"푸크스 미분방정식(Fuchsian differential equation)"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) 잔글 (찾아 바꾸기 – “<h5 (.*)">” 문자열을 “==” 문자열로) |
Pythagoras0 (토론 | 기여) |
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| (같은 사용자의 중간 판 14개는 보이지 않습니다) | |||
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==개요== | ==개요== | ||
| − | * | + | * 선형미분방정식:<math>\frac{d^n w}{dz^n} + A_1(z)\frac{d^{n-1}w}{dz^{n-1}} + \cdots + A_{n-1}(z)\frac{dw}{dz} + A_n(z)w=0</math> |
| − | * | + | * 모든 특이점이 [[정칙특이점(regular singular points)]]인 경우, 이를 푸크스 미분방정식이라 한다 |
| + | * 19세기에 많은 연구가 진행되었음 | ||
| + | * [[초기하 미분방정식(Hypergeometric differential equations)]] 은 대표적인 푸크스 미분방정식의 예이다 | ||
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==역사== | ==역사== | ||
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* http://www.google.com/search?hl=en&tbs=tl:1&q= | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
| − | * [[ | + | * [[수학사 연표]] |
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==메모== | ==메모== | ||
| + | * Dwork family http://www.math.sunysb.edu/~cschnell/pdf/notes/picardfuchs.pdf | ||
| + | * Group Theory and Differential Equations University of Minnesota Lecture Notes 1959-1960 by Lawrence Markus (with permission of the author) | ||
| + | * http://www.ima.umn.edu/~miller/Group_Theory_and_Differential_Equations.html | ||
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==관련된 항목들== | ==관련된 항목들== | ||
| + | * [[르장드르의 타원곡선 모임]] | ||
| + | * [[맴돌이군이 유한인 초기하 미분방정식에 대한 슈바르츠 목록]] | ||
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==수학용어번역== | ==수학용어번역== | ||
| + | *{{forvo|url=Fuchs}} | ||
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| − | + | ==에세이== | |
| − | + | * Gray, J. J. 1984. “Fuchs and the Theory of Differential Equations.” Bulletin of the American Mathematical Society 10 (1): 1–26. doi:[http://dx.doi.org/10.1090/S0273-0979-1984-15186-3 10.1090/S0273-0979-1984-15186-3]. | |
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==관련논문== | ==관련논문== | ||
| − | * [http://www.jstor.org/stable/2154053 Liouvillian First Integrals of Differential Equations] | + | * [http://www.jstor.org/stable/2154053 Liouvillian First Integrals of Differential Equations] |
** Michael F. Singer, Transactions of the American Mathematical Society, Vol. 333, No. 2 (Oct., 1992), pp. 673-688 | ** Michael F. Singer, Transactions of the American Mathematical Society, Vol. 333, No. 2 (Oct., 1992), pp. 673-688 | ||
| − | * [http://www.jstor.org/stable/2374541 Algebraic Relations Among Solutions of Linear Differential Equations: Fano's Theorem] | + | * [http://www.jstor.org/stable/2374541 Algebraic Relations Among Solutions of Linear Differential Equations: Fano's Theorem] |
** Michael F. Singer, American Journal of Mathematics, Vol. 110, No. 1 (Feb., 1988), pp. 115-143 | ** Michael F. Singer, American Journal of Mathematics, Vol. 110, No. 1 (Feb., 1988), pp. 115-143 | ||
| − | * [http://dx.doi.org/10.1007/3-540-15984-3_335 Elementary and Liouvillian solutions of linear differential equations] | + | * [http://dx.doi.org/10.1007/3-540-15984-3_335 Elementary and Liouvillian solutions of linear differential equations] |
** M. F. Singer and J. H. Davenport, 1985 | ** M. F. Singer and J. H. Davenport, 1985 | ||
| − | * [http://www.jstor.org/stable/2374348 Some Applications of Linear Groups to Differential Equations] | + | * [http://www.jstor.org/stable/2374348 Some Applications of Linear Groups to Differential Equations] |
| − | ** Michael F. Singer and Marvin D. Tretkoff, | + | ** Michael F. Singer and Marvin D. Tretkoff, American Journal of Mathematics, Vol. 107, No. 5 (Oct., 1985), pp. 1111-1121 |
| − | * L[http://dx.doi.org/10.1007/BF01157466 ogarithmic singularities of Fuchs equations, and a criterion for the monodromy group to be finite] | + | * L[http://dx.doi.org/10.1007/BF01157466 ogarithmic singularities of Fuchs equations, and a criterion for the monodromy group to be finite] |
** N. V. Grigorenko, MATHEMATICAL NOTESVolume 33, Number 6, 453-454 | ** N. V. Grigorenko, MATHEMATICAL NOTESVolume 33, Number 6, 453-454 | ||
| − | * [http://www.jstor.org/stable/2374045 Liouvillian Solutions of n-th Order Homogeneous Linear Differential Equations] | + | * [http://www.jstor.org/stable/2374045 Liouvillian Solutions of n-th Order Homogeneous Linear Differential Equations] |
** Michael F. SingerAmerican Journal of Mathematics, Vol. 103, No. 4 (Aug., 1981), pp. 661-682 | ** Michael F. SingerAmerican Journal of Mathematics, Vol. 103, No. 4 (Aug., 1981), pp. 661-682 | ||
| − | * Algebraic Solutions of nth Order Linear Differential Equations | + | * Algebraic Solutions of nth Order Linear Differential Equations |
| − | ** M. Singer, | + | ** M. Singer, Proceedings of the Queen's University 1979 Conference on Number Theory, Queens Papers in Pure and Applied Mathematics, (54), pp. 379-420 |
| − | * [http://www.jstor.org/stable/2373938 On Second Order Linear Differential Equations with Algebraic Solutions] | + | * [http://www.jstor.org/stable/2373938 On Second Order Linear Differential Equations with Algebraic Solutions] |
| − | ** F. Baldassari, B. Dwork, | + | ** F. Baldassari, B. Dwork, American Journal of Mathematics, Vol. 101, No. 1 (Feb., 1979), pp. 42-76 |
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==관련도서== | ==관련도서== | ||
| − | * [http://books.google.com/books?id=txinPHIegGgC Linear Differential Equations and Group Theory from Riemann to Poincare] | + | * [http://books.google.com/books?id=txinPHIegGgC Linear Differential Equations and Group Theory from Riemann to Poincare] |
| − | ** Jeremy J. Gray, | + | ** Jeremy J. Gray, 2008(2판) |
| − | * [http://repository.kulib.kyoto-u.ac.jp/dspace/handle/2433/84920 Lectures on algebraic solutions of hypergeometric differential equations] | + | * [http://repository.kulib.kyoto-u.ac.jp/dspace/handle/2433/84920 Lectures on algebraic solutions of hypergeometric differential equations] |
** Matsuda, Michihiko, 1985 | ** Matsuda, Michihiko, 1985 | ||
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| − | + | [[분류:미분방정식]] | |
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2013년 11월 22일 (금) 07:12 기준 최신판
개요
- 선형미분방정식\[\frac{d^n w}{dz^n} + A_1(z)\frac{d^{n-1}w}{dz^{n-1}} + \cdots + A_{n-1}(z)\frac{dw}{dz} + A_n(z)w=0\]
- 모든 특이점이 정칙특이점(regular singular points)인 경우, 이를 푸크스 미분방정식이라 한다
- 19세기에 많은 연구가 진행되었음
- 초기하 미분방정식(Hypergeometric differential equations) 은 대표적인 푸크스 미분방정식의 예이다
역사
메모
- Dwork family http://www.math.sunysb.edu/~cschnell/pdf/notes/picardfuchs.pdf
- Group Theory and Differential Equations University of Minnesota Lecture Notes 1959-1960 by Lawrence Markus (with permission of the author)
- http://www.ima.umn.edu/~miller/Group_Theory_and_Differential_Equations.html
관련된 항목들
수학용어번역
- Fuchs - 발음사전 Forvo
에세이
- Gray, J. J. 1984. “Fuchs and the Theory of Differential Equations.” Bulletin of the American Mathematical Society 10 (1): 1–26. doi:10.1090/S0273-0979-1984-15186-3.
관련논문
- Liouvillian First Integrals of Differential Equations
- Michael F. Singer, Transactions of the American Mathematical Society, Vol. 333, No. 2 (Oct., 1992), pp. 673-688
- Algebraic Relations Among Solutions of Linear Differential Equations: Fano's Theorem
- Michael F. Singer, American Journal of Mathematics, Vol. 110, No. 1 (Feb., 1988), pp. 115-143
- Elementary and Liouvillian solutions of linear differential equations
- M. F. Singer and J. H. Davenport, 1985
- Some Applications of Linear Groups to Differential Equations
- Michael F. Singer and Marvin D. Tretkoff, American Journal of Mathematics, Vol. 107, No. 5 (Oct., 1985), pp. 1111-1121
- Logarithmic singularities of Fuchs equations, and a criterion for the monodromy group to be finite
- N. V. Grigorenko, MATHEMATICAL NOTESVolume 33, Number 6, 453-454
- Liouvillian Solutions of n-th Order Homogeneous Linear Differential Equations
- Michael F. SingerAmerican Journal of Mathematics, Vol. 103, No. 4 (Aug., 1981), pp. 661-682
- Algebraic Solutions of nth Order Linear Differential Equations
- M. Singer, Proceedings of the Queen's University 1979 Conference on Number Theory, Queens Papers in Pure and Applied Mathematics, (54), pp. 379-420
- On Second Order Linear Differential Equations with Algebraic Solutions
- F. Baldassari, B. Dwork, American Journal of Mathematics, Vol. 101, No. 1 (Feb., 1979), pp. 42-76
관련도서
- Linear Differential Equations and Group Theory from Riemann to Poincare
- Jeremy J. Gray, 2008(2판)
- Lectures on algebraic solutions of hypergeometric differential equations
- Matsuda, Michihiko, 1985