[B! math] rekramkoobã®ãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯

ã€Žãªãœï¼’æ™‚ã‹ã‚‰ï¼•æ™‚ã¾ã§ã¯ï¼“æ™‚é–“ã§ã€ï¼’æ—¥ã‹ã‚‰ï¼•æ—¥ã¾ã§ã¯ï¼”æ—¥é–“ãªã®ã‹ï¼Ÿã€

ï¼ˆè£œæ³¨ï¼šã“ã®ã‚¢ãƒ¼ãƒ†ã‚£ã‚¯ãƒ«ã®è«–è€ƒã¯ã€ã€Žã‹ã‘ç®—ã«ã¯é †åºãŒã‚ã‚‹ã®ã‹ã€å²©æ³¢ç§‘å¦ãƒ©ã‚¤ãƒ–ãƒ©ãƒªãƒ¼ã®ç¬¬3ç« ã§æ•´ç†ã•ã‚Œã¾ã—ãŸã€‚ï¼‰ http://www.iwanami.co.jp/.BOOKS/02/2/0295800.html åã©ã‚‚ã®ã¨ãç–‘å•ã ã£ãŸã“ã®å•é¡Œã¯ã€å¡¾ã§æ•™ãˆã‚‹ã‚ˆã†ã«ãªã£ã¦ã‹ã‚‰ã€æ•°æ•™å”ã®æœ¬ï¼ˆç‰¹ã«é å±±å•“ã®æœ¬ï¼‰ã‚’èªã‚“ã§ã€åˆ†é›¢é‡ãƒ»é€£ç¶šé‡ã¨ã„ã†è€ƒãˆæ–¹ã‚’çŸ¥ã£ã¦ã€æ°·è§£ã—ã¾ã—ãŸã€‚ç§ã«ã¨ã£ã¦ã¯ã€æ•°æ•™å”ã§ç›®ã‹ã‚‰ã‚¦ãƒã‚³ã‚·ãƒªãƒ¼ã‚ºã®ãƒ™ã‚¹ãƒˆã‚¹ãƒªãƒ¼ã«å…¥ã‚‹ã‚‚ã®ã§ã—ã‚‡ã†ã€‚ã¨ã“ã‚ãŒã€mixiã§ç™ºè¨€ã—ãŸã¨ã“ã‚ã€ãªã‹ãªã‹åŒæ„ã‚’å¾—ã‚‰ã‚Œãªã‹ã£ãŸã€‚ãã‚Œè‡ªä½“ãŒã€ç§ã«ã¨ã£ã¦ã€æ–°ãŸãªç›®ã‹ã‚‰ã‚¦ãƒã‚³ã‚·ãƒªãƒ¼ã‚ºã§ã‚‚ã‚ã‚Šã¾ã—ãŸã€‚ http://mixi.jp/view_bbs.pl?id=42139232&comment_count=306&comm_id=63370 233ç•ªç™ºè¨€ä»¥é™ã€‚ ã•ã¦ã€ ï¼¡ï¼šã€Œï¼’æ™‚ã‹ã‚‰ï¼•æ™‚ã¾ã§ã¯ï¼“æ™‚é–“ã€‚ã€ ï¼¢ï¼šã€Œï¼’æ—¥ã‹ã‚‰ï¼•æ—¥ã¾ã§

rekramkoob 2009/06/01

*column
math

ãƒªãƒ³ã‚¯

æ•°å¦å¦ç¿’ãƒžãƒ‹ãƒ¥ã‚¢ãƒ«ã€€ã¾ã¨ã‚ãƒšãƒ¼ã‚¸

ã‚µãƒ¼ãƒ“ã‚¹çµ‚äº†ã®ãŠçŸ¥ã‚‰ã› ã„ã¤ã‚‚Yahoo! JAPANã®ã‚µãƒ¼ãƒ“ã‚¹ã‚’ã”åˆ©ç”¨ã„ãŸã ãèª ã«ã‚ã‚ŠãŒã¨ã†ã”ã–ã„ã¾ã™ã€‚ ãŠå®¢æ§˜ãŒã‚¢ã‚¯ã‚»ã‚¹ã•ã‚ŒãŸã‚µãƒ¼ãƒ“ã‚¹ã¯æœ¬æ—¥ã¾ã§ã«ã‚µãƒ¼ãƒ“ã‚¹ã‚’çµ‚äº†ã„ãŸã—ã¾ã—ãŸã€‚ ä»Šå¾Œã¨ã‚‚Yahoo! JAPANã®ã‚µãƒ¼ãƒ“ã‚¹ã‚’ã”æ„›é¡§ãã ã•ã„ã¾ã™ã‚ˆã†ã€ã‚ˆã‚ã—ããŠé¡˜ã„ã„ãŸã—ã¾ã™ã€‚

rekramkoob 2009/03/04

ãƒªãƒ³ã‚¯

Wikipedia (JP) - æŒ‡æ•°é–¢æ•°ï¼ˆexponential functionï¼‰

è‹±èªžç‰ˆè¨˜äº‹ã‚’æ—¥æœ¬èªžã¸æ©Ÿæ¢°ç¿»è¨³ã—ãŸãƒãƒ¼ã‚¸ãƒ§ãƒ³ï¼ˆGoogleç¿»è¨³ï¼‰ã€‚ ä¸‡ãŒä¸€ç¿»è¨³ã®æ‰‹ãŒã‹ã‚Šã¨ã—ã¦æ©Ÿæ¢°ç¿»è¨³ã‚’ç”¨ã„ãŸå ´åˆã€ç¿»è¨³è€…ã¯å¿…ãšç¿»è¨³å…ƒåŽŸæ–‡ã‚’å‚ç…§ã—ã¦æ©Ÿæ¢°ç¿»è¨³ã®èª¤ã‚Šã‚’è¨‚æ£ã—ã€æ£ç¢ºãªç¿»è¨³ã«ã—ãªã‘ã‚Œã°ãªã‚Šã¾ã›ã‚“ã€‚ã“ã‚ŒãŒæˆã•ã‚Œã¦ã„ãªã„å ´åˆã€è¨˜äº‹ã¯å‰Šé™¤ã®æ–¹é‡G-3ã«åŸºã¥ãã€å‰Šé™¤ã•ã‚Œã‚‹å¯èƒ½æ€§ãŒã‚ã‚Šã¾ã™ã€‚ ä¿¡é ¼æ€§ãŒä½Žã„ã¾ãŸã¯ä½Žå“è³ªãªæ–‡ç« ã‚’ç¿»è¨³ã—ãªã„ã§ãã ã•ã„ã€‚ã‚‚ã—å¯èƒ½ãªã‚‰ã°ã€æ–‡ç« ã‚’ä»–è¨€èªžç‰ˆè¨˜äº‹ã«ç¤ºã•ã‚ŒãŸæ–‡çŒ®ã§æ£ã—ã„ã‹ã©ã†ã‹ã‚’ç¢ºèªã—ã¦ãã ã•ã„ã€‚ å±¥æ´ç¶™æ‰¿ã‚’è¡Œã†ãŸã‚ã€è¦ç´„æ¬„ã«ç¿»è¨³å…ƒã¨ãªã£ãŸè¨˜äº‹ã®ãƒšãƒ¼ã‚¸åãƒ»ç‰ˆã«ã¤ã„ã¦è¨˜è¿°ã™ã‚‹å¿…è¦ãŒã‚ã‚Šã¾ã™ã€‚è¨˜è¿°æ–¹æ³•ã«ã¤ã„ã¦ã¯ã€Wikipedia:ç¿»è¨³ã®ã‚¬ã‚¤ãƒ‰ãƒ©ã‚¤ãƒ³#è¦ç´„æ¬„ã¸ã®è¨˜å…¥ã‚’å‚ç…§ãã ã•ã„ã€‚ ç¿»è¨³å¾Œã€{{ç¿»è¨³å‘ŠçŸ¥|en|Exponential function|â€¦}}ã‚’ãƒŽãƒ¼ãƒˆã«è¿½åŠ ã™ã‚‹ã“ã¨ã‚‚ã§ãã¾ã™ã€‚ Wikipedia:ç¿»è¨³ã®ã‚¬ã‚¤ãƒ‰ãƒ©ã‚¤ãƒ³ã«ã€ã‚ˆã‚Šè©³ç´°ãªç¿»è¨³ã®æ‰‹é †ãƒ»æŒ‡é‡ã«ã¤

rekramkoob 2009/02/26

ãƒªãƒ³ã‚¯

éƒ¨åˆ†å’Œå•é¡Œ - Wikipedia

éƒ¨åˆ†å’Œå•é¡Œï¼ˆã¶ã¶ã‚“ã‚ã‚‚ã‚“ã ã„ï¼‰ã¯ã€è¨ˆç®—è¤‡é›‘æ€§ç†è«–ãƒ»æš—å·ç†è«–ã«ãŠã‘ã‚‹å•é¡Œã§ã€ä¸Žãˆã‚‰ã‚ŒãŸ n å€‹ã®æ•´æ•° a1,...,an ã‹ã‚‰éƒ¨åˆ†é›†åˆã‚’ã†ã¾ãé¸ã‚“ã§ã€ãã®é›†åˆå†…ã®æ•°ã®å’ŒãŒä¸Žãˆã‚‰ã‚ŒãŸæ•° N ã«ç‰ã—ããªã‚‹ã‚ˆã†ã«ã§ãã‚‹ã‹ã©ã†ã‹ã‚’åˆ¤å®šã™ã‚‹å•é¡Œã§ã‚ã‚‹ã€‚NPå®Œå…¨ã§ã‚ã‚‹ã“ã¨ãŒçŸ¥ã‚‰ã‚Œã¦ã„ã‚‹ã€‚ éƒ¨åˆ†å’Œå•é¡Œã¯ã€åˆ†å‰²å•é¡Œ (Number Partitioning) ã®ä¸€èˆ¬å½¢ã§ã‚‚ã‚ã‚‹ã€‚åˆ†å‰²å•é¡Œã¨ã¯ã€ä¸Žãˆã‚‰ã‚ŒãŸ n å€‹ã®æ•´æ•° a1,...,an ã‚’äºŒã¤ã®é›†åˆã«åˆ†ã‘ã€å„ã€…ã®é›†åˆå†…ã®æ•°ã®å’ŒãŒã‚‚ã†ä¸€æ–¹ã®é›†åˆå†…ã®æ•°ã®å’Œã¨ç‰ã—ããªã‚‹ã‚ˆã†ã«ã§ãã‚‹ã‹ã©ã†ã‹ã‚’åˆ¤å®šã™ã‚‹å•é¡Œã§ã‚ã‚‹ã€‚åˆ†å‰²å•é¡Œã‚‚ã€NPå®Œå…¨ã§ã‚ã‚‹ã“ã¨ãŒç¤ºã•ã‚Œã¦ã„ã‚‹ã€‚ ãŸã¨ãˆã°ã€ã€Œ{1,3,7,10,13} ã®éƒ¨åˆ†å’Œã§ã€å’ŒãŒ 21 ã«ãªã‚‹ã‚‚ã®ã¯å˜åœ¨ã™ã‚‹ã‹ï¼Ÿã€ã§ã‚ã‚Œã°å˜åœ¨ã™ã‚‹ï¼ˆ{1,7,13}ã§ã‚ã‚‹ï¼‰ã€ãŒç”ãˆã§ã‚ã‚‹ã€‚ã¾ãŸã€Œ{2,4,6,8,10} ã®éƒ¨åˆ†å’Œã§ã€å’ŒãŒ 19 ã«ãªã‚‹

rekramkoob 2008/11/19

ãƒªãƒ³ã‚¯

ãƒ“ãƒ³ãƒ‘ãƒƒã‚ãƒ³ã‚°å•é¡Œ - Wikipedia

ãƒ“ãƒ³ãƒ‘ãƒƒã‚ãƒ³ã‚°å•é¡Œï¼ˆãƒ“ãƒ³ãƒ‘ãƒƒã‚ãƒ³ã‚°ã‚‚ã‚“ã ã„ï¼‰ã¨ã¯ã€é›¢æ•£æ•°å¦ã®çµ„åˆã›è«–ã®ä¸ã®NPå›°é›£å•é¡Œã§ã€ä¸Žãˆã‚‰ã‚ŒãŸã€Œè·ç‰©ï¼ˆé‡ã•ã‚„å€‹æ•°ãŒã¤ã„ã¦ã„ã‚‹ï¼‰ã€ã‚’ã¤ã‚ã‚‹ã€Œç®±ï¼ˆãƒ“ãƒ³ã‚„ã‚³ãƒ³ãƒ†ãƒŠãªã©ï¼‰ã€ã®æœ€å°æ•°ã‚’è¦‹ã¤ã‘ã‚‹ã‚‚ã®ã§ã‚ã‚‹ã€‚å•é¡Œã‚’è§£ããŸã‚ã«ãƒ“ãƒ³åž‹ï¼ˆç’çŠ¶åž‹ï¼‰ã®æ¨¡åž‹ã‚’ä½¿ã†ã®ã§ã“ã®ã‚ˆã†ã«å‘¼ã°ã‚Œã‚‹ã€‚ æ§˜ã€…ãªè§£æ±ºæ–¹æ³•ï¼ˆã‚¢ãƒ«ã‚´ãƒªã‚ºãƒ ï¼‰ãŒè€ƒæ¡ˆã•ã‚Œã¦ã„ã‚‹ãŒã€ã‚ã‚‰ã‚†ã‚‹å ´åˆã®ç®±ã®æœ€å°æ•°ã‚’åŠ¹çŽ‡çš„ã«è¦‹ã¤ã‘ã‚‹ã“ã¨ãŒã§ãã‚‹ã‚ˆã†ãªä¸‡èƒ½ãªã‚¢ãƒ«ã‚´ãƒªã‚ºãƒ ã¯ãªã„ï¼ˆNPå›°é›£å•é¡Œï¼‰ã€‚ 8å°ã®æ–°è»Šã‚’ãƒˆãƒ©ãƒƒã‚¯ã§ç§»å‹•ã™ã‚‹ã€‚æ–°è»Šã®é‡é‡ã¯ãã‚Œãžã‚Œ100ã‚ãƒã‚°ãƒ©ãƒ å˜ä½ã§ 33, 61, 58, 41, 50, 21, 60, 64 ã§ã‚ã‚‹ã€‚å„ãƒˆãƒ©ãƒƒã‚¯ãŒã€12,000 kg ã®é‡é‡ã¾ã§é‹ã¹ã‚‹ã¨ãã€å…¨ã¦ã®æ–°è»Šã‚’ä¸€åº¦ã«ç§»å‹•ã•ã›ã‚‹ã®ã«å¿…è¦ã¨ã•ã‚Œã‚‹ãƒˆãƒ©ãƒƒã‚¯ã®æœ€å°æ•°ã¯ã€ã„ãã¤ã§ã‚ã‚‹ã‹è€ƒãˆã‚‹ã€‚ã¾ãšã€ãƒˆãƒ©ãƒƒã‚¯ã‚’å®¹é‡120ã®ãƒ“ãƒ³ã¨ã—ã€æ–°è»Šã¯ã€ãã®ãƒ“ãƒ³ã«è©°ã‚ã‚‹è·ç‰©ã¨ã™ã‚‹ã€‚å…·ä½“çš„ã«èª¿ã¹ã‚‹

rekramkoob 2008/11/19

ãƒªãƒ³ã‚¯

ãƒŠãƒƒãƒ—ã‚µãƒƒã‚¯å•é¡Œ - Wikipedia

ã“ã®è¨˜äº‹ã¯æ¤œè¨¼å¯èƒ½ãªå‚è€ƒæ–‡çŒ®ã‚„å‡ºå…¸ãŒå…¨ãç¤ºã•ã‚Œã¦ã„ãªã„ã‹ã€ä¸ååˆ†ã§ã™ã€‚ å‡ºå…¸ã‚’è¿½åŠ ã—ã¦è¨˜äº‹ã®ä¿¡é ¼æ€§å‘ä¸Šã«ã”å”åŠ›ãã ã•ã„ã€‚ï¼ˆã“ã®ãƒ†ãƒ³ãƒ—ãƒ¬ãƒ¼ãƒˆã®ä½¿ã„æ–¹ï¼‰ å‡ºå…¸æ¤œç´¢?:Â "ãƒŠãƒƒãƒ—ã‚µãƒƒã‚¯å•é¡Œ"Â â€“Â ãƒ‹ãƒ¥ãƒ¼ã‚¹Â Â· æ›¸ç±Â Â· ã‚¹ã‚«ãƒ©ãƒ¼Â Â· CiNiiÂ Â· J-STAGEÂ Â· NDLÂ Â· dlib.jpÂ Â· ã‚¸ãƒ£ãƒ‘ãƒ³ã‚µãƒ¼ãƒÂ Â· TWL (2016å¹´9æœˆ) ãƒŠãƒƒãƒ—ã‚µãƒƒã‚¯å•é¡Œ ãƒŠãƒƒãƒ—ã‚µãƒƒã‚¯å•é¡Œï¼ˆãƒŠãƒƒãƒ—ã‚µãƒƒã‚¯ã‚‚ã‚“ã ã„ã€Knapsack probl emï¼‰ã¯ã€è¨ˆç®—è¤‡é›‘æ€§ç†è«–ã«ãŠã‘ã‚‹è¨ˆç®—ã®é›£ã—ã•ã®è°è«–ã®å¯¾è±¡ã¨ãªã‚‹å•é¡Œã®ä¸€ã¤ã§ã€n ç¨®é¡žã®å“ç‰©ï¼ˆå„ã€…ã€ä¾¡å€¤ viã€é‡é‡ wiï¼‰ãŒä¸Žãˆã‚‰ã‚ŒãŸã¨ãã€é‡é‡ã®åˆè¨ˆãŒ W ã‚’è¶…ãˆãªã„ç¯„å›²ã§å“ç‰©ã®ã„ãã¤ã‹ã‚’ãƒŠãƒƒãƒ—ã‚µãƒƒã‚¯ã«å…¥ã‚Œã¦ã€ãã®å…¥ã‚ŒãŸå“ç‰©ã®ä¾¡å€¤ã®åˆè¨ˆã‚’æœ€å¤§åŒ–ã™ã‚‹ã«ã¯å…¥ã‚Œã‚‹å“ç‰©ã®çµ„ã¿åˆã‚ã›ã‚’ã©ã®ã‚ˆã†ã«é¸ã¹ã°ã‚ˆã„ã‹ã€ã¨ã„ã†æ•´æ•°è¨ˆç”»å•é¡Œã§ã‚ã‚‹ã€‚åŒã˜ç¨®é¡žã®å“ç‰©ã‚’1ã¤ã¾ã§ã—ã‹å…¥ã‚Œã‚‰ã‚Œãªã„å ´

rekramkoob 2008/11/19

ãƒªãƒ³ã‚¯

NPå®Œå…¨å•é¡Œ - Wikipedia

NPå®Œå…¨ï¼ˆãªï¼‰å•é¡Œï¼ˆã‚¨ãƒŒãƒ”ãƒ¼ã‹ã‚“ãœã‚“ï¼ˆãªï¼‰ã‚‚ã‚“ã ã„ã€è‹±: NP-complete probl emï¼‰ã¨ã¯ã€(1) ã‚¯ãƒ©ã‚¹NPï¼ˆè‹±: Non-deterministic Polynomialï¼‰ã«å±žã™ã‚‹æ±ºå®šå•é¡Œï¼ˆè¨€èªžï¼‰ã§ã€ã‹ã¤ (2) ã‚¯ãƒ©ã‚¹NPã«å±žã™ã‚‹ä»»æ„ã®å•é¡Œã‹ã‚‰å¤šé …å¼æ™‚é–“é‚„å…ƒï¼ˆå¸°ç€ï¼‰å¯èƒ½ãªã‚‚ã®ã®ã“ã¨ã§ã‚ã‚‹ã€‚æ¡ä»¶ (2) ã‚’æº€ãŸã™å ´åˆã¯ã€å•é¡Œã®å®šç¾©ãŒæ¡ä»¶ (1) ã‚’æº€ãŸã•ãªã„å ´åˆã«ã‚‚ã€NPå›°é›£ãªå•é¡Œã¨ã‚ˆã³ãã®è¨ˆç®—é‡çš„ãªå›°é›£æ€§ã‚’ç‰¹å¾´ã¥ã‘ã¦ã„ã‚‹ã€‚å¤šé …å¼æ™‚é–“é‚„å…ƒã®æŽ¨ç§»æ€§ã‹ã‚‰ã€ã‚¯ãƒ©ã‚¹NPã«å±žã™ã‚‹å•é¡Œã§ã€ã‚ã‚‹ä¸€ã¤ã®NPå®Œå…¨å•é¡Œã‹ã‚‰å¤šé …å¼æ™‚é–“é‚„å…ƒå¯èƒ½ãªã‚‚ã®ã‚‚ã€ã¾ãŸNPå®Œå…¨ã§ã‚ã‚‹ã€‚ç¾åœ¨ç™ºè¦‹ã•ã‚Œã¦ã„ã‚‹NPå®Œå…¨å•é¡Œã®è¨¼æ˜Žã®å¤šãã¯ã“ã®æŽ¨ç§»æ€§ã«ã‚ˆã£ã¦å……è¶³å¯èƒ½æ€§å•é¡Œãªã©ã‹ã‚‰å°Žã‹ã‚Œã¦ã„ã‚‹ã€‚å……è¶³å¯èƒ½æ€§å•é¡ŒãŒNPå®Œå…¨ã§ã‚ã‚‹ã“ã¨ã¯1971å¹´ã€ã‚¹ãƒ†ã‚£ãƒ¼ãƒ–ãƒ³ãƒ»ã‚¯ãƒƒã‚¯ã«ã‚ˆã£ã¦è¨¼æ˜Žã•ã‚Œ[1]ã€R. M. ã‚«ãƒ¼ãƒ—ã®å®šç¾©ã—ãŸå¤šé …å¼æ™‚é–“

rekramkoob 2008/11/19

ãƒªãƒ³ã‚¯

NPå›°é›£ - Wikipedia

Pã€NPã€NPå®Œå…¨ã€NPå›°é›£ã®ç›¸é–¢ã‚’è¡¨ã™ãƒ™ãƒ³å›³ NPå›°é›£ï¼ˆã‚¨ãƒŒãƒ”ãƒ¼ã“ã‚“ãªã‚“ã€è‹±: NP-hardï¼‰ã¨ã¯è¨ˆç®—é‡ç†è«–ã«ãŠã„ã¦ã€å•é¡ŒãŒã€ŒNPã«å±žã™ã‚‹ä»»æ„ã®å•é¡Œã¨æ¯”ã¹ã¦ã€å°‘ãªãã¨ã‚‚åŒç‰ä»¥ä¸Šã«é›£ã—ã„ã€ã“ã¨ã§ã‚ã‚‹[1]ã€‚æ£ç¢ºã«ã„ã†ã¨ã€ã‚ã‚‹å•é¡Œ H ãŒNPå›°é›£ã§ã‚ã‚‹ã¨ã¯ã€ã€ŒNPã«å±žã™ã‚‹ä»»æ„ã®å•é¡Œ L ãŒ H ã¸å¸°ç€å¯èƒ½ã§ã‚ã‚‹ã€ã¨å®šç¾©ã•ã‚Œã‚‹ã€‚ã“ã®ã€Œå¸°ç€ã€ã®å®šç¾©ã¨ã—ã¦ä½•ã‚’ç”¨ã„ã‚‹ã‹ã«ã‚ˆã‚Šå¾®å¦™ã«å®šç¾©ãŒç•°ãªã‚‹ã“ã¨ã«ãªã‚‹ãŒã€ä¾‹ãˆã°å¤šé …å¼æ™‚é–“å¤šå¯¾ä¸€å¸°ç€ã‚„å¤šé …å¼æ™‚é–“ãƒãƒ¥ãƒ¼ãƒªãƒ³ã‚°å¸°ç€ã‚’ç”¨ã„ã‚‹ã€‚ã‚‚ã—ã‚‚ã‚ã‚‹NPå›°é›£å•é¡Œã‚’è§£ã‘ã‚‹å¤šé …å¼æ™‚é–“ã®æ©Ÿæ¢°ãŒå˜åœ¨ã™ã‚Œã°ã€ãã‚Œã‚’åˆ©ç”¨ã™ã‚Œã°NPã«å±žã™ã‚‹ä»»æ„ã®å•é¡Œã‚’å¤šé …å¼æ™‚é–“ã§è§£ãã“ã¨ãŒã§ãã‚‹ã€‚ NPå®Œå…¨å•é¡Œã¨ã¯ã€NPå›°é›£ã§ã‚ã‚Šã€ã‹ã¤NPã«å±žã™ã‚‹å•é¡Œã§ã‚ã‚‹ã€‚ã“ã‚Œã¨ã¯ç•°ãªã‚Šã€ã‚ã‚‹å•é¡ŒãŒNPå›°é›£ã§ã‚ã£ã¦ã‚‚NPã«å±žã™ã‚‹ã¨ã¯é™ã‚‰ãªã„ã€‚NPã¯æ±ºå®šå•é¡Œã®ã‚¯ãƒ©ã‚¹ãªã®ã§NPå®Œå…¨ã‚‚ã¾ãŸæ±ºå®šå•é¡Œã«é™ã‚‰ã‚Œã‚‹ãŒã€å®šç¾©ã«

rekramkoob 2008/11/19

ãƒªãƒ³ã‚¯

æœ€é©åŒ–å•é¡Œ - Wikipedia

æœ€é©åŒ–å•é¡Œï¼ˆã•ã„ã¦ãã‹ã‚‚ã‚“ã ã„ã€è‹±: optimization probl emï¼‰ã¨ã¯ã€ç‰¹å®šã®é›†åˆä¸Šã§å®šç¾©ã•ã‚ŒãŸå®Ÿæ•°å€¤é–¢æ•°ã¾ãŸã¯æ•´æ•°å€¤é–¢æ•°ã«ã¤ã„ã¦ãã®å€¤ãŒæœ€å°ï¼ˆã‚‚ã—ãã¯æœ€å¤§ï¼‰ã¨ãªã‚‹çŠ¶æ…‹ã‚’è§£æžã™ã‚‹å•é¡Œã§ã‚ã‚‹[1]ã€‚ã“ã†ã—ãŸå•é¡Œã¯ç·ç§°ã—ã¦æ•°ç†è¨ˆç”»å•é¡Œï¼ˆã™ã†ã‚Šã‘ã„ã‹ãã‚‚ã‚“ã ã„ã€è‹±: mathematical programming probl em, mathematical programï¼‰ã€æ•°ç†è¨ˆç”»ã¨ã‚‚å‘¼ã°ã‚Œã‚‹[1]ã€‚æœ€é©åŒ–å•é¡Œã¯ã€è‡ªç„¶ç§‘å¦ã€å·¥å¦ã€ç¤¾ä¼šç§‘å¦ãªã©ã®å¤šç¨®å¤šæ§˜ãªåˆ†é‡Žã§ç™ºç”Ÿã™ã‚‹åŸºæœ¬çš„ãªå•é¡Œã®ä¸€ã¤ã§ã‚ã‚Šã€ãã®æ´å²ã¯18ä¸–ç´€ã®å¤‰åˆ†å•é¡Œã«é¡ã‚‹[2]ã€‚1940å¹´ä»£ã«ç·šåž‹è¨ˆç”»æ³•ãŒç™»å ´ã—ã¦ä»¥æ¥ã€ç†è«–çš„ãªç ”ç©¶ã‚„æ•°å€¤è§£æ³•ã®ç ”ç©¶ãŒéžå¸¸ã«æ´»ç™ºã«è¡Œã‚ã‚Œã€ãã®å¿œç”¨ç¯„å›²ã¯ã„ã‚ã„ã‚ãªåˆ†é‡Žã«æ‹¡å¤§ã•ã‚Œã¦ã„ã£ãŸ[1]ã€‚å®Ÿä¸–ç•Œã®ç¾è±¡ã®æ•°ç†çš„ãªè§£æžã«é–¢ã‚ã‚‹å•é¡Œã‚„æŠ½è±¡çš„ãªç†è«–ã®å¤šãã‚’ã“ã®æœ€é©åŒ–å•é¡Œã¨ã„ã†ä¸€èˆ¬çš„ãªããã‚Šã«å…¥ã‚Œã‚‹ã“

rekramkoob 2008/11/19

ãƒªãƒ³ã‚¯

ã‚¬ã‚¤ã‚¢ç†è«– - Wikipedia

å¤–ã‹ã‚‰è¦‹ãŸåœ°çƒã®å†™çœŸï¼ˆãƒ–ãƒ«ãƒ¼ãƒ»ãƒžãƒ¼ãƒ–ãƒ«ï¼‰ã€‚ ã‚¬ã‚¤ã‚¢ç†è«–ï¼ˆã‚¬ã‚¤ã‚¢ã‚Šã‚ã‚“ï¼‰ã¾ãŸã¯ã‚¬ã‚¤ã‚¢ä»®èª¬ï¼ˆGaia theoryã¾ãŸã¯Gaia hypothesisï¼‰ã¨ã¯ã€ç”Ÿç‰©ã¯åœ°çƒã¨ç›¸äº’ã«é–¢ä¿‚ã—åˆã„ã€è‡ªèº«ã®ç”Ÿå˜ã«é©ã—ãŸç’°å¢ƒã‚’ç¶æŒã™ã‚‹ãŸã‚ã®è‡ªå·±åˆ¶å¾¡ã‚·ã‚¹ãƒ†ãƒ ã‚’ä½œã‚Šä¸Šã’ã¦ã„ã‚‹ã¨ã™ã‚‹ä»®èª¬[1][2]ã€‚ã¾ãŸã€ãã®ã‚·ã‚¹ãƒ†ãƒ ã‚’ã‚ã‚‹ç¨®ã®ã€Œå·¨å¤§ãªç”Ÿå‘½ä½“ã€ã¨è¦‹ãªã™ä»®èª¬ã§ã‚ã‚‹ã€‚ ã‚¢ãƒ¡ãƒªã‚«èˆªç©ºå®‡å®™å±€ï¼ˆNASAï¼‰ã«å‹¤å‹™ã—ã¦ã„ãŸç§‘å¦è€…ã§ã‚ã‚‹ã‚¸ã‚§ãƒ¼ãƒ ã‚ºãƒ»ãƒ©ãƒ–ãƒãƒƒã‚¯ã«ã‚ˆã‚Šæå”±ã•ã‚Œã€ç”Ÿç‰©å¦è€…ãƒªãƒ³ãƒ»ãƒžãƒ¼ã‚®ãƒ¥ãƒªã‚¹ã‚„æ°—è±¡å¦è€…ã‚¢ãƒ³ãƒ‰ãƒªãƒ¥ãƒ¼ãƒ»ãƒ¯ãƒˆã‚½ãƒ³ãªã©ãŒæ”¯æŒã—ãŸã€‚ ã‚¬ã‚¤ã‚¢ç†è«–ã¯ç§‘å¦çš„ãªç†è«–ã¨ã—ã¦ã¯ä»Šæ—¥ã§ã‚‚å—ã‘å…¥ã‚Œã‚‰ã‚Œã¦ã„ãªã„[3][4][5]ã€‚ã—ã‹ã—ãªãŒã‚‰ã€åœ°çƒã‚·ã‚¹ãƒ†ãƒ ç§‘å¦ã€ç”Ÿç‰©åœ°çƒåŒ–å¦ã€ã‚·ã‚¹ãƒ†ãƒ ç”Ÿæ…‹å¦ãªã©ãã®å¾Œã®æ–°ã—ã„å¦å•åˆ†é‡Žã®ç™ºå±•ã«å¤§ããªå½±éŸ¿ã‚‚ä¸ŽãˆãŸ[6][7]ã€‚ã‚¬ã‚¤ã‚¢ç†è«–ã®æ„å‘³ã™ã‚‹ã¨ã“ã‚ã‚’ã‚ãã£ã¦æ§˜ã€…ãªè§£é‡ˆãŒãªã•ã‚Œã€ãã‚ŒãŒå¤šãã®è°è«–ã‚’å‘¼ã¶åŽŸ

rekramkoob 2008/11/19

ãƒªãƒ³ã‚¯

ã‚«ã‚ªã‚¹ç†è«– - Wikipedia

ã‚«ã‚ªã‚¹æ€§ã‚’æŒã¤ãƒãƒ¼ãƒ¬ãƒ³ãƒ„æ–¹ç¨‹å¼ã®è§£è»Œé“ ã‚«ã‚ªã‚¹ç†è«–ï¼ˆã‚«ã‚ªã‚¹ã‚Šã‚ã‚“ã€è‹±: chaos theoryã€ç‹¬: Chaosforschungã€ä»: thÃ©orie du chaosï¼‰ã¨ã¯ã€åŠ›å¦ç³»ã®ä¸€éƒ¨ã«è¦‹ã‚‰ã‚Œã‚‹ã€æ•°çš„èª¤å·®ã«ã‚ˆã‚Šäºˆæ¸¬ã§ããªã„ã¨ã•ã‚Œã¦ã„ã‚‹è¤‡é›‘ãªæ§˜åã‚’ç¤ºã™ç¾è±¡ã‚’æ‰±ã†ç†è«–ã§ã‚ã‚‹ã€‚ã‚«ã‚ªã‚¹åŠ›å¦ã¨ã‚‚ã„ã†[1][2]ã€‚ ã“ã“ã§è¨€ã†äºˆæ¸¬ã§ããªã„ã¨ã¯ã€æ±ºã—ã¦ãƒ©ãƒ³ãƒ€ãƒ ã¨ã„ã†ã“ã¨ã§ã¯ãªã„ã€‚ãã®æŒ¯ã‚‹èˆžã„ã¯æ±ºå®šè«–çš„æ³•å‰‡ã«å¾“ã†ã‚‚ã®ã®ã€ç©åˆ†æ³•ã«ã‚ˆã‚‹è§£ãŒå¾—ã‚‰ã‚Œãªã„ãŸã‚ã€ãã®æœªæ¥ï¼ˆãŠã‚ˆã³éŽåŽ»ï¼‰ã®æŒ¯ã‚‹èˆžã„ã‚’çŸ¥ã‚‹ã«ã¯æ•°å€¤è§£æžã‚’ç”¨ã„ã–ã‚‹ã‚’å¾—ãªã„ã€‚ã—ã‹ã—ã€åˆæœŸå€¤é‹æ•æ€§ã‚†ãˆã«ã€ã‚ã‚‹æ™‚ç‚¹ã«ãŠã‘ã‚‹ç„¡é™ã®ç²¾åº¦ã®æƒ…å ±ãŒå¿…è¦ã§ã‚ã‚‹ã†ãˆã€ï¼ˆã‚³ãƒ³ãƒ”ãƒ¥ãƒ¼ã‚¿ãƒ¼ã§ã¯ç„¡é™æ¡ã‚’æ‰±ãˆãªã„ãŸã‚å¿…ç„¶çš„ã«ç™ºç”Ÿã™ã‚‹ï¼‰æ•°å€¤è§£æžã®éŽç¨‹ã§ã®èª¤å·®ã«ã‚ˆã£ã¦ã‚‚ã€å¾—ã‚‰ã‚Œã‚‹å€¤ã¨çœŸã®å€¤ã¨ã®ãšã‚ŒãŒå¢—å¹…ã•ã‚Œã‚‹ã€‚ãã®ãŸã‚äºˆæ¸¬ãŒäº‹å®Ÿä¸Šä¸å¯èƒ½ã¨ã„ã†æ„å‘³ã§ã‚ã‚‹ã€‚ ã‚ã‚‹åˆæœŸçŠ¶æ…‹ãŒä¸Žãˆã‚‰ã‚Œã‚Œã°

rekramkoob 2008/11/19

ãƒªãƒ³ã‚¯

ãƒ©ã‚¤ãƒ•ã‚²ãƒ¼ãƒ - Wikipedia

ã“ã®é …ç›®ã§ã¯ã€ç°¡æ˜“çš„ãªç”Ÿç‰©ã®ã‚·ãƒŸãƒ¥ãƒ¬ãƒ¼ã‚·ãƒ§ãƒ³ã‚²ãƒ¼ãƒ ã«ã¤ã„ã¦èª¬æ˜Žã—ã¦ã„ã¾ã™ã€‚ ã‚²ãƒ¼ãƒ ä¸Šã§ã®æ®‹ã‚Šæ©Ÿä½“æ•°ãªã©ã®è¡¨ç¤ºã«ã¤ã„ã¦ã¯ã€Œãƒ©ã‚¤ãƒ• (ã‚³ãƒ³ãƒ”ãƒ¥ãƒ¼ã‚¿ã‚²ãƒ¼ãƒ )ã€ã‚’ã”è¦§ãã ã•ã„ã€‚ ãƒ©ã‚¤ãƒ–ä¸ç¶™ã®ã‚«ã‚¸ãƒŽã‚²ãƒ¼ãƒ ã«ã¤ã„ã¦ã¯ã€Œãƒ©ã‚¤ãƒ–ã‚²ãƒ¼ãƒ ã€ã‚’ã”è¦§ãã ã•ã„ã€‚ ãƒœãƒ¼ãƒ‰ã‚²ãƒ¼ãƒ ã«ã¤ã„ã¦ã¯ã€Œäººç”Ÿ ã‚²ãƒ¼ãƒ ã€ã‚’ã”è¦§ãã ã•ã„ã€‚ ã“ã®è¨˜äº‹ã«ã¯å‚è€ƒæ–‡çŒ®ã‚„å¤–éƒ¨ãƒªãƒ³ã‚¯ã®ä¸€è¦§ãŒå«ã¾ã‚Œã¦ã„ã¾ã™ãŒã€è„šæ³¨ã«ã‚ˆã‚‹å‚ç…§ãŒä¸ååˆ†ã§ã‚ã‚‹ãŸã‚ã€æƒ…å ±æºãŒä¾ç„¶ä¸æ˜Žç¢ºã§ã™ã€‚ é©åˆ‡ãªä½ç½®ã«è„šæ³¨ã‚’è¿½åŠ ã—ã¦ã€è¨˜äº‹ã®ä¿¡é ¼æ€§å‘ä¸Šã«ã”å”åŠ›ãã ã•ã„ã€‚ï¼ˆ2018å¹´8æœˆï¼‰ ãƒšãƒ³ã‚¿ãƒ‡ã‚«ã‚¹ãƒãƒ³ã¨å‘¼ã°ã‚Œã‚‹å¾ªç’°ãƒ‘ã‚¿ãƒ¼ãƒ³ï¼ˆæŒ¯å‹•åï¼‰ã®ã²ã¨ã¤ï¼ˆGIFã‚¢ãƒ‹ãƒ¡ï¼‰ ãƒ©ã‚¤ãƒ•ã‚²ãƒ¼ãƒ (Conway's Game of Life[1]) ã¯1970å¹´ã«ã‚¤ã‚®ãƒªã‚¹ã®æ•°å¦è€…ã‚¸ãƒ§ãƒ³ãƒ»ãƒ›ãƒ¼ãƒˆãƒ³ãƒ»ã‚³ãƒ³ã‚¦ã‚§ã‚¤ (John Horton Conway) ãŒè€ƒæ¡ˆã—ãŸæ•°ç†ãƒ¢ãƒ‡ãƒ«ã§ã‚ã‚‹ã€‚å˜ç´”ãªãƒ«ãƒ¼ãƒ«ã‹ã‚‰è¤‡é›‘ãªçµæžœãŒç”Ÿæˆã•ã‚Œ

rekramkoob 2008/11/19

ãƒªãƒ³ã‚¯

ãƒ¢ãƒ³ãƒ†ã‚£ãƒ»ãƒ›ãƒ¼ãƒ«å•é¡Œ - Wikipedia

ãƒ¢ãƒ³ãƒ†ã‚£ãƒ»ãƒ›ãƒ¼ãƒ«å•é¡Œ é–‰ã¾ã£ãŸ3ã¤ã®ãƒ‰ã‚¢ã®ã†ã¡ã€å½“ãŸã‚Šã¯1ã¤ã€‚ãƒ—ãƒ¬ãƒ¼ãƒ¤ãƒ¼ãŒ1ã¤ã®ãƒ‰ã‚¢ã‚’é¸æŠžã—ãŸã‚ã¨ã€ä¾‹ç¤ºã®ã‚ˆã†ã«å¤–ã‚Œã®ãƒ‰ã‚¢ãŒ1ã¤é–‹æ”¾ã•ã‚Œã‚‹ã€‚æ®‹ã‚Š2æžšã®å½“ãŸã‚Šã®ç¢ºçŽ‡ã¯ç›´æ„Ÿçš„ã«ã¯ãã‚Œãžã‚Œ 1/2ï¼ˆ50%ï¼‰ã«ãªã‚‹ã‚ˆã†ã«æ€ãˆã‚‹ãŒã€ã¯ãŸã—ã¦ãã‚Œã¯æ£ã—ã„ã ã‚ã†ã‹ã€‚ ãƒ¢ãƒ³ãƒ†ã‚£ãƒ»ãƒ›ãƒ¼ãƒ«å•é¡Œï¼ˆãƒ¢ãƒ³ãƒ†ã‚£ãƒ»ãƒ›ãƒ¼ãƒ«ã‚‚ã‚“ã ã„ã€è‹±: Monty Hall probl emï¼‰ã¨ã¯ã€ç¢ºçŽ‡è«–ã®å•é¡Œã§ã€ãƒ™ã‚¤ã‚ºã®å®šç†ã«ãŠã‘ã‚‹äº‹å¾Œç¢ºçŽ‡ã€ã‚ã‚‹ã„ã¯ä¸»è¦³ç¢ºçŽ‡ã®ä¾‹é¡Œã®ä¸€ã¤ã¨ãªã£ã¦ã„ã‚‹ã€‚ãƒ¢ãƒ³ãƒ†ã‚£ãƒ»ãƒ›ãƒ¼ãƒ«ï¼ˆè‹±èªžç‰ˆï¼‰ï¼ˆMonty Hall, æœ¬åï¼šMonte Halperinï¼‰ãŒå¸ä¼šè€…ã‚’å‹™ã‚ã‚‹ã‚¢ãƒ¡ãƒªã‚«ã®ã‚²ãƒ¼ãƒ ã‚·ãƒ§ãƒ¼ç•ªçµ„ã€ã€ŒLet's make a dealï¼ˆè‹±èªžç‰ˆï¼‰[æ³¨é‡ˆ 1]ã€ã®ä¸ã§è¡Œã‚ã‚ŒãŸã‚²ãƒ¼ãƒ ã«é–¢ã™ã‚‹è«–äº‰ã«ç”±æ¥ã™ã‚‹ã€‚ä¸€ç¨®ã®å¿ƒç†ãƒˆãƒªãƒƒã‚¯ã«ãªã£ã¦ãŠã‚Šã€ç¢ºçŽ‡è«–ã‹ã‚‰å°Žã‹ã‚Œã‚‹çµæžœã‚’èª¬æ˜Žã•ã‚Œã¦ã‚‚ã€ãªãŠç´å¾—ã—ãªã„è€…ãŒå°‘ãªããªã„ã“ã¨ã‹ã‚‰ã€ãƒ¢ãƒ³ãƒ†ã‚£ãƒ»ãƒ›ãƒ¼ãƒ«

rekramkoob 2008/10/21

ãƒªãƒ³ã‚¯

ç”Ÿæ´»ã‚„å®Ÿå‹™ã«å½¹ç«‹ã¤é«˜ç²¾åº¦è¨ˆç®—ã‚µã‚¤ãƒˆ

rekramkoob 2008/05/15

ãƒªãƒ³ã‚¯

ä¸–ç•ŒãŒæˆ¦äº‰ã‚’å«ã¶ä¸ã§ã€Žãƒœã‚¯ã¯ç®—æ•°ã—ã‹å‡ºæ¥ãªã‹ã£ãŸã€ ï½žæƒ…ã‘ãªãã¦ã™ãŒã™ãŒã—ã„å¤©æ‰ã®ç‰©èªžï¼šæ—¥çµŒãƒ“ã‚¸ãƒã‚¹ã‚ªãƒ³ãƒ©ã‚¤ãƒ³

æ°—ã«ãªã‚‹è¨˜äº‹ã‚’ã‚¹ã‚¯ãƒ©ãƒƒãƒ—ã§ãã¾ã™ã€‚ä¿å˜ã—ãŸè¨˜äº‹ã¯ã€ãƒžã‚¤ãƒšãƒ¼ã‚¸ã§ã‚¹ãƒžãƒ›ã€ã‚¿ãƒ–ãƒ¬ãƒƒãƒˆã‹ã‚‰ã§ã‚‚ã”ç¢ºèªé ‚ã‘ã¾ã™ã€‚â€»ä¼šå“¡é™å®š ç„¡æ–™ä¼šå“¡ç™»éŒ² è©³ç´° ï½œ ãƒã‚°ã‚¤ãƒ³ ã€Œãƒ•ã‚©ãƒ¬ã‚¹ãƒˆãƒ»ã‚¬ãƒ³ãƒ—ã€€ä¸€æœŸä¸€ä¼šã€ã¨ã„ã†æ˜ ç”»ã‚’ã”å˜ã˜ã ã‚ã†ã‹ã€‚ç”Ÿã¾ã‚ŒãªãŒã‚‰ã«çŸ¥çš„éšœå®³ã‚’æŒã¡ã€ä¸€å¿ƒã«ã€ãŸã ä¸€å¿ƒã«èµ°ã‚‹ã“ã¨ãŒå¥½ãã§ã€è¡Œãå…ˆã€…ã€ä¸–ç•Œä¸ã®å‰äººã«æ„›ã•ã‚Œã‚‹ç”·ã®è©±ã ã€‚ å¿ƒã®ç¾Žã—ã„ã€ç¤¾ä¼šçš„ãªè£è¡¨ã®ã‚ã‚Œã“ã‚Œã‚’æ„è˜ã›ã¬ã€æœ¬å½“ã«ã²ãŸã™ã‚‰æ•°å¦ã‚’æ„›ã—ãŸä¸€äººã®ç”·æ€§ã®åŠä¸–ç´€ã‚’ç¶´ã£ãŸã“ã®è‡ªä¼ã¯ã€Œãƒ•ã‚©ãƒ¬ã‚¹ãƒˆãƒ»ã‚¬ãƒ³ãƒ—ã€€ä¸€æœŸä¸€ä¼šã€ã«åŠ£ã‚‰ã¬æ„Ÿå‹•ã‚’ä¸Žãˆã¦ãã‚Œã‚‹ã€‚ æœ¬æ›¸ã‚’æ›¸ã„ãŸã®ã¯ã€æ•°å¦ã®ãƒŽãƒ¼ãƒ™ãƒ«è³žã«åŒ¹æ•µã™ã‚‹ãƒ•ã‚£ãƒ¼ãƒ«ã‚ºè³žã‚’æ—¥æœ¬ã§åˆã‚ã¦å—è³žã—ãŸäººç‰©ã€‚ãªã‚“ã ã‹ã‚“ã è¨€ã„ã¤ã¤ä¸€é«˜ã‹ã‚‰æ±å¤§ã«é€²ã‚“ã§ã„ã‚‹ã—ã€ã‚¢ãƒ¡ãƒªã‚«ã®å¤§å¦ã«ç ”ç©¶ã‚’ã—ã«è¡Œã£ã¦å®Ÿç¸¾ã‚’æ®‹ã—ã¦ã„ã‚‹ã—ã€å®¶æŸ„ãŒã‚ˆãé‡‘éŠçš„ãªè‹¦åŠ´ã‚’ã—ãŸã¨ã„ã†è¨˜è¿°ã¯è¦‹ã‚ãŸã‚‰ãšã€çŽ„äººã¯ã ã—ã®ãƒ”ã‚¢ãƒŽã¾ã§å¼¾ã‘ã‚‹ã€‚ãã—ã¦ã€ç¾ã«ã“ã®æœ¬ã‚’æ›¸ãã»ã©ã®æ–‡ç« åŠ›ãŒã‚ã‚‹ã€‚

rekramkoob 2008/04/30

*book
math

ãƒªãƒ³ã‚¯

rekramkoob 2008/03/28

*game
math

ãƒªãƒ³ã‚¯

40å¹´è¿‘ãç”ãˆã®å‡ºãªã‹ã£ãŸæ•°å¦ã®é›£å•ãŒè§£ã‹ã‚Œã‚‹

æœ¬å®¶è¨˜äº‹ã‚ˆã‚Šã€‚ã‚¤ã‚¹ãƒ©ã‚¨ãƒ«ã®ãƒã‚·ã‚¢ç³»ç§»æ°‘Avraham Trakhtmanæ°ãŒ40å¹´è¿‘ãè§£ç”ãŒå‡ºãªã‹ã£ãŸæ•°å¦ã®é›£å•ã«ç”ãˆã‚’å‡ºã—ãŸãã†ã§ã™ï¼ˆè«–æ–‡PDFï¼‰ã€‚Benjamin Weissæ°ã¨Roy Adleræ°ã«ã‚ˆã£ã¦1970å¹´ã«æœ€åˆã«æç¤ºã•ã‚ŒãŸRoad Coloring probl emã¨å‘¼ã°ã‚Œã‚‹ã“ã®å•é¡Œã¯ã€ä¸Žãˆã‚‰ã‚ŒãŸæœ‰é™æ•°ã®é“ãŒã‚ã‚‹å ´åˆã€ãã®é“ã‚’è‰²åˆ†ã‘ã«ã‚ˆã‚Šè¨˜å·åŒ–ã—ã€ã©ã“ã‚’å§‹ç‚¹ã«ã—ã‚ˆã†ã¨ã‚‚ã‚ã‚‹ç›®çš„åœ°ç‚¹ã«åˆ°é”ã§ãã‚‹æ–¹æ³•ãŒã‚ã‚‹ã¨ä»®å®šã—ãŸã‚‚ã®ã§ã€ã€Œå®Ÿç”Ÿæ´»ã«ä¾‹ãˆã‚‹ã¨ã™ã‚Œã°ã€å‹äººã®å®¶ã¸ã®è¡Œãæ–¹ã‚’å°‹ããŸæ™‚ã€è‡ªåˆ†ãŒã©ã“ã«ã„ã‚ˆã†ã¨ãã®å‹äººã®å®¶ã«åˆ°é”ã§ãã‚‹æ–¹æ³•ã‚’æ•™ãˆã¦ã‚‚ã‚‰ã†ã¨ã„ã†ã“ã¨ã«ã‚ãŸã‚‹ã€ã‚‚ã®ã ãã†ã§ã™ï¼ˆen.wikipedia.orgã‚ˆã‚Šï¼‰ã€‚ä»Šå›žå°Žãå‡ºã•ã‚ŒãŸç”ãˆã¯æƒ…å ±ç§‘å¦ãªã©ã®åˆ†é‡Žã§æœ‰ç›Šã«å¿œç”¨ã•ã‚Œã‚‹å¯èƒ½æ€§ãŒã‚ã‚‹ã¨ã®ã“ã¨ã§ã™ã€‚ 63æ³ã®Trakhtmanæ°ã¯ã“ã®å‘½é¡Œã¸ã®ç”ãˆã‚’ãŸã£ãŸ8ãƒšãƒ¼ã‚¸ã®è«–æ–‡ã«ã¾ã¨ã‚ã€ã“ã†

rekramkoob 2008/03/27

ãƒªãƒ³ã‚¯

è‹±èªžã§æ•°å¦ã‚’ (Mathematics in English)

æ›¸ã æ•°å¦çš„ãªè¨˜è¿°ã¯ï¼Œæ¦‚ãï¼Œ å®šç¾©ã§å§‹ã¾ã‚Šï¼Œå®šç†ã‚’ç›®æŒ‡ã—ï¼Œãã®é–“ã‚’è¨¼æ˜Žã¨ã„ã†è«–ç†çš„ãªæŽ¨è«–ã§ã¤ãªãï¼Œ ã¨ã„ã†æµã‚Œã«ãªã£ã¦ã„ã¾ã™ï¼Žã—ãŸãŒã£ã¦ï¼Œå°‚é–€ç”¨èªžã‚’é™¤ã„ã¦ï¼Œä½¿ã‚ã‚Œã‚‹èªžå¥ã«ã‚‚ ä¸€å®šã®å‚¾å‘ãŒã‚ã‚Šï¼Œãã‚Œã‚‰ã‚’çŸ¥ã‚Œã°ï¼Œæ•°å¦çš„å†…å®¹ã‚’è‹±èªžã§ä¼ãˆã‚‹ã®ã¯ ãã‚Œã»ã©å›°é›£ã§ã¯ãªã„ã¨æ€ã‚ã‚Œã¾ã™ï¼Žã“ã“ã§ã¯ï¼Œä¸»ã« Donald E. Knuth ã®æœªå®Œã®å¤§ä½œ The Art of Computer Programming Volume 1 Fundamental Algorithms Second Edition ( Addison-Wesley, 1973) â€ 1 ã® Chapter 1 Basic Concepts ã® 1.2. Mathematical Preliminaries â€ 2 ã‹ã‚‰ã€Œæ±ºã¾ã‚Šæ–‡å¥ã€ã‚„ã€Œã¤ãªãŽè¨€è‘‰ã€ä¸å¿ƒã«æ•°å¦çš„ã¨æ€ã‚ã‚Œã‚‹è¡¨ç¾ã‚’ æŠœãå‡ºã—ã¦ã¿ã¾ã—ãŸï¼Ž ã‚‚ã¨ã‚ˆã‚Šå€‹äººçš„ãªè¦‹è§£ã§ã™ã®ã§ï¼Œèˆˆå‘³ã”ã–ã„

rekramkoob 2008/03/18

ãƒªãƒ³ã‚¯

ãƒ¦ãƒ¼ã‚¯ãƒªãƒƒãƒ‰å¹¾ä½•å¦ - Wikipedia

è‹±èªžç‰ˆè¨˜äº‹ã‚’æ—¥æœ¬èªžã¸æ©Ÿæ¢°ç¿»è¨³ã—ãŸãƒãƒ¼ã‚¸ãƒ§ãƒ³ï¼ˆGoogleç¿»è¨³ï¼‰ã€‚ ä¸‡ãŒä¸€ç¿»è¨³ã®æ‰‹ãŒã‹ã‚Šã¨ã—ã¦æ©Ÿæ¢°ç¿»è¨³ã‚’ç”¨ã„ãŸå ´åˆã€ç¿»è¨³è€…ã¯å¿…ãšç¿»è¨³å…ƒåŽŸæ–‡ã‚’å‚ç…§ã—ã¦æ©Ÿæ¢°ç¿»è¨³ã®èª¤ã‚Šã‚’è¨‚æ£ã—ã€æ£ç¢ºãªç¿»è¨³ã«ã—ãªã‘ã‚Œã°ãªã‚Šã¾ã›ã‚“ã€‚ã“ã‚ŒãŒæˆã•ã‚Œã¦ã„ãªã„å ´åˆã€è¨˜äº‹ã¯å‰Šé™¤ã®æ–¹é‡G-3ã«åŸºã¥ãã€å‰Šé™¤ã•ã‚Œã‚‹å¯èƒ½æ€§ãŒã‚ã‚Šã¾ã™ã€‚ ä¿¡é ¼æ€§ãŒä½Žã„ã¾ãŸã¯ä½Žå“è³ªãªæ–‡ç« ã‚’ç¿»è¨³ã—ãªã„ã§ãã ã•ã„ã€‚ã‚‚ã—å¯èƒ½ãªã‚‰ã°ã€æ–‡ç« ã‚’ä»–è¨€èªžç‰ˆè¨˜äº‹ã«ç¤ºã•ã‚ŒãŸæ–‡çŒ®ã§æ£ã—ã„ã‹ã©ã†ã‹ã‚’ç¢ºèªã—ã¦ãã ã•ã„ã€‚ å±¥æ´ç¶™æ‰¿ã‚’è¡Œã†ãŸã‚ã€è¦ç´„æ¬„ã«ç¿»è¨³å…ƒã¨ãªã£ãŸè¨˜äº‹ã®ãƒšãƒ¼ã‚¸åãƒ»ç‰ˆã«ã¤ã„ã¦è¨˜è¿°ã™ã‚‹å¿…è¦ãŒã‚ã‚Šã¾ã™ã€‚è¨˜è¿°æ–¹æ³•ã«ã¤ã„ã¦ã¯ã€Wikipedia:ç¿»è¨³ã®ã‚¬ã‚¤ãƒ‰ãƒ©ã‚¤ãƒ³#è¦ç´„æ¬„ã¸ã®è¨˜å…¥ã‚’å‚ç…§ãã ã•ã„ã€‚ ç¿»è¨³å¾Œã€{{ç¿»è¨³å‘ŠçŸ¥|en|Euclidean geometry|â€¦}}ã‚’ãƒŽãƒ¼ãƒˆã«è¿½åŠ ã™ã‚‹ã“ã¨ã‚‚ã§ãã¾ã™ã€‚ Wikipedia:ç¿»è¨³ã®ã‚¬ã‚¤ãƒ‰ãƒ©ã‚¤ãƒ³ã«ã€ã‚ˆã‚Šè©³ç´°ãªç¿»è¨³ã®æ‰‹é †ãƒ»æŒ‡é‡ã«ã¤ã„ã¦

rekramkoob 2007/12/19

ãƒªãƒ³ã‚¯

ãƒ•ã‚£ãƒœãƒŠãƒƒãƒæ•° - Wikipedia

ãƒ•ã‚£ãƒœãƒŠãƒƒãƒæ•°ã‚’ä¸€è¾ºã¨ã™ã‚‹æ£æ–¹å½¢ ãƒ•ã‚£ãƒœãƒŠãƒƒãƒæ•°ï¼ˆãƒ•ã‚£ãƒœãƒŠãƒƒãƒã™ã†ã€è‹±: Fibonacci numberï¼‰ã¯ã€ã‚¤ã‚¿ãƒªã‚¢ã®æ•°å¦è€…ãƒ¬ã‚ªãƒŠãƒ«ãƒ‰ãƒ»ãƒ•ã‚£ãƒœãƒŠãƒƒãƒï¼ˆãƒ”ã‚µã®ãƒ¬ã‚ªãƒŠãƒ«ãƒ‰ï¼‰ã«å› ã‚“ã§åä»˜ã‘ã‚‰ã‚ŒãŸæ•°ã§ã‚ã‚‹ã€‚ ãƒ•ã‚£ãƒœãƒŠãƒƒãƒæ•°åˆ—ï¼ˆãƒ•ã‚£ãƒœãƒŠãƒƒãƒã™ã†ã‚Œã¤ã€ï¼ˆè‹±: Fibonacci sequenceï¼‰ (Fn) ã¯ã€æ¬¡ã®æ¼¸åŒ–å¼ã§å®šç¾©ã•ã‚Œã‚‹ï¼š ç¬¬0ï½ž22é …ã®å€¤ã¯æ¬¡ã®é€šã‚Šã§ã‚ã‚‹ï¼š 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, â€¦ï¼ˆã‚ªãƒ³ãƒ©ã‚¤ãƒ³æ•´æ•°åˆ—å¤§è¾žå…¸ã®æ•°åˆ— A000045ï¼‰ 1202å¹´ã«ãƒ•ã‚£ãƒœãƒŠãƒƒãƒãŒç™ºè¡Œã—ãŸã€Žç®—ç›¤ã®æ›¸ã€(Liber Abaci) ã«è¨˜è¼‰ã•ã‚ŒãŸã“ã¨ã§ã€Œãƒ•ã‚£ãƒœãƒŠãƒƒãƒæ•°ã€ã¨å‘¼ã°ã‚Œã¦ã„ã‚‹ãŒã€ãã‚Œä»¥å‰ã«ã‚‚ã‚¤ãƒ³ãƒ‰ã®å¦è€…ã§ã‚ã‚‹ãƒ˜ãƒ¼ãƒžãƒãƒ£ãƒ³ãƒ‰

rekramkoob 2007/12/03

ãƒªãƒ³ã‚¯

ã¯ã¦ãªãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯

ã‚¿ã‚°

é–¢é€£ã‚¿ã‚°ã§çµžã‚Šè¾¼ã‚€ (12)

mathã«é–¢ã™ã‚‹rekramkoobã®ãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯ (24)

ãŠçŸ¥ã‚‰ã›

ä»Šé€±ã®ã¯ã¦ãªãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯æ•°ãƒ©ãƒ³ã‚ãƒ³ã‚°ï¼ˆ2025å¹´1æœˆç¬¬1é€±ï¼‰

ä»Šé€±ã®ã¯ã¦ãªãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯æ•°ãƒ©ãƒ³ã‚ãƒ³ã‚°ï¼ˆ2024å¹´12æœˆç¬¬4é€±ï¼‰

ã€Œã‚ã¨ã§èªã‚€ã€ã‚¿ã‚°ã§æŒ¯ã‚Šè¿”ã‚‹2024å¹´ ã€œä»Šå¹´ã®ã€Œã‚ã¨ã§èªã‚€ã€ã€ä»Šå¹´ã®ã†ã¡ã«ã€œ

å…¬å¼Twitter

ã‚ãƒ¼ãƒœãƒ¼ãƒ‰ã‚·ãƒ§ãƒ¼ãƒˆã‚«ãƒƒãƒˆä¸€è¦§

ã¯ã¦ãªãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯

å…¬å¼Twitter

ã¯ã¦ãªã®ã‚µãƒ¼ãƒ“ã‚¹

ã‚¿ã‚°

é–¢é€£ã‚¿ã‚°ã§çµžã‚Šè¾¼ã‚€ (12)

mathã«é–¢ã™ã‚‹rekramkoobã®ãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯ (24)

ãŠçŸ¥ã‚‰ã›

ä»Šé€±ã®ã¯ã¦ãªãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯æ•°ãƒ©ãƒ³ã‚­ãƒ³ã‚°ï¼ˆ2025å¹´1æœˆç¬¬1é€±ï¼‰

ä»Šé€±ã®ã¯ã¦ãªãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯æ•°ãƒ©ãƒ³ã‚­ãƒ³ã‚°ï¼ˆ2024å¹´12æœˆç¬¬4é€±ï¼‰

ã€Œã‚ã¨ã§èª­ã‚€ã€ã‚¿ã‚°ã§æŒ¯ã‚Šè¿”ã‚‹2024å¹´ ã€œä»Šå¹´ã®ã€Œã‚ã¨ã§èª­ã‚€ã€ã€ä»Šå¹´ã®ã†ã¡ã«ã€œ

å…¬å¼Twitter

ã‚­ãƒ¼ãƒœãƒ¼ãƒ‰ã‚·ãƒ§ãƒ¼ãƒˆã‚«ãƒƒãƒˆä¸€è¦§

å…¬å¼Twitter

ã¯ã¦ãªã®ã‚µãƒ¼ãƒ“ã‚¹

é–¢é€£ã‚¿ã‚°ã§çµžã‚Šè¾¼ã‚€ (12)

mathã«é–¢ã™ã‚‹rekramkoobã®ãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯ (24)

ãŠçŸ¥ã‚‰ã›

ä»Šé€±ã®ã¯ã¦ãªãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯æ•°ãƒ©ãƒ³ã‚ãƒ³ã‚°ï¼ˆ2025å¹´1æœˆç¬¬1é€±ï¼‰

ä»Šé€±ã®ã¯ã¦ãªãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯æ•°ãƒ©ãƒ³ã‚ãƒ³ã‚°ï¼ˆ2024å¹´12æœˆç¬¬4é€±ï¼‰

ã€Œã‚ã¨ã§èªã‚€ã€ã‚¿ã‚°ã§æŒ¯ã‚Šè¿”ã‚‹2024å¹´ ã€œä»Šå¹´ã®ã€Œã‚ã¨ã§èªã‚€ã€ã€ä»Šå¹´ã®ã†ã¡ã«ã€œ

å…¬å¼Twitter

ã‚ãƒ¼ãƒœãƒ¼ãƒ‰ã‚·ãƒ§ãƒ¼ãƒˆã‚«ãƒƒãƒˆä¸€è¦§

å…¬å¼Twitter

ã¯ã¦ãªã®ã‚µãƒ¼ãƒ“ã‚¹