"Hearing the shape of a drum"의 두 판 사이의 차이
Pythagoras0 (토론 | 기여) |
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| (사용자 3명의 중간 판 13개는 보이지 않습니다) | |||
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| − | + | 리만기하학의 문제 Is a Riemannianmanifold (possibly with boundary) determined by its spectrum? | |
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| + | 1964, John Milnor found two distinct 16-dimensional manifolds with the same spectrum. | ||
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| + | 1991년, CarolynGordon, David Webb, and Scott Wolpert found examples of distinct plane "drums"which "sound" the same. See the illustrations below. | ||
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Milnor, John (1964), "Eigenvalues of the Laplace operator on certain manifolds", Proceedings of the National Academy of Sciences of the United States of America 51: 542ff | Milnor, John (1964), "Eigenvalues of the Laplace operator on certain manifolds", Proceedings of the National Academy of Sciences of the United States of America 51: 542ff | ||
| 7번째 줄: | 17번째 줄: | ||
Kac, Mark (1966), "Can one hear the shape of a drum?", American Mathematical Monthly 73 (4, part 2): 1–23 | Kac, Mark (1966), "Can one hear the shape of a drum?", American Mathematical Monthly 73 (4, part 2): 1–23 | ||
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| + | ==expositions== | ||
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| + | http://www.ams.org/samplings/feature-column/fcarc-199706 | ||
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| + | <em>YouCan't Always Hear the Shape of a Drum</em> by Barry Cipra, which appeared inVolume 1 of [http://www.ams.org/samplings/feature-column/happening.html What's Happening in the MathematicalSciences]. | ||
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16 dimensioanl lattices | 16 dimensioanl lattices | ||
| 17번째 줄: | 37번째 줄: | ||
http://www.facstaff.bucknell.edu/ed012/Altoona.pdf | http://www.facstaff.bucknell.edu/ed012/Altoona.pdf | ||
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[http://math.berkeley.edu/%7Ealanw/240papers03/vitocruz.pdf http://math.berkeley.edu/~alanw/240papers03/vitocruz.pdf] | [http://math.berkeley.edu/%7Ealanw/240papers03/vitocruz.pdf http://math.berkeley.edu/~alanw/240papers03/vitocruz.pdf] | ||
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| + | http://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum | ||
| + | [[분류:수학노트(피)]] | ||
| + | [[분류:migrate]] | ||
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| + | ==메타데이터== | ||
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q5691670 Q5691670] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'hearing'}, {'LOWER': 'the'}, {'LOWER': 'shape'}, {'LOWER': 'of'}, {'LOWER': 'a'}, {'LEMMA': 'drum'}] | ||
| + | * [{'LOWER': 'can'}, {'LOWER': 'you'}, {'LOWER': 'hear'}, {'LOWER': 'the'}, {'LOWER': 'shape'}, {'LOWER': 'of'}, {'LOWER': 'a'}, {'LOWER': 'drum'}, {'LEMMA': '?'}] | ||
2021년 2월 17일 (수) 01:06 기준 최신판
리만기하학의 문제 Is a Riemannianmanifold (possibly with boundary) determined by its spectrum?
1964, John Milnor found two distinct 16-dimensional manifolds with the same spectrum.
1991년, CarolynGordon, David Webb, and Scott Wolpert found examples of distinct plane "drums"which "sound" the same. See the illustrations below.
Milnor, John (1964), "Eigenvalues of the Laplace operator on certain manifolds", Proceedings of the National Academy of Sciences of the United States of America 51: 542ff
Kac, Mark (1966), "Can one hear the shape of a drum?", American Mathematical Monthly 73 (4, part 2): 1–23
expositions
http://www.ams.org/samplings/feature-column/fcarc-199706
YouCan't Always Hear the Shape of a Drum by Barry Cipra, which appeared inVolume 1 of What's Happening in the MathematicalSciences.
16 dimensioanl lattices
[1]http://www.facstaff.bucknell.edu/ed012/bucknell.pdf
http://www.facstaff.bucknell.edu/ed012/Altoona.pdf
http://math.berkeley.edu/~alanw/240papers03/vitocruz.pdf
http://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum
메타데이터
위키데이터
- ID : Q5691670
Spacy 패턴 목록
- [{'LOWER': 'hearing'}, {'LOWER': 'the'}, {'LOWER': 'shape'}, {'LOWER': 'of'}, {'LOWER': 'a'}, {'LEMMA': 'drum'}]
- [{'LOWER': 'can'}, {'LOWER': 'you'}, {'LOWER': 'hear'}, {'LOWER': 'the'}, {'LOWER': 'shape'}, {'LOWER': 'of'}, {'LOWER': 'a'}, {'LOWER': 'drum'}, {'LEMMA': '?'}]