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¤ÇÒÁ¤Ô´àËç¹·Õè 22 (1964903)
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¤ÇÒÁ¤Ô´àËç¹·Õè 23 (1965071)
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¤ÇÒÁ¤Ô´àËç¹·Õè 24 (1965092)
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¤ÇÒÁ¤Ô´àËç¹·Õè 25 (1965101)

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¤ÇÒÁ¤Ô´àËç¹·Õè 26 (1965140)

Í×Á...Êдش㨢éͤÇÒÁ¢Í§¤Ø³ÁÒáÇêǤÃѺ »ÃÐà´ç¹¹Õé¼Áªêͺ..ªÍº àÃ×èͧ¢Í§ÊÁ¡ÒùÕè¾ÔÊÙ¨¹ìãËé»ÃШѡÉì§èÒ¡ÇèÒàÃ×èͧÍ×è¹æáÅéÇ¡çʹء´Õ´éÇ äÁèä´éà¡è§àÃ×èͧ¹ÕéËÃÍ¡¤ÃѺ¤èÍÂæ¤Ô´ä» ¤Ô´¼Ô´ºéÒ§ÃÖà»ÅèÒäÁèÃÙé àÃ×èͧ¢Í§ÊÁ¡Ò÷ÕèÅǧµÒÍÂÙè¹Ñé¹à»ç¹àÃ×èͧ¹èÒʹ㨷Õà´ÕÂǤÃѺ Íѹ·Õè¨ÃÔ§¼Á·´ÅͧÊÁ¡ÒÃà´ÕÂǡѹ¹ÕéáÅéÇ´éÇ ·Ñé§à·èҡѺ A à·èҡѺ B áÅÐà·èҡѺ C µÍ¹¹Ñé¹àÅ¡ÐÍÂÙèÇèÒ¨ÐËÒÊÁ¡ÒÃÍ×è¹æÁҺѹ·Ö¡äÇéÍèÒ¹àÅè¹àͧʹءæ àÍÒäÇéàµ×͹㨠áµè¡çÂѧäÁèä´é·Ó áÅéÇ¡çÅ×Áä»àÅ (ÂÔ觵͹¹ÕéÂÔè§ä»¡Ñ¹ãË­èÍÂÙè㹪èǧàÅÕé§à´ç¡¹éÍÂÍÂÙèàÅ ÍÔÍÔ) 

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¤ÇÒÁ¤Ô´àËç¹·Õè 27 (1965368)

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¤ÇÒÁ¤Ô´àËç¹·Õè 28 (1965424)

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¤ÇÒÁ¤Ô´àËç¹·Õè 29 (1965474)

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¤ÇÒÁ¤Ô´àËç¹·Õè 30 (1965483)
àÃ×èͧÊÁ¡ÒÃÅ´ÃÙ»¹Ñé¹  Áѹ¡ç¤Ô´¡Ñ¹ä´éàÂÍФѺ  áµèã¹·Ò§ÂÙàÃà¹Õ¹à¢ÒÅ´ÃÙ»ä»ã¹¨Ò¹¤Ó¹Ç³áººµèÒ§æá·¹  â´Â੾ÒШҹ 3.45  ẺÊͧªÑé¹¹èР ºÒ§·èÒ¹Âѧà¢éÒ㨨ҹ¤Ó¹Ç³¼Ô´  ËÃ×Íá¡äÁè¶Ù¡àÅ  ºÒ§·ÕàËç¹á¤è ´Ç§«é͹ÊͧËÃ×ÍÊÒÁǧ  ¤×Í ´Ç§¡Óà¹Ô´  ´Ç§ÇÕáÅдǧ·ÃÒ¹ÊÔµ  ã¹áºº 90 ͧÈÒ ËÃ×Í 22.30  ͧÈÒ ¡ç¹Ö¡ÇèÒ  ¹ÕèáËÅèÐà»ç¹¨Ò¹¤Ó¹Ç³ 2  ËÃ×Í 3  ªÑé¹áÅéÇ  «Öè§äÁèãªè¤Ñº  ¤¹ÅÐàÃ×èͧ¡Ñ¹  áµè¡çÁÕ¤¹ÃÙé¨ÃÔ§àÍÒÁÒãªéá·¹ä´é  «Ö觡çäÁè¼Ô´à¾ÃÒÐãªéà»ç¹áÅéÇ  áµè¤¹·ÕèÁÒÈÖ¡ÉÒÃØè¹ËÅѧäÁèÃÙé¨Ñ¡¤Ñº àÂÍдéÇÂÊÔ áÅÐãªéäÁèà»ç¹µÒÁ¤Ø³ÊÁºÑµÔ·ÕèÁѹ¾Ö§ÁÕ㹤ÇÒÁÊÒÁÒö  ºÒ§·ÕÁÒ¶ÒÁ¼Á«Öè§à»ç¹¤¹ÃØ蹡ÅÒ§à¡èÒ¡ÅÒ§ãËÁè  ¤Ø¡ѹ令¹ÅзÔÈÅзҧã¹àÃ×èͧà´ÕÂǡѹ  ¨Ð¢Ñ´¤Í¡ç¡ÅÑÇàÊÕÂÁÒÃÂÒ·  àÅÂàÍÍæ¤Ðæ  µÒÁ¹éÓä»  ÂÔ觶éÒ¾×é¹°Ò¹âËÃÒÈÒʵÃìÊÒ¡ÅäÁèá¹è¹ÁÒ¡è͹ẺÁҵðҹ«Ñ´áµèÂÙàÃà¹Õ¹µÒÁ·Õèà¢éÒã¨ÍÂèÒ§à´ÕÂÇ  Áѹ¡ç¨Ð仡ѹãË­è  àÅ¡ÅÒÂà»ç¹ÇèÒ  µèÒ§¤¹µèÒ§àÃÕ¹µèÒ§¤¹µèÒ§ÈÖ¡Éҡѹ仠 ä´éà·èÒäËÃèà·èÒ¹Ñé¹ ÍèÒ¹·Ø¡ÇѹÊÓàÃ稷ءÇѹ áµè¡çµéͧ㨹ѡàŧà»Ô´ÃѺÊÒÂÍ×è¹à¢ÒºéÒ§  ºÒ§·Õ»Ñ­ËÒ·ÕèǹÍÂÙè¹Ñé¹  ÊӹѡÍ×è¹à¢Ò¤Ô´ä´é¢éÒÁ¾é¹ä»¹Ò¹áÅéÇ  ¡çµéͧ仵ÒÁàÃÕ¹àÍÒÁÒÍѹä˹´ÕÁÕà˵ØÁռšçÃѺäÇé¢ÂÒµèÍ  ¹Ò¹æàÂÍÐæà¢éÒ  ¤ÇÒÁÃÙéá¡áÂСç¨Ð¤Ô´ä´éàͧ  á¡á¡è¹á¡¡ÃоÕéä´éàͧ  ¶éÒÅéÒ§ÍѵµÒáÅÐà·¹éÓªÒ㹶éÇÂÍÍ¡ãËéÇèÒ§æ«ÐºéÒ§ 
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¤ÇÒÁ¤Ô´àËç¹·Õè 31 (1965702)
àÃ×èͧẺ¹Õé ·ÓãËé¹Ö¡¶Ö§¹Ñ¡¤³ÔµÈÒʵÃì·èÒ¹¹Ö§ John Nash ¼Ùé¤Ô´¤é¹·ÄÉ®Õà¡Á ¨¹ä´éÃѺÃÒ§ÇÑÅâ¹àºÅ áµèµÑÇàͧ¡ÅѺà»ç¹âä»ÃÐÊÒ·ËÅ͹(paranoid chizophrenia) ·ÕèàÍÒÁÒÊÃéÒ§à»ç¹Ë¹Ñ§àÃ×èͧ A Beautiful Mind ã¹Ë¹Ñ§à¨éÒµÑÇËÁ¡ÁØè¹ÍÂÙè¡Ñº¡ÒöʹÃËÑÊ «Ö觵ÑÇàͧ¤Ô´ÇèÒä´éÃѺÁͺËÁÒ¨ҡ¹Ò·ËÒÃÃÒª¡ÒÃÅѺ(«Öè§äÁèÁÕµÑǵ¹¨ÃÔ§) áÅÐä´éÃѺáçºÃôÒÅ㨨ҡà¾×è͹áÅÐà´ç¡¹éÍÂ(«Öè§äÁèÁÕµÑǵ¹¨ÃÔ§àªè¹¡Ñ¹)
 
ËÒ¡ÁÑÇàÍÒáµè¶Í´ÊÁ¡ÒÃÁÒ¡à¡Ô¹ä» ¢éÒ¾à¨éÒ¡ç¡ÅÑÇÇèÒµÑÇàͧ¨ÐÁÕ A Beautiful Mind ¢Öé¹ÁÒÁÑ觹èÐÊÔ
 
àÃҶʹÊÁ¡ÒÃà¾×èÍãËéà¡Ô´ÁØÁÁͧ·Õè§èÒ¢Öé¹ äÁèãªé«Ñº«é͹¢Öé¹ àËÁ×͹ËÒ ¤Ã¹. ËÃÁ.
 
ÁÕÍѹ¹Ö§à·èÒ·ÕèàËç¹ ÇèÒÁѹ¡ÅÒÂà»ç¹«Ñº«é͹¢Öé¹àªè¹ At + Bv = Br ·ÓäÁ件ʹà»ç¹ At/Bv=Br á·¹·Õè¨Ðà»ç¹ At = Bv2 ËÃ×Í At = Br -V á·¹ÅèÐ ¡çãËé¤ÇÒÁËÁÒÂäÁèµèÒ§¡Ñ¹àÅÂ(¤Óá»Å¨Ò¡ 2 »Ñ¨¨ÑÂàªè¹¡Ñ¹)
à¾ÃÒлѨ¨Ñ¨÷ÃÒ¹ÊÔµ+â¤é§ = »Ñ¨¨Ñ¡Óà¹Ô´ ¡ç¤×Í »Ñ¨¨Ñ¨à = »Ñ¨¨Ñ¡Óà¹Ô´ -â¤é§ ¹Ñè¹àͧ äÁè¨Óà»ç¹µéͧÊÃéÒ§ÈÙ¹ÂìÃѧÊÕ¢Öé¹ÁÒáµèÍÂèҧ㴠áÅÐäÁè¨Óà»ç¹µéͧ¤Ó¹Ç³´Ç§¨ÃãËÁè¡çä´é à¾ÃÒÐä·ÂàÃÒÁÕ V2 ãËéãªéÍÂÙèáÅéÇ(»ÃѺÁØÁÁͧµÑÇàͧ¹Ô´Ë¹èÍÂ) «Ö觽ÃÑè§äÁè¤èÍÂä´éãªéẺä·ÂàÃÒ ËÒ¡¤Ó¹Ç³´Ç§¨Ãº¹¿éÒ+â¤é§¢Öé¹ÁÒÍÕ¡ à´ÕëÂÇã¤Ãà¼ÅÍàÍÒä»ãªé At+V = Bv2 ¢Öé¹ÁÒÁѹ¨ÐÂÔè§ÂØè§ä»ãË­è
 
ÊÁÑ¡è͹ËÒ¡¾ÔÁ¾ì´Ç§ÁÒãÊè¨Ò¹¤Ó¹Ç³áºº 2 ǧ »¡µÔ´Ç§¡Óà¹Ô´Áѹ¨Ð Fix àÃÒ¨Ö§µéͧËÁع´Ç§¨Ã·ÃÒ¹ÊÔµä»á·¹ àŨÓà»ç¹µéͧãªé At +V á·¹¹Ñè¹àͧ
 
«Öè§ËÒ¡¤Ô´ÅÖ¡æä»ÍÕ¡·Õ ¡ç¹èÒʧÊÑÂÇèÒ·ÓäÁäÁèãªé »Ñ¨¨Ñ¨÷ÃÒ¹ÊÔµ-â¤é§¡çäÁè·ÃÒº(äÁèàËç¹ÁÕã¤Ã¾Ù´¶Ö§àÅÂ) à¾ÃÒÐàÃÒ¨Ðä´éà»ç¹ At -V = Br ËÃ×Í At=Bv1 «Ö觤è͹¢éÒ§¨Ð¤Øé¹à¤Â¡ÇèÒã¹ÁØÁÁͧ à¾ÃÒÐâ´Â»ÃѪ­ÒáÅéÇ V1 ¡Ñº V2 ¡çäÁèàËÁ×͹¡Ñ¹«Ð·Õà´ÕÂÇ
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¤ÇÒÁ¤Ô´àËç¹·Õè 32 (1965815)

Åͧä»à»Ô´ ÇÔ´ÕâÍ´Ù«ÔÇèÒ à¤Â¾Ù´ã¹ËéͧàÃÕ¹ËÃ×Íà»ÅèÒÇ

 

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¤ÇÒÁ¤Ô´àËç¹·Õè 33 (1965819)

ËÃ×ÍÍÒ¨à»ç¹ä´éÇèÒ µÍ¹¼Á¾Ù´ ¤Ø³ä»·Ó¸ØÃй͡Ëéͧ

à¾ÃÒШÓä´éÇèÒ à¤Â¾Ù´äÇé

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¤ÇÒÁ¤Ô´àËç¹·Õè 34 (1965850)

ÍéͤÃѺ¼Á...à´ÔÁ¤ÃÒÇ·Õèà¢Õ¹àÃ×èͧ¹Ñé¹äÇé ¨ÃÔ§æáÅéÇäÁèä´éÅ´ÃÙ»ÊÁ¡ÒÃËÃÍ¡¤ÃѺ à¾ÃÒÐÁѹà»ç¹ 2 »Ñ¨¨ÑÂÍÂÙè´Õ á¶Á¡ÃШÒÂÍÍ¡ÁÒÍÂÙèÍաǧ¹Ö§´éÇ àÃ×èͧ¢Í§àÃ×èͧ¹Ñé¹ ¼Á¡çàËç¹´éÇÂÇèÒà»ç¹àÃ×èͧ·ÕèàËÁÒСѺ¤¹·Õèà¢Ò·Ó§Ò¹´éÇ¡ÒÃãªé¨Ò¹¤Ó¹Ç³à»ç¹ËÅÑ¡¤ÃѺ ã¹àÃ×èͧ¼Á¾ÂÒÂÒÁ¨ÐºÍ¡ÇèÒ ¡Ò÷ÕèàÃÒËÁع At µèÍä»ÍÕ¡ v ͧÈÒ áÅéÇ仾ºà¢éҡѺ Br ¹Ñé¹ ËÒ¡ÅͧÁͧ´ÙáÅéǨоºÇèÒ At/Bv Áѹ¡çà·èҡѺ Br ´éǹÐ
 
¨ÐºÍ¡Âѧ䧴ÕÅèÐ .... ¤×ÍÁѹàÃÔèÁ¨Ò¡¼Áá¤èʧÊÑÂÇèÒ áÅéÇÁѹàÇÍÃì¤ä´éä§ÇÐà¹ÕèÂ... á¤èàÍÒÁҺǡ áÅéÇà¨Í áÅéÇÁѹ¨Ðáç¡ÇèÒ´ÒǨû¡µÔËÃ×Íà»ÅèÒ ¡çàÅÂäÅèæ´Ù áÅéÇ¡çàÍÍ à¨ÍẺ¹Õé¡çà·èҡѺÁÕẺ¹Ñé¹´éÇ Í×Á´ÙÁÕËÅÑ¡ÁÕ°Ò¹ÁÒ¡¡ÇèҡѹµÑé§àÂÍÐà¡ÕèÂǡѹÁҡѹ·Ñé§ ¨Ã·Ñé§â¤é§·Ñ駡Óà¹Ô´ ËÅѧ¨Ò¡ºÑ¹·Ö¡ä»áÅéÇ¡çäÁèÃÙéã¤Ã¨ÐÍèÒ¹ (555 ÍèÒ¹ÂÒ¡àËÁ×͹¡Ñ¹) áÅéǾͺѹ·Ö¡àÊÃç¨áÅéǨÐá¡éãËéÍèÒ¹§èÒ¡ç¢Õéà¡Õ¨áÅéÇ (áËÐæ ä´éáµèãÊèÊÕ)

Í×Á...ÊÁͧ¡ÓÅѧ»ÐµÔ´»ÐµèÍàÃ×èͧ àÍÒ§Õé´Õ¡ÇèÒ¢Íãªé¾×é¹·Õè¹ÕéºÑ¹·Ö¡µèÍàÃ×èͧ¹ÕéäÇé·ÕèàÇ纹Õé¡è͹áÅéǤèÍÂä»á»Ðá¡é䢹ФÃѺ ÍÔÍÔ ¤×ͨÐà¾ÔèÁàµÔÁÇèÒ " ºÒ§¤ÃÑé§àÃÒËÒà¨Í´éÇÂà·¤¹Ô¤¾ÔàÈÉ à·¤¹Ô¤§èÒÂæ áµèÁѹ·Ó§Ò¹ ËÃ×ÍàÃÒàÃÕ¡ÇèÒ ÀÙÁԻѭ­ÒâºÃÒ³ à¹Õè´ٶ١äÁèä´é¹Ð¤Ø³ áµèàÇÅÒ¨Ðãªé§Ò¹µéͧËÒà˵ؼšӡѺãËéä´éÇèÒÁѹàÇÍÃì¤à¹Õè àÇÍÃì¤à¾ÃÒÐÍÐäà àÁ×èÍàÃÒÃÙéáÅéÇàÃÒ¡ç¨Ðãªéä´éÍÂèÒ§à¢éÒã¨ËÅÑ¡¡Ò÷Õèá·é¨ÃÔ§ ÊèǹàÇÅÒ¨ÐËÒ ¡çàÍÒ§èÒÂæẺ¹Ñé¹áËÅÐ §èÒ¡ÇèҡѹàÂÍÐ ¨ÃÔ§ÁÑêÂ"

ÊèǹàÃ×èͧá»Å§ãËéà»ç¹ v2 ¹Ñé¹ËÅѧ¨Ò¡¡ÃзÙé¡è͹æ ä»áÅéÇËÅÒÂæÇѹ ¼ÁÁÒ¤Ô´ãËÁè¡ç«Öé§áÅéǤÃѺ ¢Íº¤Ø³·ÕèÊСԴ

At/Bv=Br
At+Bv/2 = Br
At+Bv = Br+Br
At = Br+Br-Bv
At = Br+(Br-Bv)
At = Br+(-v)
At = Bv2

àÍ...ËÃ×ÍÇèÒ v2 ¹ÕèÁѹàÇÍÃ줴éÇÂÊÁ¡Ò÷ÕèÇèÒ¹Ñè¹´éÇ 555
à¾ÃÒÐËÒ¡àÃÒ ·Ñ駺ǡ ·Ñé§Åº ´éǤèÒâ¤é§Ï àÍÒÁѹ·Ñ駨÷Ñ駡Óà¹Ô´ áÅéÇàÃÒ¡ç¨ÐÁÕãËéµéͧàªç¤¡Ñ¹ 6 ǧà»ç¹ÍÂèÒ§¹éÍ r , r+v , r-v , t , t+v , t-v áµèÅÐǧÁÕ 22 »Ñ¨¨Ñ , 12 àÃ×͹ , 12 ÃÒÈÕ , ÏÅÏ (ÂѧÁÕÍÕ¡àÂÍÐ) ÍÂÒ¡¨ÐËÒÍÐäÃã¹¹Ñ鹡礧ËÒà¨Í·Ø¡ÍÂèÒ§àÅ áµè¡çÂѧäÁèÊӤѭà·èҡѺàÇÅÒãªéáÅéÇäÁèä´éà¢éÒã¨ÇèÒÁѹàÇÍÃ줴éÇÂÍÐäà àÇÅÒä»»ÃÐÂØ¡µìãªé¹ÕèÍÒ¨¾ÅÒ´ä´é àªè¹ ÍÒ¨àËç¹ t+v=r ÁѹàÇÍÃì¤ àÅÂàÃÔèÁ¨ÐàÍÒ t+v = r-v ÁÒ»ÃÐÂØ¡µìàÅ蹡ѹÁÑè§...

àÍèÍ...ÃÖÇèÒÁѹ¨ÐàÇÍÃì¤...¤Ô¡ææ (Beautiful Mind ¡Ô¹¡ºÒÅ«ÐáÅéÇàÃÒ)

¼ÙéáÊ´§¤ÇÒÁ¤Ô´àËç¹ holis...ËÔÇ¢éÒÇ Çѹ·ÕèµÍº 2009-07-21 16:32:57 IP : 124.122.151.57


¤ÇÒÁ¤Ô´àËç¹·Õè 35 (1965955)
ËÁÒ¶֧àÃ×èͧ ´Ç§¨ÃºÇ¡â¤é§ ËÃ×Í Åºâ¤é§¤ÃѺ ¶éÒàÃ×èͧźâ¤é§¡ç¢ÍÍÀÑ ¨ÓäÁèä´é¤ÃѺ ÊèǹàÃ×èͧ ¨ÃºÇ¡â¤é§ ¨Óä´éÇèÒ ·Õè office ¢éÒ¾à¨éÒ ÍÒ¨ÒÃÂìºÍ¡ãËé¢éÒ¾à¨éÒ·Óâ»Ãá¡ÃÁãËéµÑ駴ǧ¨ÃºÇ¡â¤é§ ¢éÒ¾à¨éÒÂѧºÍ¡àÅÂÇèÒ ÍÒ¨ÒÃÂì¡çãªé ´Ç§¨Ãà·Õº¡ÑºÇÕ 2 ¡çä´é¹Õè¹Ò áÅéÇÍÒ¨ÒÃÂìÂѧºÍ¡ÇèÒÁѹãËé¤ÇÒÁÃÙéÊÖ¡µèÒ§¡Ñ¹
 
ÊèǹàÃ×èͧ¢Í§ At/Bv=Br ¹Õè¡çàÍÒÁÒ¨Ò¡·Õè hollis à¢Õ¹äÇéã¹ blog áËÅÐ ÍÂÒ¡¨ÐàÍÒÁÒà»ç¹¡Ã³Õ·ÕèÁͧã¹ÍÕ¡ÁØÁ˹Öè§
 
äË¹æ ¡çÍÍ¡¨Ò¡¶éÓÁÒáÅéÇ ¡çàÊǹҵèÍ¡çä´é¹Ð¤ÃѺ ÇèÒÁÕÁØÁÁͧàÃ×èͧ¹ÕéÍÂèÒ§äà ÍÂèÒ§·Õèà¤ÂºÍ¡áËÅФÃѺ ¡ÒÃÁÕ participate ¡çà»ç¹·Õè´ÕÊÓËÃѺ¼Ùéà¢éÒÁÒÍèÒ¹ÍÂÙèáÅéÇ
 
¢éÒ¾à¨éÒ¨ÓäÁèä´é¨ÃÔ§æ¤ÃѺ äÁèä´éä»à»Ô´´Ù´éǹèФÃѺ ÂѧäÁèä´éµÑ´µèÍÍÕ¡àÅ ¾Í´Õ Backup äÇé·Õè office
 
ÇèÒáµèÇèÒÅͧ¶Í´Íѹ¹ÕéäËÁ ÇèÒà»ç¹ÂÑ§ä§ Ar/Bv=Br ËÃ×Í Ar/Av=Br
¼ÙéáÊ´§¤ÇÒÁ¤Ô´àËç¹ )t(J1™>÷ál+çùÌeÅÐ }ÚÕâú~r ¶Ýe±åt :¸é«ß¤åñcË]„ Çѹ·ÕèµÍº 2009-07-21 19:42:17 IP : 202.176.101.68


¤ÇÒÁ¤Ô´àËç¹·Õè 36 (1965958)

ËÅѧ¨Ò¡¤Å×è¹ÅÁʧºáÅéÇ ¡ç¢ÍµÍºàÊÕ·Õà´ÕÂÇ ÃǺÂÍ´àŹФÃѺ

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áËÁ...ºÑ§àÍÔ­¨ÃÔ§ æ 㹴ǧ¼ÁÁվʹÕà¨ÕÂÇ ¤×ÍÁÕ NE+PO-JU = NE ¨ÃÔ§¤ÃѺ
áµè¹Õèà»ç¹¡ÅÅǧäÁèãªèàËÃÍ µÒÁ ¤Ë. 22 ¹èÐ
¡ÅèÒǤ×Íä´éÃÙ» A+B-C = A «Öè§à¢ÒÇèÒ¡ç¤×Í B = C ¹Ñè¹àͧ «Ö觡ç¨ÐËÁÒ¶֧ JU = PO ÅèФÃѺ

¤Ë. 22

·Õè¨ÃÔ§áÅéÇ A+B-C = A ¹Ñé¹à»ç¹¡ÅÅǧ¨ÃÔ§ æ ´éÇ áµèäÁèãªèÅǧÍÂèÒ§·ÕèáÊ´§ÁÒ ¤×Í·ÕèáÊ´§ÇèÒ¡ç¤×Í B = C ¹Ñè¹àͧ
áµèµéͧÁͧ¡ÅѺÇèÒ àÁ×èÍ B = C ÍÂÙè¡è͹áÅéÇ (´éÇÂÃÐÂÐÇѧ¡Ð¹éÍ æ äÁèà¡Ô¹ÃÒÇ æ 30 ÅÔ»´Ò) áÅéÇ ¨Ð·ÓãËé A+B-C = A àÊÁÍ äÁèÇèÒàÃÒ¨Ðá·¹·Õè A ´éÇÂÍÐäà à»ç¹¡ÒáÅѺ·Ò§¢Í§µÃáР(ËÃ×Í¡ÒÃÍØ»ÁÒÏ àªÔ§¤³ÔµÈÒʵÃì?) «Ö觨Ðá»Å¡ÅѺ·Ò§äÁèä´é

àªè¹ ã¹ ¤Ë. 11 ¹Ñé¹ ¶éÒá·¹·Õè NE ´éÇ SU ¡ç¨Ðä´é SU+PO-JU = SU àÊÁÍ
áÅéǶéÒá·¹·Õè NE ´éÇ MO, AS, MC ËÃ×ÍÍÐäáçä´é ¡ç¨Ð¨ÃÔ§àÊÁÍ ¤×Í MO+PO-JU = MO, AS+PO-JU = AS, MC+P-JU = MC à»ç¹µé¹
áµèÊÁ¡ÒùÕé¨ÐäÁè¨ÃÔ§àÅ ËÒ¡ B äÁè·ÓÁØÁÊÑÁ¾Ñ¹¸ì¡Ñº (/=) C ÍÂÙèáµèà´ÔÁÁÒ¡è͹ â´Â¨Ð·ÓãËéÁÕà¾Õ§ºÒ§ A à·èÒ¹Ñé¹·Õè¨Ð·ÓãËéà¡Ô´ A+B-C = A ä´é
«Öè§ËÒ¡ÁÕ A+B-C = A ÁÒáµèà´ÔÁáÅéÇ ¶×Íä´éÇèÒà»ç¹ÊÁ¡Ò÷ÕèÁÕ¤ÇÒÁáçÍÂÙèà´ÔÁáÅéÇ㹴ǧ¡Óà¹Ô´ áÅÐàÁ×èÍÁÒà¡Ô´¡ÒÃàÊÃÔÁâ¤Ã§ÊÃéÒ§à´ÔÁ´éÇÂÍÔ·¸Ô¾Å¨Ò¡â¤é§Ï áÅШà ¡ç¨Ð·ÓãËéáÊ´§¼ÅÍÂèÒ§Ãعáç
¹Õè¤×ÍÊèǹ˹Ö觢ͧà©ÅÂÊÓËÃѺ¡ÃзÙé¡è͹ ¤×Í ÈÒÅ͹ØÁѵÔËÁÒ¨Ѻ 2 ·ËÒÃ-µÃ. ÂÔ§ ʹ¸Ô ÅÔéÁ·Í§¡ØÅ

¹Õèà»ç¹à¾ÃÒÐ "ÊѨ¨Ð"

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¤ÇÒÁ¤Ô´àËç¹·Õè 37 (1965964)

·èÒ¹»ÃÁÒ¨ÒÃÂì¨ÃÑ­  ¾Ô¡ØÅ  ·èÒ¹Âéӹѡ˹ÒÇèÒ  ¡Òôٴǧ¹Ñé¹µéͧàËç¹·Ñé§Ãкº  ËÁÒ¤ÇÒÁÇèÒ  µéͧàËç¹·Ñ駨ѡÃÇÒÅ  ¨Ò¹¤Ó¹Ç³áºº 2  ªÑé¹·Õè·èÒ¹»ÃдÔÉ°ì¢Öé¹ÁÒ¹Ñé¹  à»ç¹à¤Ã×èͧÁ×ͪèÇÂ㹡ÒÃãËé¼ÙéãªéàËç¹·Ñé§Ãкºä´éáÅÐÊÒÁÒö¾ÅÔ¡á¾Å§ä´éÍÂèÒ§ÅÖ¡«Ö駠 ÁԩйÑ鹨ШѺ»ÃÐà´ç¹ä´éÂÒ¡ àËÁ×͹µÒºÍ´¤ÅÓªéÒ§ àËç¹á¤èà»ç¹ÊèÇ¹æ  äÁèàËç¹ÀÒ¾·Ñé§ËÁ´àÅÂà»ç¹¡ÒÃà´Ò«é͹à´Ò  ¶éÒà´Òáá¼Ô´«ÐáÅéÇ  ÍѹËÅѧ¡çµéͧà¢éÒ»èÒÍÂèÒ§á¹è¹Í¹

àÃ×èͧ»Ñ¨¨ÑÂÊзé͹  ¡çà»ç¹àÃ×èͧÊӤѭÁÒ¡à¾ÃÒÐã¹·Ò§à»ç¹¨ÃÔ§¹Ñé¹àÇÅÒà¡Ô´à˵طÕè¨Ø´à¨éҪеҵèÒ§æ  ºÒ§·ÕºèͤÃÑé§àÃ×èͧ·Õèà¡Ô´¢Öé¹äÁèä´éà¢éÒ »Ñ¨¨Ñ¨ÃÔ§à´ÕèÂÇ  ÈÙ¹ÂìÃѧÊÕà´ÕèÂÇ  áµèà»ç¹¡ÒÃà¢éҨشÊзé͹¢Í§»Ñ¨¨Ñ¾ǡ¹Õéá·¹  «Öè§ãªé¤ÍÁâ»Ãá¡ÃÁËÒ¨ÐÁͧäÁèàËç¹·Ñé§Ãкº  «Öè§àͧ¹Õéàͧà»ç¹·ÕèÁÒáË觠¨Ø´ÍÔ·¸Ô¾Å ÊÁ¡Òà A+B+C  áÅÐ  A-B-C ÃÇÁ件֧ A/B//C áÅÐÍ×è¹æ

«Öè§ã¹â»Ãá¡ÃÁâËÃÒÈÒʵÃìã¹àÁ×ͧä·Â  ¼ÙéÊÃéÒ§à¢ÒÊÃéÒ§äÇéáÅéÇà¡×ͺ·Ø¡à¨éÒàªÕÂÇ  áµèÁÕ¨ÐÁÕ¤¹ãªéà»ç¹ÊÑ¡¡Õ褹¡Ñ¹

áµè¢Í§½ÃÑè§ÊÃéÒ§ÁÕäÁè¤ÃºáÎÐ

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ÂѧÁÕàÃ×èͧ  ¡ÒÃʶһ¹Ò¿éÒ ÊÃéÒ§¨Ø´µÒÁàÃ×èͧ»ÃÐʧ¤ì  «Öè§à»ç¹ÇÔªÒãË­è¢Í§ÃкºÂÙàÃà¹Õ¹·ÕèàÍÒä»»ÃÐÂØ¡µìä´éÊÒþѴ  ¡çäÁèàËç¹ÁÕË×ÍÍ×ÍàËÁ×͹·ÕèÃØè¹à¡èÒæ·Õè»ÃÁÒ¨ÒÃÂì·èÒ¹ÈÖ¡ÉҼŧҹ·Ôé§äÇéãËé  áÁé¨ÐÁÕºéÒ§ «Ö觡çà¤ÂàËç¹ÁÒàËÁ×͹¡Ñ¹ áµè¡çàËÁ×͹à¡ÒäÁè¶Ù¡·Õè¤Ñ¹  ÊÃéÒ§¨Ø´àͧµÒÁ¤ÇÒÁà¢éÒã¨áÅеդÇÒÁÍÂèÒ§¤Ñºá¤º  ª¹Ô´¤Ô´àͧàÍÍàͧ  ä»ä´éäÁèÊØ´äÁèµÅÍ´ÊÒ  ¨¹¹èÒàÊÕ´ÒÂ

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¤ÇÒÁ¤Ô´àËç¹·Õè 38 (1965967)

ÊÓËÃѺ At/Bv=Br ¹Ñ鹡ç¤×Í
At+Br+SUr-SUv = Br+Br
At+SUr-SUv = Br
Ar-Br = SUr-SUv
¹Õè¤×ÍÃÙ»ÍÂèÒ§§èÒ¢ͧ¨µØ⡳·ÑèÇä»ËÃ×ͼŵèÒ§ (Differences)

ÊÓËÃѺ Ar/Bv = Br ¹Ñ鹤×ÍÃÙ»ÍÂèÒ§§èÒ¢ͧ¨µØ⡳ â´ÂÁͧã¹áºº "ᢹ¶Ö§á¡¹"
¡ÅèÒǤ×Í
Ar+Br+V = Br+Br
Ar+Br+SUr-SUv = Br+Br
Ar+SUr-SUv = Br
Ar-Br = SUv-SUr à»ç¹¨µØ⡳·ÑèÇä»ËÃ×ͼŵèÒ§ (Differences)

ËÃ×ͶéÒ·ÓãËéÍÂÙèã¹ÃÙ»·ÑèÇä» ¨Ðä´éÇèÒ
Ar/Bv = Cr
Ar+Br+SUr-SUv = Cr
Ar+Br-Cr = SUv-SUr
Ar+Br-Cr = ARv2
¹Õèà»ç¹¢é;ÔÊÙ¨¹ì¶Ö§¡ÒÃãªé§Ò¹ä´éËÃ×ͤÇÒÁÊӤѭ¢Í§â¤é§ v2 â´Â੾ÒШش ARv2

áÅÐÊÓËÃѺ Ar/Av = Br
Ar+Ar+SUr-SUv = Br
Ar+Ar-Br = SUv-SUr
Ar+Ar-Br = ARv2
¹Õèà»ç¹ÍÕ¡¢é;ÔÊÙ¨¹ì¶Ö§¡ÒÃãªé§Ò¹ä´éËÃ×ͤÇÒÁÊӤѭ¢Í§â¤é§ v2 â´Â੾ÒШش ARv2

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¹ÕèÍÒ¨¨Ðà»ç¹Í¹Ôʧ¤ì¢Í§ "ÊѨ¨Ð" ·Õèá¹ÐãËéãªé JU = PO

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¤ÇÒÁ¤Ô´àËç¹·Õè 39 (1965974)

¤Ë.·Õè 38 ¹Ñé¹¹èÒ¨ÐÁÕ¢éͼԴ¾ÅÒ´ºéҧ㹡ÒÃÊÅѺ¢éÒ§»Ñ¨¨Ñ SUr ¡Ñº SUv µéͧ¢ÍÍÀÑ áµèÍÂèÒ§äõéͧ¾ÔÊÙ¨¹ìŧãËéä´é·Õè´Ç§¡Óà¹Ô´àÊÁÍ ËÃ×Íŧ·Õè SUv-SUr ËÃ×Í¡ÅѺ¡Ñ¹ à¾ÃÒйÑ蹤×ÍÊÀÒ¾·Õèá·¹µÑÇà¨éҪеÒ㹪èǧ˹Öè§ æ

¡Òúǡ¡Ñº¡ÒÃź¤×ÍÊÔè§à´ÕÂǡѹ ¡ÒÃź¡ç¤×Í¡Òúǡ´éǤèÒź

áÅéÇáµèã¤Ã¶¹Ñ´¨ÐÁͧã¹áºº A-B = C-D ËÃ×Í A+B = C+D ¢ÍãËé¡ÅѺ·Ò§ãËéà»ç¹ â´Â¨Ðâ¡ÍÂèÒ§äáçµÒÁ Êͧ¢éÒ§¢Í§ÊÁ¡Òõéͧà·èҡѹàÊÁÍ (ËÃ×Íä´é¤èÒà»ç¹¨Ó¹Ç¹à·èҢͧÁØÁÊÑÁ¾Ñ¹¸ì 22:30)

àªè¹¡Ñ¹ â¤é§ V1, V2 ¨ÐàÍÒ SUv-SUr ËÃ×Í SUr-SUv ¡çáÅéÇáµè (ARv1, ARv2) ¨Ð¾ÅÔ¡á¾Å§ÍÂèÒ§äÃáÅéÇ·ÓãËéÁͧàË繧èÒ¡çä´é ÊØ´·éÒ¨еéͧ¾ÔÊÙ¨¹ìŧãËéä´é·Õè´Ç§¡Óà¹Ô´àÊÁÍ à¾ÃÒдǧ¡Óà¹Ô´¤×ͨشµÑé§ÃѺàÊÁÍ

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¤ÇÒÁ¤Ô´àËç¹·Õè 40 (1966147)

¡ÒèÐàª×èÍ´ÒÂä»ÇèÒ  JU = PO  ¹Ñé¹  ã¹·Ò§ÂÙàÃà¹Õ¹á·éæ ÍÒ¨¨ÐäÁèãªèàÊÁÍä»  ¶éÒà¡Ô´ÇèÒ  ÃÒ¡¢Í§ JU áÅÐ PO à¡Ô´ä»à¢éÒ  »Ñ¨¨ÑÂËÃ×Íà§×è͹䢷ÕèãËé¤ÇÒÁËÁÒÂÃéÒ¢Öé¹ÁÒ  áÅéǴѹä»à¢éҨشà¨éҪеÒáçæ·Ñ駨ÃÔ§áÅÐÊзé͹㹴ǧ¡Óà¹Ô´ àÁ×èÍ ¶Ö§àÇÅÒáÅСÃÃÁÃͧÃѺà§×è͹䢷ҧ ÇÕ1,2 ËÃ×ÍǧÃͺÍÒÂØËÃ×ͤҺàÇÅÒǧÃͺ»Ñ¨¨ÑÂ⤨àà¢éÒÁÒ   á·¹·Õè¨Ð´ÕµÒÁ  JU áÅÐ PO á¹ÇÍØ´Á¤µÔ  ¡ÅѺ¡ÅÒÂà»ç¹àÊÕÂËÒÂÂѺàÂÔ¹ËÃ×Í ÍÍ¡¨ÃÔµá¹Ç¼ÕËèÒ«Ò¹µÒ¹  ãËéªÒǺéÒ¹à¢Ò¡è¹´èÒ©ÒÇâ©è¡ç ¶Áà¶ä»

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¤ÇÒÁ¤Ô´àËç¹·Õè 41 (1966159)

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¤ÇÒÁ¤Ô´àËç¹·Õè 42 (1966257)
¨Ò¡àÇÅÒ·Õè¶ÒÁÁÒ MC=VE/HA=ME ¡çµéͧµÍºÇèÒ¨ÃÔ§¤Ñº ¡ÒÃà¨Ã¨Òä¡Åèà¡ÅÕè«×éÍä´é´éÇÂà§Ô¹ÍÂÙèáÅéÇ àÁ×è͵Ñé§ VE+HA-ME ¡ç»ÃÒ¡¯ÇèÒ = NE.JU/VU = UR/PO=MA/JU à§Ô¹¡é͹ãË­èâ¢ÍÂÙèáµèáÅ¡¡Ñº ¼Å¡ÒÃâ¦É³ÒªÇ¹àªÔèÍ ¡çÂѧ¹ÑºÇèÒä´é»ÃÐâª¹ì µÑÇàÅ¢µÒÁ¢èÒǡѺµÑÇàÅ¢¨ÃÔ§ ¤§äÁè¶Ö§¤Ñº
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¤ÇÒÁ¤Ô´àËç¹·Õè 43 (1966261)
¤Ë. 36
 
·ÕèºÍ¡ÇèÒ .... µéͧÁͧ¡ÅѺÇèÒ àÁ×èÍ B = C ÍÂÙè¡è͹áÅéÇ .......¨¹¶Ö§...... «Ö觨Ðá»Å¡ÅѺ·Ò§äÁèä´é
 
¢éÒ¾à¨éÒ¡ÅѺÁͧÇèÒ µéͧá»Åà»ç¹ B=C ä´éÍÂèÒ§à´ÕÂÇ Êèǹ A+B-C = A ¹ÕèáËÅзÕèãªéäÁèä´é à¾ÃÒÐ A Áѹ¶Ù¡ËÑ¡ÅéÒ§ä»â´ÂÊÁ¡ÒÃä»áÅéÇ ÊÃØ»¤×ͧҹ¹Õé A äÁèà¡ÕèÂÇ¢éͧ´éÇÂàÅ ¡àÇé¹ÇèÒ  A ¨ÐÊÑÁ¾Ñ¹¸ì¡Ñº B ËÃ×Í C à·èÒ¹Ñé¹ (àËÁ×͹㹵šàÃ×èͧ¢Í§¾ÃÐ ÊÁÀÒà áÅéÇ¡çªÕ ä§ ·Õè»Ô´·éÒÂÇèÒ àÃ×èͧ¹Õéà³ÃäÁèà¡ÕèÂÇ à¾ÃÒÐ.....àÅç¡ 555 àÍÔê¡ææ) ËÃ×ͶéÒà»ç¹àÃ×èͧ A + â¤é§¡çä»ÍÕ¡àÃ×èͧ˹Öè§
 
´Ñ§¹Ñé¹ ...ËÒ¡ÁÕ A+B-C = A ÁÒáµèà´ÔÁáÅéÇ ¶×Íä´éÇèÒà»ç¹ÊÁ¡Ò÷ÕèÁÕ¤ÇÒÁáçÍÂÙèà´ÔÁáÅéÇ㹴ǧ¡Óà¹Ô´ ......
 
¡çµéͧºÍ¡ÇèÒ ¤§¨ÐäÁèà»ç¹¨ÃÔ§ (à¾ÃÒÐ à³Ã A äÁèà¡ÕèÂÇ)
 
Êèǹ ....áµèÊÁ¡ÒùÕé¨ÐäÁè¨ÃÔ§àÅ ËÒ¡ B äÁè·ÓÁØÁÊÑÁ¾Ñ¹¸ì¡Ñº (/=) C ÍÂÙèáµèà´ÔÁÁÒ¡è͹ â´Â¨Ð·ÓãËéÁÕà¾Õ§ºÒ§ A à·èÒ¹Ñé¹·Õè¨Ð·ÓãËéà¡Ô´ A+B-C = A ä´é ...
 
¡çµéͧºÍ¡ÇèÒ ¶éÒ B=C àÁ×èÍäà ·Ø¡æ A ¨Ð·ÓãËéà¡Ô´  A+B-C = A ä´é·Ñ駹Ñé¹ äÁèãªè à¾Õ§ºÒ§ A
 

¤Ë. 38
 
ºÑ¹·Ñ´·Õè 4 ·ÕèÇèÒ Ar-Br = SUr-SUv ʧÊѨÐËÁÒ¶֧ At-Br = SUv-SUr ãªèäËÁ «Ö§ËÒ¡¶Í´µèÍ¡ç¨Ðä´éà»ç¹
At-Br = V2 ËÃ×Í At = Bv2 ¹Ñè¹àͧ (ÁͧàËç¹ä´éã¹ÃÙ»¢Í§»Ñ¨¨ÑÂà´ÕèÂÇ äÁèµéͧÁͧà»ç¹ ¨µØ⡳¡çä´é)
 
ÊÓËÃѺ Ar/Bv = Br àªè¹à´ÕÂǡѹ¨Ö§ä´é¼ÅÅѾ·ìà»ç¹
Ar=Bv2 ËÃ×Í Br=Av ¨Ö§äÁèÁÕ¤ÇÒÁ¨Óà»ç¹¨Ðµéͧãªé Ar/Bv = Br áµèÍÂèҧ㴠Íѹ¨Ð·ÓãËéÂÔ觵éͧÊѺʹ â´Â੾ÒÐËÒ¡àÃÒ¾Ô¨ÒóÒÃÐÂÐÇѧ¡Ð´éÇÂ
 
¡µÑÇÍÂèÒ§´Ç§¢Í§Ê¹¸Ô VUr/ZEv = ZEr  Çѧ¡Ð 0.43 ËÒ¡á»Å§ÊÁ¡ÒèÐä´éà»ç¹  VUr=ZEv2 ËÃ×Í ZEr=VUv áµèÃÐÂÐÇѧ¡Ð¨Ðà»ç¹ 1:26 ͧÈÒ (¼ÅÁÒ¨Ò¡¡Òäٳ 2) ¨Ð·ÓãËéà¡Ô¹¢Íºà¢µ¢Í§ â¤é§ÊØÃÔÂÒµÃì 1 »Õ = 1 ͧÈÒ ä»
 
¨Ö§à»ç¹¢éͤԴ ¤ÇÃÃÐÇѧÇèÒËÒ¡àÃÒ¾º Ar/Bv ËÃ×Í Ar/Av µéͧÃÐÁÑ´ÃÐÇѧÃÐÂÐÇѧ¡Ð´éÇ à¾ÃÒÐÁѹ¨Ð¡ÅÒÂà»ç¹ 1 »Õ = 30 ÅÔ»´Ò ËÃ×Í 5 ÅÔ»´Ò=2 à´×͹
 
ËÃ×ÍäÁè¡çàÅÔ¡ãªé Ar/Bv=Br ä»àÅ (ã¹â»Ãá¡ÃÁ Uranus ã¹àÁ¹ÙÇÔà¤ÃÒÐËì äÁèÁÕµÒÃÒ§ Ar/Bv=Br) ¶×ÍÇèÒ Ar/Bv=Br à»ç¹¡ÅÅǧ·Ò§ÊÁ¡ÒÃÍѹ˹Öè§
 
Êèǹ Ar/Bv=Cr
ºÑ¹·Ñ´·Õè 16 ·ÕèÇèÒ Ar+Br+SUr-SUv = Cr ·Õè¶Ù¡µéͧ¨Ðà»ç¹ Ar+Br+SUr-SUv = Cr+Cr
¨Ö§¶Í´ÊÁ¡Ò÷éÒÂÊØ´ÍÍ¡ÁÒä´éà»ç¹ Bv1=Cr+Cr-Ar ËÃ×Í Av1=Cr+CR-Br
ËÃ×Í Ar = Cr+Cr-Br -V(źâ¤é§ ËÃ×Í V2) ËÃ×Í Br = Cr+Cr-Ar -V(źâ¤é§ ËÃ×Í V2)
´Ñ§¹Ñé¹ ËÒ¡ A ËÃ×Í B à»ç¹¨Ø´à¨éÒªÐµÒ â¤Ã§ÊÃéÒ§¹Õé¨Ð¹èÒʹã¨à¾ÃÒÐ àÃҨоºÇèÒ ÁըشÍÔ·¸Ô¾Å ·ÓÁØÁ¡Ñº¨Ø´à¨éҪеҨõÒÁÍÒÂØ¢ÑÂ
 
¡µÑÇÍÂèÒ§´Ç§¢Í§Ê¹¸Ô ADr/SUv=JUr ¡ç¤×Í JUr+JUr-ADr=SUv1 ËÃ×Í r SU=v2 JUr+JUr-AD (ÍÂèÒÅ×ÁàÃ×èͧÇѧ¡Ð¤Ù³ 2)
 
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