing Characteristics in Newspaper Articles
More informationCONTENTS Public relations brochure of Higashikawa November No.745 Higashikawa 215 November 2
11 215 November No.745 CONTENTS 2 6 12 17 17 18 2 21 22 23 24 28 3 31 32 Public relations brochure of Higashikawa 11 215 November No.745 Higashikawa 215 November 2 816,18 832,686 8,326,862 196,93 43,573
More information日本ロータリー史
2680 RI ( ) RI 1971 50 1 2 FUKUSHIMA Kisaji 38 1912 Southern Products William 1915 1920 KISOJO 3 1918 10 1919 1920 1 Albert Adams 4 In Japan authority to organize Rotary in Tokyo, its capital, has been
More information1974 259210 1983
2007.7.1 No. 22 京都外国語大学校友会 1974 259210 1983 1 2007 221 60 60 60 1860 60 4537 12 6045 222 1 2007 200751860 45 60 60 6060 1947 60 223 1 2007 194722 60 2005 2 414020 3 18 16 60 20093 5 199411 13 197633 100
More information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
More information¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡
                      H E L L O I N T E R N November 2007 Vol. 142  "I think you are a good teacher." INTERN REPORT 
More informationAn Aspect of Development in Clothing Education in Japan (Part 2) The Method of Teaching Sewing in the Meiji Era ( 2 ) Tetsuko HIGUCHI 1. Following Part 1, here I have analyzed and discussed some characteristic
More information日本版 General Social Surveys 研究論文集[2]
Implementing a Social Networks Module in the Japanese General Social Surveys (JGSS): Results of the Pretest Keiko NAKAO, Ken ichi IKEDA, and Satoko YASUNO The project of Japanese General Social Surveys
More informationfx9860G Manager PLUS_J
fx9860g J fx9860g Manager PLUS http://edu.casio.jp k 1 k III 2 3 1. 2. 4 3. 4. 5 1. 2. 3. 4. 5. 1. 6 7 k 8 k 9 k 10 k 11 k k k 12 k k k 1 2 3 4 5 6 1 2 3 4 5 6 13 k 1 2 3 1 2 3 1 2 3 1 2 3 14 k a j.+(),m1
More information<33318FBC89598E81332E696E6464>
The Chinese Books Printed at Japan were transported by Chinese Ships during Edo Era: The Works included in the Zhibuzuzhai Congshu MATSUURA Akira The exchanges between Japan and China in the Edo period
More information2 except for a female subordinate in work. Using personal name with SAN/KUN will make the distance with speech partner closer than using titles. Last
1 北陸大学 紀要 第33号 2009 pp. 173 186 原著論文 バーチャル世界における呼びかけ語の コミュニケーション機能 ポライトネス理論の観点からの考察 劉 艶 The Communication Function of Vocative Terms in Virtual Communication: from the Viewpoint of Politeness Theory Yan
More informationMSOLUTIONS writer: yokozuna A: Sum of Interior Angles For International Readers: English editorial starts on page 7. N 180(N 2) C++ #i n
MSOLUTIONS writer: yokozuna 57 2019 6 1 A: Sum of Interior Angles For International Readers: English editorial starts on page 7. N 180(N 2) C++ #i n c l u d e using namespace std ; i n t main
More information1) 1) Props of preparation. Wire Scale Spike Cutter Hammer Tape Marker (, ) Rope(For Sezing) 2) 2) Marking A 22 A point Position of twentytwo times t
1) 1) Props of preparation. Wire Scale Spike Cutter Hammer Tape Marker (, ) Rope(For Sezing) 2) 2) Marking A 22 A point Position of twentytwo times the Dia, from the end of the rope. B A B point Position
More information2 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 informationR R S K K S K S K S K S K S Study of Samuhara Belief : Transformation from Protection against Injuries to Protection against Bullets WATANABE Kazuhiro Samuhara, which is a group of letters like unfamiliar
More information< D8291BA2E706466>
A 20 1 26 20 10 10 16 4 4! 20 6 11 2 2 3 3 10 2 A. L. T. Assistant Language Teacher DVD AV 3 A. E. T.Assistant English Teacher A. L. T. 40 3 A 4 B A. E. T. A. E. T. 6 C 2 CD 4 4 4 4 4 8 10 30 5 20 3 5
More informationVol92.indd
年男年女インタビュー ベイタウン野鳥物語 With the holidays coming to an abrupt end, let us not forget the true meaning they provide. There is a certain spirit that people attain during the holidays. The "Holiday spirit" comes
More informationuntitled
1 2 3 4 5 OPERATION 44.4% 20.4% 14.8% 20.4% RECEIVING OPERATION CALLING OTHERS 6 (Evaluation) (Synthesis) (Analysis) (Application) (Comprehension) (Knowledge) 7 Level 3 Level 2 Level 1 Level
More informationOHTA Motoko SummaryThe purpose of this paper is to review "KEISEIKANDIARY()", which is possessed in Tanaka Library of Aizutakadamachi, Oonumagun, Fukushima Prefecture. The author of this diary is Tanaka
More informationZ B B PHP   [ ] PHP New York Times, December,,. The origins of the JapanU.S. War and Adm. Isoroku Yamamoto Katsuhiko MATSUKAWA Abstract There are huge amount of studies concerning the origins
More information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
More information22 1,936, ,115, , , , , , ,
21 * 2 3 1 1991 1945 200 60 1944 No. 41 2016 22 1,936,843 1945 1,115,594 1946 647,006 1947 598,507 1 60 2014 501,230 354,503 5 2009 405,571 5 1 2 2009 2014 5 37,285 1 2 1965 10 1975 66 1985 43 10 3 1990
More information2010EIGOKYOIKU.indd
1. 1990 2. 1970 1980 1990 2000 6 19 1993 1 2 35 英 語 と 英 語 教 育 の 眺 望 120 15~40 90 2009:280 1970 36 実 用 英 語 教 育 偏 向 への 批 判 的 考 察 3.? 10 3.1.? TOEIC 37 英 語 と 英 語 教 育 の 眺 望 ENGLISH JOURNAL CNN ENGLISH EXPRESS
More informationOn the Wireless Beam of Short Electric Waves. (VII) (A New Electric Wave Projector.) By S. UDA, Member (Tohoku Imperial University.) Abstract. A new e
On the Wireless Beam of Short Electric Waves. (VII) (A New Electric Wave Projector.) By S. UDA, Member (Tohoku Imperial University.) Abstract. A new electric wave projector is proposed in this paper. The
More information{.w._.p7_.....\.. (Page 6)
1 1 2 1 2 3 3 1 1 8000 75007000 4 2 1493 1 15 26 5 6 2 3 5 7 17 8 1614 4 9 7000 2 5 1 1542 10 11 1592 12 1614 1596 1614 13 15691615 16 16 14 15 6 2 16 1697 17 7 1811 18 19 20 1820 21 1697 22 1 8 23 3 100
More information27 1 NP NPcompleteness of Picross 3D without segmentinformation and that with height of one
27 1 NP NPcompleteness of Picross 3D without segmentinformation and that with height of one 115282 216 2 26 1 NP.,,., NP, 1 P.,, 1 NP, 3SAT., NP, i Abstract NPcompleteness of Picross 3D without segmentinformation
More informationMEET 270
Traditional Idiom & Slang can t make heads or tails of something Keener : I m not sure now if I want to marry Gloria or not. I still love Lisa. Slacker : Really. What are you going to do? Keener : I don
More information1999b Astroarts ver 8 Note about the notion of heaven in Wakoku ancient Japan before acceptance of Chinese astrology belief in heaven and the almanac Hiroshi HOSOI Ancient Japanese accepted the
More information:
An Analysis of TV Game Market: From the viewpoints of network externalities and whole of services Masaki Matsumura, Hiroyuki Kurimoto, and Toshio Kobayashi It has been understood that a standard would
More informationA study of actual condition of ownership and intention of utilizing the land in Local City  Case Study of Central District in Fukui City Toshinari Fukuoka Shinji Nojima' This paper aims to clarify the
More information2
Unit Children of the World NEW HORIZON English Course 'Have you been to?' 'What have you done as a housework?' 1 2 Study Tour to Bangladesh p26 P263 Example: I am going to Bangladesh this spring.
More informationuntitled
Show & Tell Presentation  170  Presentation 1) Choose 1 topic 2) Write the reasons why you chose the topic. 3) Think about 3 points for the topic. Class No Name What would you like to do after graduation?
More information;~ (Summary) The Study on the Effects of Foot Bathing on Urination Kumiko Toyoda School of Human Nursing, University of Shiga Prefecture Background Foot bathing is one of the important nursing care for
More information第4回 JISSスポーツ科学会議 ポスターセッション
 33   34   35   36   37   38  投 球 方 向 1 日 目 3 日 目 50cm  39  [First half] [Second half] Segment angle (deg) 40 30 20 110 100 90 80 70 60 50 40 30 80 70 Torso Thigh CM Z Torso Y Thigh Shank
More informationPublic relations brochure of Higashikawa 4 2016 April No.750 CONTENTS 3 13 15 16 20 22 23 24 25 26 28 36 37 38 2
4 2016 April No.750 Public relations brochure of Higashikawa 4 2016 April No.750 CONTENTS 3 13 15 16 20 22 23 24 25 26 28 36 37 38 2 3 5 4 7 6 9 8 11 10 12 13 14 キトウシ 森 林 公 園 シーズン イン HIGASHIKAWA TOWN NEWS
More informationPowerPoint Presentation
鬼はどこですか? Proositional logic (cont ) 命題論理 Reasoning where is wumus 鬼がいる場所を推理する 1 命題論理 : 意味論 semantics 論理積 A B A かつ B 論理和 A B A または B 否定 A A でない 含意 A B A ならば B を意味する 同等 A B (A ならば B) かつ (B ならば A) 命題論理では記号は命題
More information「プログラミング言語」 SICP 第4章 ～超言語的抽象～ その6
SICP 4 6 igarashi@kuis.kyotou.ac.jp July 21, 2015 ( ) SICP 4 ( 6) July 21, 2015 1 / 30 4.3: Variations on a Scheme Nondeterministic Computing 4.3.1: amb 4.3.2: 4.3.3: amb ( ) SICP 4 ( 6) July 21, 2015
More information3 2
1 2016 January No.747 3 2 CONTENTS 2 5 9 10 16 17 18 19 20 26 27 28 Public relations brochure of Higashikawa 1 2016 January No.747 4 HIGASHIKAWA TOWN NEWS 5 HIGASHIKAWA TOWN NEWS HIGASHIKAWA TOWN NEWS
More informationHow to read the marks and remarks used in this parts book. Section 1 : Explanation of Code Use In MRK Column OO : Interchangeable between the new part
Reservdelskatalog MIKASA MT65H vibratorstamp EPOX Maskin AB Postadress Besöksadress Telefon Fax epost Hemsida Version Box 6060 Landsvägen 1 08754 71 60 08754 81 00 info@epox.se www.epox.se 1,0 192 06
More informationAnswers Practice 08 JFD1
Practice 8 Sentence Connectors 1) I / went / to Japan / for the first time last year. At first, I didn t understand / Japanese / *at all. [ ] [ ] [ ] [ ] * 2) I m / not hungry / because I *already ate
More informationHow to read the marks and remarks used in this parts book. Section 1 : Explanation of Code Use In MRK Column OO : Interchangeable between the new part
Reservdelskatalog MIKASA MVB85 rullvibrator EPOX Maskin AB Postadress Besöksadress Telefon Fax epost Hemsida Version Box 6060 Landsvägen 1 08754 71 60 08754 81 00 info@epox.se www.epox.se 1,0 192 06
More information1 # include < stdio.h> 2 # include < string.h> 3 4 int main (){ 5 char str [222]; 6 scanf ("%s", str ); 7 int n= strlen ( str ); 8 for ( int i=n 2; i
ABC066 / ARC077 writer: nuip 2017 7 1 For International Readers: English editorial starts from page 8. A : ringring a + b b + c a + c a, b, c a + b + c 1 # include < stdio.h> 2 3 int main (){ 4 int a,
More informationDO(Sep2014)
Mathematics Diagnostic Examination Guidance Examination Overview The Mathematics Examination will contain two sections. Section A contains fifteen 2point questions and Section B contains five 4point
More informationC. S2 X D. E.. (1) X S1 10 S2 X+S1 3 X+S S1S2 X+S1+S2 X S1 X+S S X+S2 X A. S1 2 a. b. c. d. e. 2
I. 200 2 II. ( 2001) 30 1992 Do X for S2 because S1(is not desirable) XS S2 A. S1 S2 B. S S2 S2 X 1 C. S2 X D. E.. (1) X 12 15 S1 10 S2 X+S1 3 X+S2 4 13 S1S2 X+S1+S2 X S1 X+S2. 2. 3.. S X+S2 X A. S1 2
More information