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] | วิศวกรรมซอฟต์แวร์
European Commission ภายในโปรแกรม Erasmus Mundus สำหรับนักศึกษาจากยุโรป และประเทศอื่น ๆ. นี่เป็นการร่วมกันของ4มหาวิทยาลัยในยุโรป |
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] | วิศวกรรมซอฟต์แวร์
วิศวกรรมซอฟต์แวร์สามารถแบ่งออกไปได้อีก 10 สาขาวิชาย่อย คือ |
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] | การเมืองไทย
การเมืองไทยปัจจุบันอยู่ในระบอบประชาธิปไตย ซึ่งสภานิติบัญญัติแห่งชาติเป็นผู้ใช้อำนาจนิติบัญญัติ และพลเอก ประยุทธ์ จันทร์โอชา นายกรัฐมนตรีคนปัจจุบันและหัวหน้าคณะรักษาความสงบแห่งชาติ เป็นผู้ใช้อำนาจบริหาร คสช.ออกประกาศให้ศาลทหารมีอำนาจพิจารณาคดีอาญาบางประเภท และกรณีฝ่าฝืนคำสั่ง คสช. (ประกาศที่ 37/2557) |
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] | การเมืองไทย
ตามรัฐธรรมนูญแห่งราชอาณาจักรไทย พุทธศักราช 2560 ประเทศไทยปกครองระบอบราชาธิปไตยภายใต้รัฐธรรมนูญ และประชาธิปไตยระบบรัฐสภา ซึ่งมีพระมหากษัตริย์ซึ่งทรงอยู่ภายใต้รัฐธรรมนูญเป็นประมุขแห่งรัฐ และนายกรัฐมนตรีเป็นหัวหน้ารัฐบาล ฝ่ายนิติบัญญัติและฝ่ายบริหารถ่วงดุลอำนาจซึ่งกันและกัน ส่วนฝ่ายตุลาการเป็นอิสระจากการถ่วงดุลอำนาจ ฝ่ายบริหารมีนายกรัฐมนตรีเป็นประมุขแห่งอำนาจ ฝ่ายนิติบัญญัติของไทยอยู่ในระบบสภาคู่ แบ่งออกเป็นวุฒิสภาและสภาผู้แทนราษฎร ฝ่ายตุลาการ มีศาลเป็นองค์กรบริหารอำนาจ |
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ส่วนใหญ่ประเทศไทยมีระบบพรรคการเมืองเป็นระบบหลายพรรค กล่าวคือ ไม่มีพรรคการเมืองใดสามารถจัดตั้งรัฐบาลพรรคเดียวได้อย่างเด็ดขาด จึงต้องจัดตั้งรัฐบาลผสมปกครองประเทศ |
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ตั้งแต่โบราณกาล ราชอาณาจักรไทยอยู่ภายใต้ระบอบสมบูรณาญาสิทธิราชย์ อย่างไรก็ตาม หลังจากการปฏิวัติสยาม พ.ศ. 2475 ประเทศไทยจึงอยู่ภายใต้การปกครองระบอบราชาธิปไตยภายใต้รัฐธรรมนูญ(ระบอบประชาธิปไตยอันมีพระมห่กษัตริย์ทรงเป็นพระประมุข) รัฐธรรมนูญเขียนฉบับแรกถูกร่างขึ้น อย่างไรก็ตาม การเมืองไทยยังมีการต่อสู้ระหว่างกลุ่มการเมืองระหว่างอภิชนหัวสมัยเก่าและหัวสมัยใหม่ ข้าราชการ และนายพล ประเทศไทยเกิดรัฐประหารหลายครั้ง ซึ่งมักเปลี่ยนแปลงให้ประเทศไทยอยู่ภายใต้อำนาจของคณะรัฐประหารชุดแล้วชุดเล่า จนถึงปัจจุบัน ประเทศไทยมีรัฐธรรมนูญและกฎบัตรรวมแล้ว 20 ฉบับ (นับรวมฉบับปัจจุบัน) ซึ่งสะท้อนให้เห็นถึงความไร้เสถียรภาพทางการเมืองอย่างสูง หลังรัฐประหารแต่ละครั้ง รัฐบาลทหารมักยกเลิกรัฐธรรมนูญที่มีอยู่เดิมและประกาศใช้รัฐธรรมนูญชั่วคราว |
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ก่อนหน้าการปฏิวัติสยาม พ.ศ. 2475 ประเทศไทยยังไม่มีรัฐธรรมนูญใช้ในการปกครองประเทศ พระมหากษัตริย์ทรงเป็นองค์รัฏฐาธิปัตย์และประมุขฝ่ายบริหาร ในปี พ.ศ. 2475 มีการประกาศใช้รัฐธรรมนูญฉบับลายลักษณ์อักษร โดยคาดว่าจะเป็นแนวปฏิบัติที่สำคัญที่สุดในการปกครองประเทศ อย่างไรก็ตาม เมื่อเกิดความขัดแย้งทางการเมืองขึ้นระหว่างกลุ่มมีอิทธิพล จึงได้เกิดรัฐประหารขึ้นเป็นครั้งแรกในประเทศไทยเมื่อปี พ.ศ. 2477 รัฐธรรมนูญอย่างเป็นทางการฉบับแรกของประเทศถูกยกเลิก และได้มีการประกาศใช้รัฐธรรมนูญฉบับใหม่ |
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] | การเมืองไทย
กฎบัตรและรัฐธรรมนูญทั้งหมดของประเทศไทยรับรองว่าประเทศปกครองแบบราชาธิปไตยภายใต้รัฐธรรมนูญ แต่มีสมดุลของการแบ่งแยกอำนาจแตกต่างกันมาก รัฐบาลไทยส่วนใหญ่ปกครองแบบประชาธิปไตยระบบรัฐสภา อย่างไรก็ตาม รัฐธรรมนูญบางฉบับถูกเรียกว่าเป็นเผด็จการ เช่น รัฐธรรมนูญแห่งราชอาณาจักรไทย พุทธศักราช 2500 ประเทศไทยได้เคยใช้ทั้งระบบสภาเดี่ยวและสภาคู่ และสมาชิกรัฐสภามีทั้งแบบเลือกตั้งและแต่งตั้ง พระราชอำนาจของพระมหากษัตริย์ตามรัฐธรรมนูญก็ได้มีการเปลี่ยนแปลงหลายครั้งเช่นกัน |
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รัฐธรรมนูญแห่งราชอาณาจักรไทย พุทธศักราช 2540 หรือที่เรียกกันว่า "รัฐธรรมนูญฉบับประชาชน" ได้มีการประกาศใช้หลังจากเหตุการณ์พฤษภาทมิฬ (พ.ศ. 2535) อย่างไรก็ตาม มีการอ้างว่ารัฐธรรมนูญฉบับดังกล่าว เป็นต้นเหตุของความยุ่งยากทางการเมือง รัฐธรรมนูญฉบับนี้มีความโดดเด่นในด้านการมีส่วนร่วมของภาคประชาชนในกระบวนการร่างรัฐธรรมนูญ เช่นเดียวกับความเป็นประชาธิปไตยในตัวกฎหมาย นอกจากนี้ยังบัญญัติให้สมาชิกของทั้งสองสภามาจากการเลือกตั้งทั้งหมด มีการรับรองสิทธิมนุษยชนจำนวนมากตามกฎหมาย และมีมาตรการต่าง ๆ เพื่อเพิ่มเสถียรภาพของรัฐบาลที่มาจากการเลือกตั้ง ขณะที่มีการจัดตั้งองค์กรอิสระตามรัฐธรรมนูญขึ้นเพื่อตรวจสอบฝ่ายบริหารเป็นครั้งแรก เช่น ศาลรัฐธรรมนูญ ศาลปกครอง และสำนักงานผู้ตรวจการแผ่นดินของรัฐสภา |
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อย่างไรก็ตาม หลังจากรัฐประหารในประเทศไทย พ.ศ. 2549 รัฐธรรมนูญ พ.ศ. 2540 ถูกยกเลิก คณะรัฐประหารได้ประกาศกฎอัยการศึกและรัฐธรรมนูญฉบับชั่วคราวขึ้นปกครองประเทศ ซึ่งมีเนื้อหาให้คณะรัฐประหารมีอำนาจแต่งตั้งนายกรัฐมนตรี ฝ่ายนิติบัญญัติและสภาร่างรัฐธรรมนูญ คณะรัฐประหารถูกบีบให้ยินยอมจัดการเลือกตั้งท้องถิ่นและเทศบาลเป็นปกติในปี พ.ศ. 2550 รัฐธรรมนูญแห่งราชอาณาจักรไทย พุทธศักราช 2550 มีการประกาศใช้หลังลงประชามติ และการตรวจสอบการใช้อำนาจรัฐผ่านองคกรอิสระตามรัฐธรรมนูญ แต่ได้ถูกวิพากษ์วิจารณ์ว่ามาจากคณะรัฐประหารปี 2549 ทั้งนี้ คณะกรรมการร่างรัฐธรรมนูญมาจากการสรรหา |
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] | การเมืองไทย
ภายหลังความขัดแย้งทางการเมืองช่วงปี 2556-2557 เกิดรัฐประหารในประเทศไทย พ.ศ. 2557 พร้อมกับการยกเลิกรัฐธรรมนูญ พ.ศ. 2550 ภายใต้การควบคุมอำนาจของคณะรักษาความสงบแห่งชาติ คณะรัฐประหารประกาศกฎอัยการศึกและรัฐธรรมนูญแห่งราชอาณาจักรไทย (ฉบับชั่วคราว) พุทธศักราช 2557 ปัจจุบัน ประเทศไทยใช้ รัฐธรรมนูญแห่งราชอาณาจักรไทย พุทธศักราช 2560 ซึ่งผ่านการออกเสียงประชามติร่างรัฐธรรมนูญแห่งราชอาณาจักรไทย พุทธศักราช 2559 และแก้ไขตามข้อสังเกตพระราชทานจำนวน 3 มาตราโดยพระราชประสงค์ของสมเด็จพระเจ้าอยู่หัวมหาวชิราลงกรณ บดินทรเทพยวรางกูร |
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รัฐบาลไทยมีบทบาทขึ้นอย่างชัดเจนในสมัยรัฐชาติอันสถานปนาขึ้นครั้งสมัยพระบาทสมเด็จพระจุลจอมเกล้าเจ้าอยู่หัวภายหลังทรงผนวกดินแดนและอาณาจักรภายใต้ปกครองของอาณาจักรสยามขึ้นเป็นสยามประเทศ แบ่งอำนาจออกเป็น 3 ส่วน คือ อำนาจนิติบัญญัติ อำนาจบริหาร และอำนาจตุลาการ |
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] | การเมืองไทย
สภานิติบัญญัติแห่งชาติเป็นองค์กรบริหารอำนาจนิติบัญญัติ ประกอบด้วยสมาชิกไม่เกินสองร้อยยี่สิบคนนายกรัฐมนตรีและคณะรัฐมนตรีมีหน้าที่รับผิดชอบการบริหารราชการแผ่นดิน รวมกันไม่เกิน 36 คน ส่วนศาลไทยเป็นองค์กรบริหารอำนาจตุลาการ แบ่งออกเป็น 4 ประเภท ได้แก่ ศาลรัฐธรรมนูญ ศาลยุติธรรม ศาลปกครอง และศาลทหาร |
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นโยบายการต่างประเทศของไทยรวมไปถึงการสนับสนุนอาเซียน เน้นเสถียรภาพในภูมิภาค และให้ความสำคัญกับสัมพันธภาพอันยาวนานกับสหรัฐอเมริกา |
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] | การเมืองไทย
ประเทศไทยเข้าไปมีบทบาทเต็มในองค์กรทั้งระดับภูมิภาคและระดับระหว่างประเทศ โดยได้พัฒนาความสัมพันธ์ใกล้ชิดกับประเทศสมาชิกอาเซียน ซึ่งมีการจัดการประชุมรัฐมนตรีกระทรวงการต่างประเทศและกระทรวงเศรษฐกิจทุกปี ความร่วมมือในภูมิภาคกำลังดำเนินการทั้งในด้านเศรษฐกิจ การค้า การธนาคาร การเมืองและวัฒนธรรม ประเทศไทยยังได้ส่งทหารเข้าร่วมในกองกำลังนานาชาติในติมอร์ตะวันออก, อัฟกานิสถาน, อิรัก, บุรุนดี และปัจจุบัน ในดาร์ฟูร์ ประเทศซูดาน อีกด้วย |
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] | การเมืองไทย
ณ 5 กุมภาพันธ์ พ.ศ. 2556 มีพรรคการเมืองจดทะเบียนในประเทศไทยทั้งหมด 53 พรรคและยังมีสถานะเป็นพรรคการเมือง พรรคการเมืองที่มีชื่อเสียงในประเทศไทย ได้แก่ พรรคเพื่อไทย พรรคประชาธิปัตย์ พรรคภูมิใจไทย เป็นต้น |
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] | การเมืองไทย
ขณะนี้ คณะรักษาความสงบแห่งชาติห้ามมิให้พรรคการเมืองดำเนินการประชุมหรือทำกิจกรรมใด ๆ ทางการเมืองตามกฎอัยการศึก และประกาศที่ 57/2557 นอกจากนั้น กิจกรรมทางการเมืองของประชาชนถือเป็นสิ่งต้องห้าม ช่วงต้นเดือนมิถุนายน 2557 ทางกกต.ทำหนังสือแจ้งพรรคการเมืองให้คืนเงินจากกองทุนเพื่อพัฒนาพรรคการเมือง เนื่องจากไม่มี พ.ร.บ.พรรคการเมือง รัฐธรรมนูญ พ.ศ. 2550 ได้สิ้นสุดไปแล้ว หลังจากหลายพรรคการเมืองออกมาขอให้ยกเลิกโดยให้พรรคการเมืองสามารถประชุมพรรคเพื่อการมีส่วนร่วมกับการร่างรัฐธรรมนูญนั้น ทางพล.อ. เลิศรัตน์ รัตนวาณิช คณะกรรมการธิการยกร่างรัฐธรรมนูญ ในฐานะโฆษกคณะกรรมาธิการ ได้พูดว่า "ทุกพรรคการเมืองจะให้ความร่วมมือ เพราะทุกพรรคคงต้องการเข้ามามีส่วนร่วมในการแสดงความคิดเห็นการยกร่างรัฐธรรมนูญ แต่อาจจะติดในเรื่องของห้วงเวลาที่อาจต้องขอเลื่อนออกไปบ้าง เพื่อการเตรียมความพร้อม ส่วนข้ออ้างของพรรคการเมือง ที่ระบุว่ายังไม่พร้อมให้ความเห็น เพราะไม่สามารถประชุมกรรมการบริหารพรรคได้ เนื่องจากติดคำสั่งห้ามของคณะรักษาความสงบแห่งชาติ (คสช.) นั้น เรื่องนี้พรรคการเมืองสามารถทำหนังสือถึง คสช. เพื่อขอประชุมกรรมการบริหารพรรคตามเงื่อนไขได้" |
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] | การเมืองไทย
ในอดีต ประเทศไทยเคยมีระบบหลายพรรคการเมือง กล่าวคือ มักไม่ค่อยประสบความสำเร็จในการจัดตั้งรัฐบาลพรรคเดียว การจัดตั้งรัฐบาลจึงต้องอาศัยพรรคการเมืองหลายพรรคที่เรียกว่า "รัฐบาลผสม"
ภายหลังรัฐธรรมนูญปี 2540 ได้สร้างระบบการเลือกตั้งใหม่ ซึ่งใช้ระบบเลือกตั้งแบบเขตละคน ส่งผลให้พรรคใหญ่ได้เปรียบในการเลือกตั้ง |
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ในปี พ.ศ. 2545 มีการควบรวมพรรคความหวังใหม่ เข้ากับ พรรคไทยรักไทย โดยที่สมาชิก พรรคความหวังใหม่ ส่วนใหญ่ไปเข้าร่วมกับ พรรคไทยรักไทย(พรรครัฐบาล)ยกเว้นพันโทหญิงฐิฏา รังสิตพล มานิตกุลสมาชิกสภาผู้แทนราษฎร และ รองเลขาการพรรค ที่ย้ายไปพรรคประชาธิปัตย์ (พรรคฝ่ายค้าน) จนถึงปัจจุบันยังคงเป็นสมาชิกสภาผู้แทนราษฎรคนเดียวที่ย้ายจากพรรคฝ่ายรัฐบาลไปพรรคฝ่ายค้าน ระหว่างดำรงตำแหน่งสมาชิกสภาผู้แทนราษฎร |
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] | การเมืองไทย
สังศิต พิริยะรังสรรค์แสดงความเห็นว่า "รัฐธรรมนูญฉบับปี 2540 ก็มีจุดอ่อนบางประการที่เป็นที่รับรู้กันอยู่โดยทั่วไปแล้วคือ รัฐธรรมนูญมีอคติที่ส่งเสริมพรรคการเมืองขนาดใหญ่มากกว่าพรรคการเมืองขนาดเล็ก นอกจากนี้ รัฐธรรมนูญปี 2540 ทำให้ ส.ส. ในสภาฯ ตรวจสอบการใช้อำนาจของนายกรัฐมนตรี และ รมต. ได้ค่อนข้างยาก เมื่อประกอบกับการที่นักการเมืองมีปัญหาเรื่องการคอร์รัปชั่นและการมีผลประโยชน์ทับซ้อนอย่างรุนแรง การเมืองไทยจึงตกอยู่ในภาวะวิกฤติที่ระบบการเมืองไม่สามารถเยียวยา แก้ไขตัวเองได้ด้วยตนเอง จนนำไปสู่การต่อต้านของภาคประชาชน และจบลงด้วยการรัฐประหารของคณะทหาร" |
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] | การเมืองไทย
ระบบสองพรรคในประเทศไทย ตัวอย่างเช่น สมัยที่ทักษิณ ชินวัตรเป็นนายกรัฐมนตรี ซึ่งรัฐบาลครองเสียงข้างมากในสภาจนไม่จำเป็นต้องอาศัยพรรคร่วมรัฐบาล นอกจากนี้ พรรคไทยรักไทย (ต่อมาคือ พรรคพลังประชาชนและพรรคเพื่อไทย) และพรรคประชาธิปัตย์ เป็นสองพรรคการเมืองใหญ่สุด |
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การเลือกตั้งของประเทศไทย เป็นกระบวนการตามรัฐธรรมนูญแห่งราชอาณาจักรไทย เพื่อให้ได้มาซึ่งบุคคลเข้าไปทำหน้าที่ในการปกครองประเทศไทย อาทิ สมาชิกสภาผู้แทนราษฎรไทย, วุฒิสภาไทย, ผู้ว่าราชการกรุงเทพมหานคร, ผู้ว่าเมืองพัทยา และผู้บริหารท้องถิ่นอื่น ๆ ด้วยการให้ประชาชนออกเสียงเลือกบุคคลที่เห็นสมควร |
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] | การเมืองไทย
ประเทศไทยมีการเลือกตั้งสมาชิกสภาผู้แทนราษฎรเป็นการทั่วไปมาแล้ว 25 ครั้ง นับตั้งแต่ปี พ.ศ. 2476 เป็นต้นมา โดยครั้งล่าสุดมีขึ้นเมื่อปี พ.ศ. 2557 |
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สำหรับประเทศไทย การเลือกตั้งเป็นหน้าที่ และตั้งแต่ พ.ศ. 2540 เป็นต้นมา อำนวยการโดย คณะกรรมการการเลือกตั้ง ที่เป็นองค์กรอิสระตามรัฐธรรมนูญฯ |
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ตั้งแต่สมัยสุโขทัยมาจนถึงสมัยรัตนโกสินทร์ตอนต้นนั้น คนไทยรวมตัวกันอยู่ในลักษณะนครรัฐ โดยยกตัวอย่างเช่นในสมัยกรุงศรีอยุธยา ที่ถึงแม้ว่าจะมีกรุงศรีอยุธยาเป็นศูนย์กลางการปกครอง แต่ก็ยังคงมีอำนาจภายในกลุ่มแคว้นต่าง ๆ เช่น สุพรรณบุรี ลพบุรี สุโขทัย เชียงใหม่ และนครศรีธรรมราช ซึ่งหากกลุ่มอำนาจใดที่ครองอำนาจอยู่ในเมืองหลวงเพลี่ยงพล้ำให้แก่กลุ่มอื่น ๆ แล้วก็สามารถถูกชิงอำนาจไปได้เช่นกัน เช่น ราชวงศ์อู่ทองถูกแคว้นสุพรรณบุรีชิงอำนาจไปในสมัยขุนหลวงพะงั่ว |
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อย่างไรก็ตาม อาณาจักรอยุธยาสามารถรวบรวมอำนาจบางกลุ่มผนวกเข้าเป็นส่วนหนึ่งเดียวกับตนได้สำเร็จ โดยสมเด็จพระบรมไตรโลกนาถทรงใช้กุศโลบายต่าง ๆ ทั้งความสัมพันธ์เครือญาติ การปฏิรูปการปกครองไปจนถึงการใช้กำลังทหาร เพื่อผนวกเอาแคว้นสุโขทัยมาเป็นส่วนหนึ่งของอยุธยา สมัยดังกล่าวยังมีการปกครองที่เป็นปึกแผ่นมากขึ้น กระทั่งการล่มสลายอย่างสิ้นเชิงก็ไม่สามารถทำลายความรู้สึกของผู้คนตามไปด้วยได้ จึงนำไปสู่การเกิดใหม่ของกรุงศรีอยุธยาเป็นกรุงธนบุรีและกรุงรัตนโกสินทร์ |
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การปกครองของไทย ในสมัยสุโขทัยเป็นแบบพ่อปกครองลูก ในสมัยอยุธยาเป็นแบบเทวราชา ก่อนจะเปลี่ยนเป็นธรรมราชาจากอิทธิพลของศาสนาพุทธต่อการเมืองการปกครอง ซึ่งใช้มาจนถึงสมัยรัตนโกสินทร์ตอนต้น |
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ท่ามกลางภัยคุกคามลัทธิอาณานิคมของยุโรป พระบาทสมเด็จพระจอมเกล้าเจ้าอยู่หัวทรงเริ่มการปรับปรุงบ้านเมืองโดยการสร้างรัฐชาติ อันเป็นการยกระดับจากชุมทางแห่งอำนาจมาเป็นศูนย์กลางแห่งอำนาจบนดินแดนที่เป็นอันหนึ่งอันเดียวกันแทน ซึ่งได้พัฒนาต่อมาจนถึงรัชกาลพระบาทสมเด็จพระจุลจอมเกล้าเจ้าอยู่หัว โดยมีการเปลี่ยนแปลงสำคัญ คือ การก่อตั้งกระทรวงเพื่อให้การบริหารราชการแผ่นดินเป็นไปอย่างทันสมัย และการดึงอำนาจเข้าสู่ศูนย์กลาง ระหว่างการเปลี่ยนแปลงนี้ ได้มีการยกเลิกเจ้าเมืองท้องถิ่นตามหัวเมืองเพื่อประโยชน์ของการกระชับอำนาจเข้าสู่ศูนย์กลาง นอกจากประโยชน์เพื่อป้องกันการเป็นเมืองขึ้นชาติอื่นแล้ว การเปลี่ยนแปลงครั้งใหญ่ครั้งนี้ได้เปลี่ยนความสัมพันระหว่างขุนนางและพระมหากษัตริย์ไทย โดยทำให้พระมหากษัตริย์ไทยมีอำนาจมากขึ้น ตามความเห็นของนครินทร์ เมฆไตรรัตน์ อดีตคณบดีคณะรัฐศาสตร์ มหาวิทยาลัยธรรมศาสตร์ รูปแบบความสัมพันธ์แบบสมบูรณาญาสิทธิราชย์ได้เกิดขึ้นในช่วงรัชกาลที่ 5 นอกจากแนวคิดแบบตะวันตกเรื่องการรวมศูนย์อำนาจและชาติรัฐแล้ว แนวคิดด้านการเลิกทาสได้เข้ามาในไทยด้วยเช่นกันซึ่งได้ส่งผลให้มีการเลิกทาส ในระยะหลังเริ่มมีความพยายามเปลี่ยนแปลงการปกครองมาสู่ระบอบประชาธิปไตย เนื่องจากเป็นแนวคิดที่เข้ามาจากการติดต่อกับตะวันตกเช่นกัน |
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] | การเมืองไทย
ต่อมาได้มี การปฏิวัติสยาม พ.ศ. 2475 ซึ่งมีการตั้งข้อสังเกตว่าเป็นพฤตการณ์ "ชิงสุกก่อนห่าม" ในขณะที่บางส่วนตั้งข้อสังเกตว่าเกิดขึ้นช้าเกินไป อันเป็นสาเหตุของ "วงจรอุบาทว์" เพราะเกิดช้าเกินกว่าที่ประชาธิปไตยจะพัฒนาไปอย่างมั่นคงในประเทศไทย อีกทั้งการปฏิวัติด้วยมือของคณะทหารทำให้การเมืองเป็นลูกไล่ของทหารและข้าราชการ |
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ภายหลังเหตุการณ์พฤษภาทมิฬ พลังของชนชั้นกลางเริ่มเข้ามามีบทบาทในการเมืองไทยมากขึ้น ซึ่งถึงแม้ว่าเขตชนบทจะให้คะแนนเสียงส่วนใหญ่มาจัดตั้งรัฐบาล แต่เสถียรภาพของรัฐบาลจะมาจากประชาชนในเขตเมือง |
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] | การเมืองไทย
เหตุการณ์ 14 ตุลาคม และ พฤษภาทมิฬ เป็นสองเหตุการณ์ที่ประชาชนชาวไทยมีความเห็นต่อต้านเผด็จการทหารในขณะนั้น อย่างไรก็ตาม การรัฐประหารในประเทศไทย พ.ศ. 2549 และ การรัฐประหารในประเทศไทย พ.ศ. 2557 ประชาชนชาวไทยกลับไม่มีการชุมนุมต่อต้านคณะรัฐประหารอย่างกว้างขวางเหมือน 2 เหตุการณ์ก่อนหน้าสืบเนื่องจากความขัดแย้งทางการเมืองที่รุนแรงระหว่างประชาชนชาวไทยด้วยกัน หนำซ้ำยังมีประชาชนชาวไทยส่วนหนึ่งสนับสนุนการรัฐประหารในขณะนั้น ความเห็นของคนไทยมีทั้งต่อต้านและสนับสนุนเผด็จการทหาร |
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] | การเมืองไทย
ตั้งแต่ปี พ.ศ. 2551 ถึง พ.ศ. 2557 คณะรัฐมนตรีไทย คณะที่ 57 ถึง คณะรัฐมนตรีไทย คณะที่ 60 ไทยมีการประกาศสถานการณ์ฉุกเฉินในทุกคณะรัฐบาล การเมืองไทยอยู่ภายใต้ความขัดแย้งที่รุนแรง จนนำไปสู่การบาดเจ็บและเสียชีวิตจำนวนมาก และใน คณะรัฐมนตรีไทย คณะที่ 61 ได้มีการประกาศกฎอัยการศึกทั่วราชอาณาจักรเป็นระยะเวลายาวนานที่สุดตั้งแต่มีคณะรัฐมนตรีไทย |
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] | พระพุทธเจ้า
พระสัมมาสัมพุทธเจ้า หรือ พระพุทธเจ้า เป็นพระสมัญญานามที่ใช้เรียกพระบรมศาสดาของศาสนาพุทธ พระพุทธศาสนาทั้งฝ่ายเถรวาทและมหายานต่างนับถือพระพุทธเจ้าว่าเป็นศาสดาของตนเหมือนกันแต่รายละเอียดปลีกย่อยต่างกัน ฝ่ายเถรวาทให้ความสำคัญกับพระพุทธเจ้าพระองค์ปัจจุบันคือ "พระโคตมพุทธเจ้า" ซึ่งเชื่อว่าเป็นพระองค์ที่ 4 ในภัทรกัปนี้ และมีกล่าวถึงพระพุทธเจ้าในอดีตกับในอนาคตบ้างแต่ไม่ให้ความสำคัญเท่า ฝ่ายมหายานนับถือพระพุทธเจ้าของฝ่ายเถรวาททั้งหมดและเชื่อว่านอกจากพระพุทธเจ้า 28 พระองค์ ที่ระบุในพุทธวงศ์ของพระไตรปิฎกภาษาบาลีแล้ว ยังมีพระพุทธเจ้าอีกมากมายเพิ่มเติมขึ้นมาจากตำนานของเถรวาท |
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ผู้ปรารถนาจะเป็นพระพุทธเจ้าต้องบำเพ็ญบารมีเป็นพระโพธิสัตว์ก่อน เมื่อบารมีเต็มแล้วจึงจะได้ตรัสรู้เป็นพระพุทธเจ้าในชาติสุดท้าย พระพุทธเจ้าทุกพระองค์มีลักษณะพิเศษตรงกันคือ เป็นมนุษย์เพศชายเกิดในวรรณะกษัตริย์หรือพราหมณ์ พระวรกายสมบูรณ์ด้วยมหาปุริสลักขณะ ก่อนออกผนวชจะอภิเษกสมรสมีพระโอรสพระองค์หนึ่ง หลังจากนั้นทรงพบเทวทูตทำให้ตัดสินใจออกผนวช วันออกผนวชจะตรงกับวันเพ็ญเดือนอาสาฬหะ |
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] | พระพุทธเจ้า
ตามคัมภีร์ฝ่ายพุทธ ถือกันว่าพระโคตมพุทธเจ้าดำรงพระชนม์ชีพอยู่ระหว่าง 80 ปีก่อนพุทธศักราช จนถึงเริ่มพุทธศักราชซึ่งเป็นวันปรินิพพาน ตรงกับ 543 ปีก่อนคริสตกาลตามตำราไทยอ้างอิงปฏิทินสุริยคติไทยและปฏิทินจันทรคติไทย และ 483 ปีก่อนคริสตกาลตามปฏิทินสากล |
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] | พระพุทธเจ้า
ในพระพุทธศาสนา พุทธะ ( แปลว่า "ผู้รู้ ผู้ตื่น ผู้เบิกบาน") หมายถึงบุคคลผู้ตรัสรู้อริยสัจ 4 แล้วอย่างถ่องแท้ |
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ธชัคคสูตร กล่าวว่าพระพุทธเจ้ามีคุณลักษณะ 9 ประการ เรียกว่า พุทธคุณ 9 ได้แก่ |
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] | พระพุทธเจ้า
ในพระไตรปิฎกภาษาบาลีกล่าวว่า ในภัทรกัปนี้มีพระพุทธเจ้าอุบัติขึ้นแล้ว 4 พระองค์ พระพุทธเจ้าพระองค์ปัจจุบันเป็นองค์ที่ 4 และพระพุทธเจ้าพระองค์ถัดไปคือพระศรีอริยเมตไตรย ในทัศนะเถรวาทถือว่าพระพุทธเจ้าเป็นมนุษย์ธรรมดา แต่ที่เหนือกว่าคนทั่วไปคือพระองค์พบทางดับทุกข์ได้ด้วยพระองค์เอง และเผยแผ่หนทางนั้นต่อสรรพสัตว์ ทรงเป็นบุคคลในประวัติศาสตร์ เมื่อทรงดับขันธปรินิพพาน คือดับไปโดยไม่เหลือเชื้อใด ๆ ผู้จะเป็นพระพุทธเจ้าต้องทำความดี (บารมี) มาในชาติก่อน ๆ นับชาติไม่ถ้วน (ก่อนที่จะเป็นพระพุทธเจ้าเรียกว่าพระโพธิสัตว์) |
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พระโพธิสัตว์ผู้ที่จะจุติจากสวรรค์ชั้นดุสิตลงมาตรัสรู้เป็นพระพุทธเจ้านั้น ก่อนจะจุติจะทรงพิจารณา 5 อย่าง เรียกว่า มหาวิโลกนะ 5 คืออายุขัยของมนุษย์ขึ้นอยู่กับกระแสสังขารและการทำความดี หากทำดีมากขึ้นอายุก็จะเพิ่มขึ้น หากทำดีน้อยอายุขัยก็จะลดลง อายุขัยของมนุษย์อยู่ระหว่าง 10 ปีถึง 1 อสงไขยปี (1 × 10 ปี) แต่พระโพธิสัตว์ทรงเลือกอายุขัยมนุษย์ระหว่าง 100-100,000 ปี ถ้าหากน้อยกว่า 100 ปีมนุษย์จะมีจิตใจหยาบช้าเกินกว่าจะฟังธรรมให้แตกจนบรรลุพระนิพพานได้ ถ้าเกิน 100,000 ปีมนุษย์จะเริ่มประมาทความแก่ ความเจ็บ ความตายเพราะอายุยืนความตายมาถึงช้า จะไม่เห็นอริยสัจ 4 หรือธรรมใดๆพระโพธิสัตว์เลือกชมพูทวีปเป็นทวีปที่จะจุติทุกครั้ง เพราะมนุษย์ในชมพูทวีปมีทั้งความสุขและความทุกข์ มีความเห็นทุกข์ เห็นสุข ได้ดีกว่ามนุษย์ในทวีปอื่นๆ |
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สาเหตุอีกอย่างที่เลือกลงมามนุษยภูมิเพราะมนุษย์เห็นสุขทุกข์ได้ง่ายที่สุด สัตว์ในอบายภูมิ 4 มีแต่ความทุกข์ไม่เห็นสุขกระจ่าง เทวดาพรหมก็เห็นสุขมากกว่าทุกข์จนยากที่จะทำให้เป็นพระอรหันต์ได้ อีกทั้งมนุษย์ทำบุญได้ จึงทรงเลือกมนุษย์พระโพธิสัตว์จะทรงเลือกประเทศที่มีความเจริญรุ่งเรือง เศรษฐกิจดี มีประชากรหนาแน่น มีนักปราชญ์ เจ้าสำนัก เป็นที่รวมของการศึกษาและศิลปวิทยามากมาย มีผู้มีคุณธรรมมากมาย จะสามารถเผยแพร่ธรรมให้รุ่งเรือง มีคนรู้มากได้ พระโพธิสัตว์ทรงเลือกได้ระหว่าง วรรณะกษัตริย์ กับ วรรณะพราหมณ์ ว่าในช่วงเวลานั้นตระกูลใดเจริญมากกว่ากัน ได้รับการยอมรับมากกว่ากัน ใน 4 อสงไขยแสนมหากัปล่าสุดนี้มีพระพุทธเจ้าจากตระกูลกษัตริย์มากกว่า แต่ในภัทรกัปนี้มีพระพุทธเจ้าจากตระกูลพราหมณ์มากกว่า (พระกกุสันธะ พระโกนาคมณ์ พระกัสสปะ และพระเมตไตรยะ) มีเพียงพระโคตมพุทธเจ้าเพียงพระองค์เดียวที่มาจากตระกูลกษัตริย์ |
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] | พระพุทธเจ้า
พระโพธิสัตว์ผู้ได้มาจุติเป็นพระพุทธเจ้าองค์ปัจจุบันนี้ ทรงเลือกตระกูลศากยโคตมวงศ์แห่งกรุงกบิลพัสดุ์นคร เพราะได้รับความนับถือมาก และบริสุทธิ์มา 7 รุ่นแล้ว ถ้าไม่บริสุทธิ์แล้วลงมาจุติแล้วเป็นพระพุทธเจ้าก็ยากที่จะได้รับการนับถือ สาเหตุที่เลือกตระกูลกษัตริย์เพราะในช่วงเวลานั้นมีการแบ่งชนชั้นวรรณะกัน และวรรณะกษัตริย์เป็นวรรณะที่มีคนนับถือมากที่สุด จึงทรงเลือกวรรณะกษัตริย์พระโพธิสัตว์จะทรงเลือกผู้หญิงจากตระกูลกษัตริย์หรือพราหมณ์ที่รักษาศีล รักษาธรรมได้ดีที่สุด บริสุทธิ์ทางกาย วาจา ใจ ไม่ดื่มสุรา ไม่หลงในอบายมุข ไม่โลเลในบุรุษ และทรงกำหนดอายุของพระมารดาว่ามีประมาณเท่าใด เพราะพระครรภ์ที่ประทับแห่งพระโพธิสัตว์ผู้จะได้เสด็จอุบัติตรัสรู้เป็นพระสัมมาสัมพุทธเจ้านั้น เปรียบประดุจพระคันธกุฎีแห่งพระบรมศาสดา ไม่สมควรแก่ผู้อื่น |
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] | พระพุทธเจ้า
พระบรมโพธิสัตว์ทรงเลือกพระมารดาที่บริสุทธิ์ไม่แปดเปื้อนมลทินโทษ มิฉะนั้นจะยากแก่การเผยแผ่ศาสนา เพราะจะถูกโจมตีว่ามารดาของพระศาสดาไม่บริสุทธิ์ พระนางสิริมหามายาได้อธิษฐานเป็นพระพุทธมารดามาแต่อดีตกาล เมื่อประสูติพระบรมโพธิสัตว์เจ้าได้ 7 วันก็เสด็จทิวงคต ไปบังเกิดเป็นเทพบุตรสถิตในดุสิตเทวโลก ตามประเพณี พระพุทธมารดาไม่ได้เป็นหญิงอย่างเก่า ที่เกิดเป็นหญิงเพราะอธิษฐานขอเป็นมารดาพระพุทธเจ้า |
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] | พระพุทธเจ้า
ในพระไตรปิฎกภาษาบาลีกล่าวถึงพระพุทธเจ้าไว้ 2 ประเภท คือ |
673#12 | [
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ต่อมาในคัมภีร์มโนรถปูรณี อรรถกถาของอังคุตตรนิกาย พระพุทธโฆสะได้กล่าวถึงพุทธะทั้งหมด 4 ประเภท อีกประเภท 2 ประเภทที่เพิ่มเข้ามา คือ |
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นอกจากนั้นพระพุทธเจ้ามีอยู่ 3 ประเภทตามกำลังบุญบารมีที่ได้สร้างสั่งสมมาคือ |
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] | พระพุทธเจ้า
ในคัมภีร์อนาคตวงศ์นั้น ได้กล่าวถึงพระพุทธเจ้าในอนาคต 10 พระองค์ที่จะบังเกิดขึ้นในอนาคตอันใกล้ ดังนี้ |
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] | พระพุทธเจ้า
นิกายมหายานยอมรับพระพุทธเจ้าตามคัมภีร์ฝ่ายเถรวาททั้งหมดและยังสร้างพระพุทธเจ้าอีกมากมาย ทั้งที่เป็นมนุษย์และมีสถานะเหมือนเทพเจ้าในศาสนาฮินดู นิกายมหายานเชื่อว่าเมื่อพระพุทธเจ้าปรินิพพานไปแล้วไม่ดับสูญแต่ไปประทับ ณ พุทธเกษตรซึ่งเป็นดินแดนที่งดงามกว่าสวรรค์ พระพุทธเจ้าตามคติมหายานแบ่งได้เป็น 3 ประเภท คือ |
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ในคัมภีร์ของทางมหายานนั้นได้ระบุนามของพระพุทธเจ้าไว้เป็นจำนวนมาก มีทั้งพระพุทธเจ้า 35 พระองค์ พระพุทธเจ้า 53 พระองค์ และที่มากที่สุดคือพระพุทธเจ้า 3,000 พระองค์ โดยแบ่งเป็น |
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] | ทฤษฎีกราฟ
ทฤษฎีกราฟ () เป็นหนึ่งในสาขาคณิตศาสตร์และวิทยาการคอมพิวเตอร์ ที่ศึกษาถึงคุณสมบัติต่าง ๆ ของกราฟ |
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] | ทฤษฎีกราฟ
ทฤษฎีกราฟนั้น มีจุดเริ่มจากผลงานตีพิมพ์ของ เลออนฮาร์ด ออยเลอร์ ภายใต้ชื่อ "Solutio problematis ad geometriam situs pertinentis" ในปี ค.ศ. 1736 (พ.ศ. 2279) หรือที่รู้จักกันในนาม "ปัญหาสะพานทั้งเจ็ดแห่งเมืองโคนิกส์เบิร์ก" (Seven Bridges of Königsberg) เขาสนใจวิธีที่จะข้ามสะพานทั้ง 7 แห่งนี้ โดยข้ามแต่ละสะพานเพียงครั้งเดียวเท่านั้น ผลงานนี้ยังถือว่าเป็นงานแนวทอพอโลยีชิ้นแรกในเรขาคณิต กล่าวคือเป็นงานที่สนใจเฉพาะโครงสร้างของรูปเรขาคณิตที่ไม่ขึ้นกับขนาด ระยะ หรือการวัดใดๆ งานชิ้นสำคัญนี้ยังได้แสดงความเกี่ยวข้องอย่างลึกซึ้งระหว่างทฤษฎีกราฟและทอพอโลยี |
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ในปี ค.ศ. 1845 (พ.ศ. 2388) กุสตาฟ คีร์คฮอฟฟ์ ได้เผยแพร่ผลงานที่รู้จักกันภายใต้ชื่อกฎวงจรไฟฟ้าของคีร์คฮอฟฟ์ ที่แสดงความสัมพันธ์ของกระแสและความต่างศักย์ บนกราฟที่แทนวงจรไฟฟ้า |
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] | ทฤษฎีกราฟ
ต่อมาในปี ค.ศ. 1852 (พ.ศ. 2395) ฟรานซิส กัทธรี ได้ตั้ง"ปัญหาสี่สี" (Four color problem) เพื่อศึกษาถึงความเป็นไปได้ที่จะใช้สีเพียง 4 สี เพื่อระบายให้กับประเทศต่าง ๆ บนแผนที่ใด ๆ โดยที่ประเทศเพื่อนบ้านจะไม่มีสีเดียวกัน. ปัญหานี้ได้ถูกแก้ในอีกมากกว่า 100 ปีถัดมา ในปี ค.ศ. 1976 (พ.ศ. 2519) โดย เคนเนธ แอปเพล และวูล์ฟกัง ฮาเคน ซึ่งใช้คอมพิวเตอร์เข้าช่วยในการพิสูจน์ ซึ่งทำให้ได้รับการวิพากษ์วิจารณ์อย่างกว้างขวาง. อย่างไรก็ตามจากความพยายามในการแก้ปัญหา 4 สีนี้ ทำให้มีการสร้างแนวคิดและนิยามพื้นฐานในทฤษฎีกราฟขึ้นอย่างมากมาย จนอาจจะกล่าวได้ว่าจุดเริ่มต้นของทฤษฎีกราฟเกิดจากปัญหาสี่สีนี้เอง |
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กราฟมักถูกนำเสนอในลักษณะของรูปภาพ โดยใช้จุดแทนจุดยอดแต่ละจุด และลากเส้นระหว่างจุดยอดถ้าจุดยอดทั้งสองนั้นมีเส้นเชื่อมถึงกัน ถ้ากราฟมีทิศทาง ทิศทางของเส้นเชื่อมจะถูกระบุโดยใช้ลูกศร |
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เราไม่ควรจะสับสนระหว่างกราฟที่วาดออกมากับกราฟ (ที่เป็นโครงสร้างนามธรรม) เนื่องจากกราฟหนึ่ง ๆ สามารถเขียนออกมาได้หลายแบบ และสาระหลักของกราฟนั้นมีแค่ว่าจุดยอดใด เชื่อมต่อกับจุดยอดใด ด้วยเส้นเชื่อมกี่เส้น ไม่ใช่วิธีการที่วาดมันออกมา ในทางปฏิบัติแล้ว การจะตัดสินว่ากราฟที่วาดออกมาสองกราฟนั้น มาจากกราฟเดียวกัน ในบางกรณี การวาดกราฟบางแบบอาจมีความเหมาะสมและทำให้เข้าใจได้ง่ายกว่าแบบอื่น |
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มีหลายวิธีในการจัดเก็บกราฟในระบบคอมพิวเตอร์ โดยโครงสร้างข้อมูลที่ใช้ขึ้นอยู่กับโครงสร้างของกราฟ และขั้นตอนวิธีสำหรับประมวลผลกราฟนั้น ในทางทฤษฎีเราอาจแยกแยะโครงสร้างที่เป็นแบบรายการกับที่เป็นเมทริกซ์ได้ แต่ในทางปฏิบัติมักพบว่าโครงสร้างที่ดีมักเป็นลูกผสมของโครงสร้างทั้งสองแบบ โครงสร้างแบบรายการนั้นมักใช้ในกรณีของกราฟเบาบาง (sparse graph) เนื่องจากมีการใช้หน่วยความจำที่น้อยกว่า ในทางกลับกันโครงสร้างแบบเมทริกซ์นั้น มีการเข้าถึงที่รวดเร็วกว่า แต่ก็ใช้หน่วยความจำขนาดใหญ่ถ้าจำนวนจุดยอดของกราฟมีมาก |
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] | การรู้จำแบบ
การรู้จำแบบ (pattern recognition) เป็นสาขาย่อยหนึ่งของ วิทยาการคอมพิวเตอร์ เป็นศาสตร์ที่มีจุดประสงค์ในเพื่อการจำแนก วัตถุ (objects) ออกเป็นประเภท (classes) ตาม รูปแบบของวัตถุ โดยในการคำนวณจะมีการใช้เทคนิคจากสาขาอื่น ๆ มากมาย เช่น การประมวลผลสัญญาณ ปัญญาประดิษฐ์ และสถิติ |
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] | การรู้จำแบบ
รูปแบบ (pattern) ในที่นี้หมายถึง รูปร่าง หรือ คุณลักษณะ ของวัตถุ ที่เราสนใจ โดยวัตถุนั้นอาจเป็น รูปธรรม หรือ นามธรรม ก็ได้ หรือจะเป็นรูปแบบ ที่กระจายบนพื้นที่ หรือ เปลี่ยนแปลงตามเวลา ก็ได้คำ การแบ่งประเภท (classification) และ การแบ่งกลุ่ม (clustering) นี้ในทางวิทยาการคอมพิวเตอร์ จะใช้ในความหมายที่เฉพาะเจาะจง โดย การแบ่งประเภท คือ การแยกแบบมีผู้สอน และ การแบ่งกลุ่ม คือ การแยกแบบไม่มีผู้สอน |
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] | ทฤษฎีสารสนเทศ
ทฤษฎีสารสนเทศ () เป็นสาขาหนึ่งใน ทฤษฎีความน่าจะเป็น และคณิตศาสตร์เชิงสถิติ ขอบข่ายเนื้อหาของทฤษฎีนี้จะเกี่ยวข้องกับสารสนเทศ, เอนโทรปีของสารสนเทศ, ระบบการสื่อสาร, การส่งข้อมูล, ทฤษฎีอัตราการบิดเบือน, วิทยาการเข้ารหัสลับ, สัดส่วนสัญญาณต่อสัญญาณรบกวน, การบีบอัดข้อมูล, การแก้ความผิดพลาด และหัวข้ออื่น ๆ ที่เกี่ยวข้อง |
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] | ทฤษฎีสารสนเทศ
คำแปลที่ตามราชบัณฑิต คือ "ทฤษฎีสารสนเทศ" นี้ มาจากคำว่า "information theory" ซึ่งคำว่า information เป็นคำเดียวกันกับที่หมายถึง สารสนเทศ แต่เนื่องจากความหมายของ information theory นั้นจะเกี่ยวเนื่องกับ เนื้อความในแง่ของสัญญาณ จึงอาจจะใช้คำว่า ทฤษฎีข้อมูล แทนความหมายของสารสนเทศ ที่เป็นในแง่ของเนื้อหาข่าวสาร และ สื่อตัวกลาง หรือสื่อบันทึกในบางกรณี |
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คลาวด์ อี. แชนนอน ได้รับการขนานนามว่าเป็น "บิดาแห่งทฤษฎีสารสนเทศ" ทฤษฎีของแชนนอนนี้ เป็นทฤษฎีแรกที่ได้ทำการวินิจฉัยปัญหาทางการสื่อสาร ในรูปของปัญหาคณิตศาสตร์เชิงสถิติ เป็นทฤษฎีที่ได้เปิดหนทาง ให้วิศวกรการสื่อสาร สามารถคำนวณขนาด หรือปริมาณสูงสุดของช่องสัญญาณ ออกมาในหน่วยบิต (bits) |
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] | ทฤษฎีสารสนเทศ
ทฤษฎีสารสนเทศที่เรารู้จักอยู่ในทุกวันนี้ เป็นที่ยอมรับโดยทั่วไปว่า เริ่มต้นจากผลงานตีพิมพ์ของแชนนอนเรื่องทฤษฎีเชิงคณิตศาสตร์ของการสื่อสาร ("The Mathematical Theory of Communication") ลงในวารสารทางเทคนิคเบลล์ซิสเต็ม (Bell System Technical Journal) ฉบับเดือนมิถุนายน ในปี พ.ศ. 2491 (ค.ศ. 1948) ซึ่งงานชิ้นนี้นั้น เป็นงานที่ได้สร้างเสริมต่อมาจาก ผลงานของ แฮร์รี นายควิสท์ () และ ราล์ฟ ฮาร์ทลีย์ () |
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ในงานของแชนนอน ที่ทำให้วิศวกรระบบสื่อสาร สามารถออกแบบระบบสื่อสารที่มีประสิทธิภาพสูงขึ้นได้นั้น แชนนอนได้นิยามเอนโทรปีของสารสนเทศเท่ากับ |
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] | ทฤษฎีสารสนเทศ
สูตรนี้เมื่อนำไปใช้กับ แหล่งกำเนิดสารสนเทศ จะทำให้สามารถคำนวณขนาดของช่องสัญญาณ ที่จำเป็นต้องใช้ในการส่งข้อมูลนั้น ในรูปของรหัสฐานสองได้ โดยถ้าลอการิทึมในสมการข้างต้น เป็นฐานสอง เอนโทรปีที่วัดจะอยู่ในหน่วยบิตเช่นกัน แต่ถ้าเป็น ลอการิทึมฐานธรรมชาติ หรือ ฐาน formula_2 เอนโทรปีที่วัดจะอยู่ในหน่วย แนท (nats) [1] การวัดเอนโทรปีของแชนนอน เป็นการวัดขนาดของสารสนเทศซึ่งอยู่ในข้อความ |
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] | ทฤษฎีสารสนเทศ
เมื่อไม่นานมานี้ ได้ปรากฏหลักฐานว่า เอนโทรปี นั้นได้ถูกค้นพบและนิยามในช่วงสงครามโลกครั้งที่สอง โดยแอลัน ทัวริง ที่ เบล็ทชลีย์ พาร์ค () ทัวริง ได้ตั้งชื่อปริมาณนี้ว่าน้ำหนักของหลักฐาน (weight of evidence) และใช้หน่วยวัดเป็น bans และ decibans (อย่าสับสนคำ "weight of evidence" นี้กับคำเดียวกันที่ใช้ในบทความทางด้านการอนุมานทางสถิติ หรือ บัญญัติขึ้นโดย กู๊ด () ซึ่งมีความหมายตรงกับคำที่ทัวริงใช้คือ "log-odds" หรือ "lods") ถึงแม้ว่า ทัวริง และ แชนนอน นั้นได้ทำงานร่วมกันในช่วงสงครามแต่ดูเหมือนว่าทั้งคู่นั้นต่างคนต่างพัฒนาแนวความคิดนี้ขึ้นมาด้วยตนเอง (สำหรับเอกสารอ้างอิงดู Alan Turing: The Enigma โดย แอนดรูว์ ฮอดจส์ Andrew Hodges) |
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เอนโทรปีของสารสนเทศ ที่พัฒนาต่อมาจากแนวความคิดดั้งเดิมของ แชนนอน นั้นมีความสัมพันธ์อย่างใกล้ชิดกับ เอนโทรปี ของ อุณหพลศาสตร์ |
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ลุดวิก โบลทซ์แมน ( และ วิลลาร์ด กิบส์ () นั้นมีส่วนสำคัญในการพัฒนาทางด้าน อุณหพลศาสตร์เชิงสถิติ () งานของเขานั้นเกิดจากความพยายามในการที่จะนำคำ "เอนโทรปี" จาก ทฤษฎีสารสนเทศมาใช้ เอนโทรปี จากแนวความคิดของ ทฤษฎีสารสนเทศ และ แนวความคิดของ อุณหพลศาสตร์เชิงสถิติ นี้มีความสัมพันธ์กันที่ลึกซึ้ง ตัวอย่างหนึ่งที่ใช้แสดงความสัมพันธ์ระหว่าง สารสนเทศ และ เอนโทรปีของอุณหพลศาสตร์ คือ ปีศาจของแมกซ์เวลล์ () ซึ่งเป็นปิศาจเฝ้าตูดควบคุมการเลือกผ่านของโมเลกุล เพื่อสร้างการไหลของพลังงานสวนทางกับเอนโทรปีของอุณหพลศาสตร์ ในการแหกกฎข้อที่สองของอุณหพลศาสตร์ แต่ในขณะเดียวกัน ในการคุมตูดนั้นปีศาจก็ต้องการข้อมูล ที่แม่นยำ ซึ่งทั้งสองนี้หักล้างกันไปทำให้ปิศาจไม่สามารถสร้างความได้เปรียบทางอุณหพลศาสตร์สวนกฎข้อที่สองได้ |
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] | ทฤษฎีสารสนเทศ
ปริมาณที่ใช้วัดข้อมูลที่มีประโยชน์ อีกปริมาณหนึ่งก็คือ สารสนเทศร่วม () ซึ่งเป็นปริมาณที่บ่งบอกถึงความขึ้นแก่กันทางสถิติของตัวแปรสุ่มสองตัว นิยามของสารสนเทศที่เกิดร่วมกันของเหตุการณ์ formula_3 และ formula_4 คือ |
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โดยที่ formula_6 คือ เอนโทรปีร่วม นิยามโดย |
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] | ทฤษฎีสารสนเทศ
และ formula_8 คือ เอนโทรปีตามเงื่อนไข () ของ formula_3 มีเงื่อนไขขึ้นกับค่าสังเกตการณ์ของ formula_4 ดังนั้น สารสนเทศร่วม สามารถตีความ หมายถึง ปริมาณของความไม่แน่นอนของค่า formula_3 ที่ลดลงเมื่อรู้ค่าที่แน่นอนของ formula_4 และในทางกลับกัน |
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] | ดนตรี
ดนตรี () คือ เสียงและโครงสร้างที่จัดเรียงอย่างเป็นระเบียบแบบแผน ซึ่งมนุษย์ใช้ประกอบกิจกรรมศิลปะที่เกี่ยวข้องกับเสียง โดยดนตรีนั้นแสดงออกมาในด้านระดับเสียง (ซึ่งรวมถึงท่วงทำนองและเสียงประสาน) จังหวะ และคุณภาพเสียง (ความต่อเนื่องของเสียง พื้นผิวของเสียง ความดังค่อย) นอกจากดนตรีจะใช้ในด้านศิลปะได้แล้ว ยังสามารถใช้ในด้านสุนทรียศาสตร์ การสื่อสาร ความบันเทิง รวมถึงใช้ในงานพิธีการต่าง ๆ ได้ |
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] | ดนตรี
คำว่า "ดนตรี" มีรากศัพท์มาจากภาษาสันสกฤต คือ तन्त्री (ตนฺตฺรี) ซึ่งแปลว่า ดนตรี ในภาษาอื่นที่มีรากศัพท์เดียวกัน ได้แก่ ภาษาเขมร คือ តន្ត្រី (ดนฺตฺรี) และ ภาษาลาว คือ ດົນຕີ (ดนตี) |
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] | การประมวลผลสัญญาณดิจิทัล
การประมวลผลสัญญาณดิจิทัล หรือ ที่เรียกกันติดปากสั้น ๆ ว่า ดีเอสพี (DSP - digital signal processing) เป็นการศึกษาการประมวลผลสัญญาณที่อยู่ในรูปดิจิทัล (digital) |
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] | การประมวลผลสัญญาณดิจิทัล
ดีเอสพีนี้อาจแบ่งออกได้เป็นในส่วนของซอฟต์แวร์และฮาร์ดแวร์ หรือตามการประยุกต์เป็น การประมวลผลสัญญาณเสียง (audio signal processing) การประมวลผลภาพดิจิทัล (digital image processing) และ การประมวลผลคำพูด (speech processing) |
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] | การประมวลผลสัญญาณดิจิทัล
ถึงแม้ว่าในดีเอสพีนั้น สัญญาณที่เราพิจารณากันจะเป็นดิจิทัล แต่โดยทั่วไปสัญญาณเหล่านี้จากแหล่งกำเนิด จะอยู่ในรูปเดิมที่เป็นแอนะล็อก การได้มาซึ่งสัญญาณดิจิทัลซึ่งเป็นตัวแทนสัญญาณแอนะล็อกที่เราสนใจนี้ จะต้องผ่านกระบวนการแปลงสัญญาณแอนะล็อกเป็นดิจิทัล (Analog-to-Digital Conversion - ADC) หรือการดิจิไทซ์ (digitization) ซึ่งประกอบด้วยการสุ่มตัวอย่าง (sampling) (อย่าสับสนกับคำว่า สุ่ม ที่มาจาก random หรือ stochastic) และการควอนไทซ์ (quantization) ให้อยู่ในรูปดิจิทัลก่อนที่จะทำการประมวลผลต่อไป |
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รูปข้างต้นแสดงกระบวนการชักตัวอย่างสัญญาณและควอนไทซ์ |
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ตัวอย่างสัญญาณในรูปของตัวแปรเวลา หรือ temporal signal : เสียง |
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ตัวอย่างสัญญาณในรูปตัวแปรของสถานที่ หรือ spatial signal : รูปภาพ |
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ภาพนี้เป็นภาพหนึ่งที่ถือได้ว่าเป็นภาพมาตรฐานที่เป็นที่รู้จักและใช้กันอย่างกว้างขวางในวงการการประมวลผลภาพ
จึงมีเรื่องราวที่น่าสนใจเบื้องหลังภาพนี้ ดู ภาพลีนา หรือ ภาพเลนา |
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ในคณิตศาสตร์และวิทยาการคอมพิวเตอร์ กราฟ () ประกอบไปด้วยเซตของวัตถุที่เรียกว่าจุดยอด (vertex) ซึ่งเชื่อมต่อกันด้วยเส้นเชื่อม (edge) โดยทั่วไปแล้วเรามักวาดรูปแสดงกราฟโดยใช้จุด (แทนจุดยอด) เชื่อมกันด้วยเส้น (แทนเส้นเชื่อม) กราฟเป็นวัตถุพื้นฐานของการศึกษาในวิยุตคณิต หัวข้อทฤษฎีกราฟ |
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] | กราฟ (คณิตศาสตร์)
เส้นเชื่อมอาจมีทิศทางหรือไม่ก็ได้ ตัวอย่างเช่น สมมุติให้จุดยอดแทนคนและเส้นเชื่อมแทนการจับมือกัน เส้นเชื่อมก็จะเป็นเส้นเชื่อมไม่มีทิศ เพราะการที่ "A" จับมือ "B" ก็แปลว่า "B" จับมือ "A" อย่างไรก็ตาม สมมุติถ้าจุดยอดแทนคนและเส้นเชื่อมแทนการรู้จัก เส้นเชื่อมก็ต้องเป็นเส้นเชื่อมมีทิศทาง เพราะ "A" รู้จัก "B" ไม่จำเป็นว่า "B" ต้องรู้จัก "A" หรือนั่นก็คือความสัมพันธ์การรู้จักไม่เป็นความสัมพันธ์สมมาตร |
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] | กราฟ (คณิตศาสตร์)
จุดยอดอาจจะถูกเรียกว่า"โหนด" "ปม" หรือ"จุด" ในขณะที่เส้นเชื่อมอาจถูกเรียกว่า"เส้น" คำว่า "กราฟ" ถูกใช้ครั้งแรกโดย J.J. Sylvester ในปี พ.ศ. 2421 |
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] | กราฟ (คณิตศาสตร์)
โดยทั่วไป กราฟ "G" คือคู่อันดับ "G" = ("V", "E") โดยที่ "V" คือเซตของจุดยอด และ "E" คือเซตของเส้นเชื่อมซึ่งเป็นคู่ไม่อันดับของจุดยอด อันที่จริงนิยามที่กล่าวไปเป็นเพียงประเภทหนึ่งของกราฟที่เรียกว่า กราฟไม่ระบุทิศทาง และเป็น กราฟอย่างง่าย |
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] | กราฟ (คณิตศาสตร์)
กราฟประเภทอื่นๆจะมีรายละเอียดของเซตเส้นเชื่อม ("E") ที่แตกต่างกัน เช่น สังเกตว่านิยามข้างต้นจะไม่สามารถมีเส้นเชื่อมในกราฟสองเส้นที่เชื่อมจุดยอดสองจุดในลักษณะเดียวกันได้ เนื่องจาก "E" เป็นเซต ซึ่งสมาชิกที่เหมือนกันจะถูกมองเป็นเพียงแค่หนึ่งตัว หากเปลี่ยน "E" ให้กลายเป็นมัลติเซตก็จะได้สิ่งที่เรียกว่ามัลติกราฟหรือกราฟเทียมแทนกราฟปกติ ซึ่งรองรับเส้นเชื่อมหลายๆเส้นที่เชื่อมระหว่างจุดยอดสองจุดที่เหมือนกัน หรือที่เรียกว่า เส้นเชื่อมขนาน (เส้นเชื่อมสีแดงตามภาพด้านขวา) |
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] | กราฟ (คณิตศาสตร์)
สำหรับประเภทของกราฟต่างๆที่สมบูรณ์มากกว่านี้ โปรดดูข้างล่าง |
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] | กราฟ (คณิตศาสตร์)
จุดยอดที่อยู่ที่ปลายของเส้นเชื่อมจะเรียกว่าจุดยอดปลายของเส้นเชื่อม แต่จุดยอดอาจจะไม่เป็นจุดยอดปลายก็ได้ (ในกรณีที่จุดยอดนั้นไม่มีเส้นเชื่อมมาต่อเลย) |
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] | กราฟ (คณิตศาสตร์)
"V" และ "E" โดยปกติจะเป็นเซตจำกัด ถึงแม้ว่าจะเป็นไปได้ที่ "V" หรือ "E" จะเป็นเซตอนันต์ แต่นิยามหลายๆอย่างจะใช้ไม่ได้ในกรณีนั้น อันดับของกราฟคือ |"V"| (จำนวนจุดยอด) ส่วนขนาดของกราฟคือ |"E"| (จำนวนเส้นเชื่อม) ระดับขั้นของจุดยอดคือจำนวนของเส้นเชื่อมที่ต่อกับจุดยอดนั้นๆ ในกรณีที่มีเส้นเชื่อมที่ปลายสองด้านต่อเข้ากับจุดยอดเดียวกัน หรือที่เรียกว่าวงวน (เส้นเชื่อมสีน้ำเงินตามภาพด้านขวา) ให้นับระดับขั้นเพิ่ม 2 สำหรับ 1 วงวน |
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เส้นเชื่อม {"u" , "v"} อาจเขียนให้สั้นว่า "uv" ก็ได้.. |
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] | กราฟ (คณิตศาสตร์)
ตามที่ได้กล่าวมาแล้วว่ากราฟมีหลายประเภท อย่างไรก็ตามกราฟในความหมายโดยทั่วไปจะหมายถึงกราฟไม่ระบุทิศทางอย่างง่ายและจำกัด |
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กราฟไม่ระบุทิศทาง (undirected graph) "G" คือคู่อันดับ "G" = ("V", "E") ที่ "E" คือ เซตของเส้นเชื่อมซึ่งเป็นคู่ไม่อันดับของจุดยอด "e" = {"x", "y"} จะถูกพิจารณาว่าเป็นเส้นเชื่อม เชื่อมระหว่าง "x" กับ "y" โดยที่ทั้ง "x" และ "y" จะถูกเรียกว่า จุดยอดปลาย (end vertices) ของเส้นเชื่อม |
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กราฟระบุทิศทาง (directed graph) หรือ ไดกราฟ "D" คือคู่อันดับ "D" = ("V", "A") ที่ "A" คือ เซตของเส้นเชื่อมระบุทิศทางซึ่งเป็นคู่อันดับของจุดยอด เส้นเชื่อมระบุทิศทาง (directed edges) อาจถูกเรียกว่า อาร์ก (arcs) หรือ ลูกศร (arrows) เส้นเชื่อม "e" = ("x", "y") จะถูกพิจารณาว่าเป็นเส้นเชื่อม จาก "x" ไป "y" โดยที่ "y" จะถูกเรียกว่า หัว (head) และ "x" จะถูกเรียกว่า หาง (tail) ของเส้นเชื่อม เส้นเชื่อม ("y", "x") จะถูกเรียกว่าเป็นเส้นเชื่อมกลับทิศของ ("x", "y") |
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] | กราฟ (คณิตศาสตร์)
กราฟระบุทิศทาง "D" จะถูกเรียกว่า สมมาตร ก็ต่อเมื่อทุกๆเส้นเชื่อม ("x","y") มีเส้นเชื่อม ("y","x") อยู่ในกราฟด้วย ในแง่การไปถึงกันได้ กราฟระบุทิศทางที่สมมาตร "D" จะเทียบเท่ากับกราฟไม่ระบุทิศทาง "G" โดยเส้นเชื่อม ("x","y") และ ("y","x") เทียบเท่ากับเส้นเชื่อม {"x","y"} ดังนั้น หากเปรียบเทียบระหว่างกราฟระบุทิศทางที่สมมาตรและกราฟไม่ระบุทิศทาง ที่เทียบเท่ากัน จะได้ว่า |"E"| = |"A"|/2 |
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] | กราฟ (คณิตศาสตร์)
กราฟอวัฏจักรระบุทิศทาง (directed acyclic graph: DAG) คือ กราฟระบุทิศทาง ที่ไม่มีวัฏจักร |
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กราฟผสม (mixed graph) "G" คือสามสิ่งอันดับ (3-tuple) "G" = ("V","E","A") โดยที่ "V", "E" และ "A" เหมือนดังนิยามด้านบน |
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] | กราฟ (คณิตศาสตร์)
กราฟอย่างง่าย หรือ กราฟเชิงเดียว (simple graph) เป็นกราฟที่ไม่มี วงวน (loop) ซึ่งเกิดจากเส้นเชื่อมที่มีจุดเริ่มต้นเป็นจุดเดียวกับจุดปลาย และไม่มีเส้นเชื่อมขนาน (parallel edge) ซึ่งเกิดจากเส้นเชื่อมที่มีจุดเริ่มต้นและจุดปลายเหมือนกัน |
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] | กราฟ (คณิตศาสตร์)
มัลติกราฟ (multigraph) เป็นกราฟที่อนุญาตให้มีเส้นเชื่อมขนานได้ โดยเซตของเส้นเชื่อม "E" หรือ "A" จะถูกกำหนดเป็นมัลติเซตแทน เพื่อให้สามารถใส่เส้นเชื่อมสองเส้นที่เหมือนกันลงในกราฟได้ |
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] | กราฟ (คณิตศาสตร์)
อย่างไรก็ตาม มัลติกราฟก็ยังถูกนิยามไม่ตรงกัน บ้างก็นิยามว่ามัลติกราฟไม่มีวงวน บ้างก็นิยามว่ากราฟมีวงวนได้ จึงมีการใช้คำว่ากราฟเทียม (pseudo graph) เพื่อระบุว่ากราฟสามารถมีได้ทั้งเส้นเชื่อมซ้ำและวงวน |
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