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共同筆記 / 沈昭亮教授

人物記事/沈昭亮教授

 

先生於 1951年5月3日出生於台灣高雄。1958 年隨全家北遷三重後,先後進入新莊初級中學、臺北市立建國中學就讀,隨後於1968 年間進入國立台灣師範大學數學系。1972 年大學畢業後,順利考取預官並擔任龍潭第一士校少尉教官。退役後,旋進入三重市光榮國中擔任數學教師。

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由於先生對數學研究富有熱情,遂于1975年通過教育部自費留學考試並於1976年負笈美國留學,進入了 University of Pennsylvania ,師事 Edward George Effros 教授學習算子代數理論,並建立了 Shen’s criterion 、 Effros-Handelman-Shen theorem等重要理論 。先生於1979-1980 間任教於 Suny Stony Brook 大學, 1980 年返台,執教於清華大學數學系。返台後,先生逐漸將研究重心轉移到微分算子譜理論和反問題的領域,為台灣反問題研究的先驅。除致力於研究之外,先生於教學富有極大熱誠,不論於課堂上或討論班中,常能將自身對數學的熱情灌注於學生,使學生感受到數學之美好,曾榮獲三次傑出教學獎。先生除了指導過 7 位博士生 和 18 位碩士生獲得學位外,所教導過的學生更遍及學術界、教育界、商界、醫界....等各行各業 。先生於清華大學任教凡33年,作育英才無數,不幸於 2013年12月16日早晨病逝於台大醫院,享壽 63 歲。


沈昭亮教授生平著作:

1979-1983 算子代數
1.  A note on ternary quadratic forms, Bulletin of Institute of Mathematics, Academia Sinica, 11 (1983, March), No. 1, 61-74.

2. Automorphisms of dimension groups and the construction of AF algebras, Pacific Journal of Mathematics, 10 (1981, Dec.), No. 2, 461-469.

3. The geometry of finite rank dimension groups (with E.G. Effros), Illinois Journal of Mathematics, 25 (1981, Spring), No. 1, 27-38.

4. A classification of nonsimple dimension groups, Mathematics Research Center Research Reports, 10 (1981-82), 275-281.

5. A note on the automorphism groups of simple dimension group, Pacific Journal of Mathematics, 89 (1980, July), No. 1, 199-207.

6. Dimension groups and their affine representations (with E.G. Effros and D. Handelman), American Journal of Mathematics, 102 (1980, April), No. 2, 385-407

7. Approximately finite C^*-algebras and continued fractions (with E.G. Effros), Indiana University Mathematics Journal, 29 (1980), No. 2, 191-204.

8. On the classification of the ordered goups associated with approximately finite dimensional C^*-algebras, Duke Mathematical Journal, 46 (1979 Sept.), No. 3, 613-633.

9. Dimension groups and finite difference equations, (with E.G. Effros), Journal of Operator Theory, 2 (1979, Fall), No. 2, 215-231.

1986-1994 Eigenvalue Problems
1.On the maximum and minimum of some functionals for the eigenvalue problem of Sturm-Liouville type (with Hua-Huai Chern), Journal of Differential Equations, 107 (1994, January), No. 1, 68-79.
2.On the nodal set of the eigenfunctions of certain homogeneous and nonhomogeneous membranes, SIAM Journal on Mathematical Analysis, 24 (1993, September), No. 5, 1277-1282.
3.On the second eigenvalue and the second eigenfunction of a class of selfadjoint second order linear system, Rocky Mountain Journal of Mathematics, 23 (1993, Fall), No. 4, 1431-1442.
4.
4.Some properties of the first eigenvalue of the Laplace operator on the spherical bands in S^2 (with Chung-Tsun Shieh), SIAM Journal on Mathematical Analysis, 23 (1992, September), No. 5, 1305-1308.

5.On the nodal sets of the eigenfunctions of the string equation, SIAM Journal on Mathematical Analysis, 19 (1988, November), No. 6, 1419-1424.
6.
Remarks on the second eigenvalue of a symmetric simply connected plane region, SIAM Journal on Mathematical Analysis, 19 (1988, January), No. 1, 167-171.

7.On the first eigenfunction of convex symmetric domains, Bulletin of Institute of Mathematics, Academic Sinica, 14 (June, 1986), No. 2, 105-115.

1995-2013 Inverse Spectral, Inverse nodal and inverse discret Discrete SchrodingerProblems
1.   An isospectral problem related to the Dirichlet eigenvalues and the Neumann eigenvalues of a string equation and some related problems, Inverse Problems, 27 (2011), 075005 (27pp).
2.    The nodal sets of the eigenfunctions of a nonhomogeneous square membrane, Inverse Problems, 24(2008), 055007 (31pp.).
3.    On some inverse spectral problems related to the Ambarzumyan problem and the dual string of the string equation, Inverse Problems, 23(2007), 2417-2436.
4.    On the Barcilon formula for the string equation with a piecewisely continuous density function, Inverse Problems, 21 (2005), 635-655.
5.    On the Liouville transformation and some inverse spectral problems, Inverse Problems, 21(2005), 591-614.
6.    The Liouville transformation, the density function, and the complete transformability problem of the potential equation, Inverse Problems, 21(2005), 615-634.
7.    On some inverse spectral problems for vectorial Sturm-Liouville equations, Inverse Problems, 17(2001, October), 1253-1294.
8.   An inverse nodal problem for vectorial Sturm-Liouville equations, (with Chung-Tsun Shieh), Inverse Problems, 16(2000, April), 349-356.
9.    Some eigenvalue problems for the vectorial Hill's equation, Inverse Problems, 16 (2000, June), 749-784.
10.  The inverse nodal problem on the smoothness of the potential function, (with Chun-Kong Law and Ching-Fu Yang), Inverse Problems, 15(1999), 253-263.
11.  On the multiplicity of eigenvalues of a vectorial Sturm-Liouville differential equation and some related spectral problems (with Chung-Tsun Shieh), Proceedings of American Mathematical Society, 127(1999), No.10, 2943-2952.
12.  Two inverse eigenvalue problems for vectorial Sturm-Liouville equation, (with Chung-Tsun Shieh), Inverse Problems, 14 (1998), 1331-1343.
13.  On the asymptotic behavior of the solutions of a class of selfadjoint second order linear systems, Rocky Mountain Journal of Mathematics, 27 (1997, Spring), 619-634.
14.  On the n-dimensional Ambarzumyan's theorem (with Hua-Huai Chern), Inverse Problems, 13 (1997, February), No. 1, 15-18.
15.  On a uniform approximation of the density function of a string equation using   eigenvalues and nodal points and some related inverse nodal problems (with Tzong-Mo Tsai), Inverse Problems, 11 (1995), 1113-1123.


其他
1.  『連分式與反面問題』,數學傳播,第27卷,第3期,第35--47頁(2003年九月出版)。

2.  


『秋風夜雨-----話蚯蚓,談連分數』,數學傳播,第27卷, 第2期,第17-23頁 (2003年6月出版)。
3.  

『獵殺紅色十月-----談正弦函數的數學』,數學傳播,第27卷,第1期,第9-13頁 (2003年3月出版)。
4.  


Introduction to Operator Algebras, Institute of Mathematics, National Tsing Hua University, 1982.



 
 

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