"Hearing the shape of a drum"의 두 판 사이의 차이

수학노트
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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
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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
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[[격자의 세타함수]]
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[http://www.facstaff.bucknell.edu/ed012/bucknell.pdf ]http://www.facstaff.bucknell.edu/ed012/bucknell.pdf
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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]
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http://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum
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[[분류:수학노트(피)]]
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[[분류:migrate]]
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q5691670 Q5691670]
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===Spacy 패턴 목록===
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* [{'LOWER': 'hearing'}, {'LOWER': 'the'}, {'LOWER': 'shape'}, {'LOWER': 'of'}, {'LOWER': 'a'}, {'LEMMA': 'drum'}]
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* [{'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

격자의 세타함수

[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

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': '?'}]
원본 주소 "https://wiki.mathnt.net/index.php?title=Hearing_the_shape_of_a_drum&oldid=51678"