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鄭彥修

基本資料

  • 姓名:鄭彥修
  • 職稱:教授
  • 研究專長:Schrodinger 方程正問題與反問題之研究; p-Laplacian 方程正問題與反問題之研究; 微分方程之正解分枝問題
  • 授課領域:微積分、線性代數、高等微積分、微分方程、代數、普通數學、數學遊戲
  • 聯絡電話:27321104#55821
  • 電子郵件:yhcheng@tea.ntue.edu.tw
  • Office hour:下載

個人介紹


學歷
國立中山大學應用數學系博士


經歷
2003/082004/07 國立中山大學應用數學系兼任講師
2005/082005/10 國立中山大學應用數學系博士後研究
2007/032008/07 國家理論科學研究中心數學組博士後研究
2008/082010/07 國立中山大學應用數學系約聘助理教授
2010/092012/07 國立清華大學數學系博士後研究
 
 

個人著作與發表


學位論文

Inverse Problems for Various Sturm-Liouville Operators國立中山大學應用數學系博士班,93學年度。

期刊論文
  1. Y.H. Cheng, C.K. Law* and J. Tsay, 2000, Remarks on a new inverse nodal problemJournal of Mathematical Analysis and Applications 248, 145-155. (SCI, 2000 Impact Factor : 0.431)
  2. Y.T. Chen, Y.H. Cheng, C.K. Law* and J. Tsay, 2002, L1 convergence of the reconstruction formula for the potential function, Proceedings of the American Mathematical Society 130, 2319-2324. (SCI, 2002 Impact Factor : 0.334, Ranking : 116/170 = 68.2%, Subject Category : Mathematics)
  3. Y.H. Cheng, C.T. Shieh* and C.K. Law, 2005, A vectorial inverse nodal problem, Proceedings of the American Mathematical Society 133, 1475-1484. (SCI, 2005 Impact Factor : 0.429, Ranking : 101/181 = 55.8%, Subject Category : Mathematics)
  4. Y.H. Cheng and C.K. Law*, 2006, On the quasinodal map for the Sturm-Liouville problem, Proceedings of the Royal Society of Edinburgh: Section A 136, 71-86. (SCI, 2006 Impact Factor : 0.684, Ranking : 55/187 = 29.4%, Subject Category : Mathematics)
  5. Y.H. Cheng and C.K. Law*, 2006, The inverse nodal problem for Hill's equation, Inverse Problems 22, 892-901. (SCI, 2006 Impact Factor : 1.319, Ranking : 18/150 = 12%, Subject Category : Mathematics, Applied)
  6. Y.H. Cheng*, T.E. Wang and C.J. Wu, 2010/07, A note on eigenvalue asymptotics for Hill's equation, Applied Mathematics Letters 23, 1013-1015. (SCI, 2010 Impact Factor : 1.155, Ranking : 63/236 = 26.7%, Subject Category : Mathematics, Applied)
  7. Y.H. Cheng*, S.Y. Kung, C.K. Law and W.C. Lian, 2010/11, The dual eigenvalue problems for the Sturm-Liouville system, Computers & Mathematics with Applications 60, 2556-2563. (SCI, 2010 Impact Factor : 1.472, Ranking : 33/236 = 14.0%, Subject Category : Mathematics, Applied)
  8. X. Chen, Y.H. Cheng and C.K. Law*, 2011/09, Reconstructing potentials from zeros of one eigenfunction, Transactions of the American Mathematical Society 363, 4831-4851. (SCI, 2011 Impact Factor : 1.093, Ranking : 33/289 = 11.4%, Subject Category : Mathematics)
  9. W.C. Wang*, Y.H. Cheng and W.C. Lian, 2011/12, Inverse nodal problems for the p-Laplacian with eigenparameter dependent boundary conditions, Mathematical and Computer Modelling 54, 2718-2724. (SCI, 2011 Impact Factor : 1.346, Ranking : 40/245 = 16.3%, Subject Category : Mathematics, Applied)
  10. Y.H. Cheng*, 2012/09, Reconstruction of the Sturm-Liouville operator on a p-star graph with nodal data, Rocky Mountain Journal of Mathematics 42, no. 5, 1431-1446. (SCIE, 2012 Impact Factor : 0.389, Ranking : 232/295 = 78.6%, Subject Category : Mathematics)
  11. X. Chen, Y.H. Cheng and C.K. Law*, 2012/11, A Tikhonov Regularization for the Inverse Nodal Problem for p-Laplacian, Journal of Mathematical Analysis and Applications 395, 230-240. (SCI, 2012 Impact Factor : 1.050, Ranking : 34/295 = 11.5%, Subject Category : Mathematics)
  12. Y.H. Cheng*, 2012/12, An eigenvalue problem for vibrating strings with concave densities, Applied Mathematics Letters 25, 2077-2080. (SCI, 2012 Impact Factor : 1.501, Ranking : 33/247 = 13.4%, Subject Category : Mathematics, Applied)
  13. W.C. Lian*, W.C. Wang and Y.H. Cheng, 2013/03, Existence of sign-changing solutions for the nonlinear p-Laplacian boundary value problem, Analysis and Applications 11(2), 1350004, 15pp. (SCIE, 2013 Impact Factor :1.500, Ranking : 14/299 = 4.7%, Subject Category : Mathematics)
  14. Y.H. Cheng*, K.C. Hung and S.H. Wang, 2013/09, Global bifurcation diagrams and exact multiplicity of positive solutions for a one-dimensional prescribed mean curvature problem arising in MEMS, Nonlinear Analysis: Theory, Methods and Applications 89, 284-298. (SCI, 2013 Impact Factor :1.612, Ranking : 12/302 = 4.0%, Subject Category : Mathematics)
  15. Y.H. Cheng*, W.C. Lian and W.C. Wang, 2014/02, The dual eigenvalue problems for p-Laplacian, Acta Mathematica Hungarica 142(1), 132-151. (SCIE, 2014 Impact Factor :0.429, Ranking : 233/310 =75.2 %, Subject Category : Mathematics)
  16. W.C. Wang* and Y.H. Cheng, 2014/3, An inverse problem related to a half-linear eigenvalue problem, Boundary Value Problems, 2014:65. (SCIE, 2014 Impact Factor :1.014, Ranking : 48/310 = 15.5%, Subject Category : Mathematics)
  17. W.C. Wang* and Y.H. Cheng, 2014/6, On the existence of sign-changing radial solutions to nonlinear p-Laplacian equations in Rn, Nonlinear Analysis: Theory, Methods and Applications 102, 14–22. (SCI, 2014 Impact Factor :1.327, Ranking : 26/310 = 8.4%, Subject Category : Mathematics)
  18. Y.H. Cheng*, 2014/6, Eigenvalue problems with p-Laplacian operators, Electronic Journal of Differential Equations, Vol. 2014 (2014), No. 139, pp. 1-11. (SCIE, 2014 Impact Factor :0.524, Ranking : 185/310 = 59.68%, Subject Category : Mathematics)
  19. K.C. Hung*, Y.H. Cheng, S.H. Wang, and C.H. Chuang, 2014/11, Exact multiplicity and bifurcation diagrams of positive solutions of a one-dimensional multiparameter prescribed mean curvature problem, Journal of Differential Equations, Vol. 257 (2014), Issue 9, 3272–3299. (SCI, 2014 Impact Factor :1.680, Ranking : 16/310 = 5.2%, Subject Category : Mathematics)
  20. Y.H. Cheng, C.K. Law* and Y.C. Luo, 2014/12, Distribution of the Prufer angle in p-Laplacian eigenvalue problems, Electronic Journal of Differential Equations, Vol. 2014 (2014), No. 255, pp. 1-8. (SCIE, 2014 Impact Factor :0.524, Ranking : 185/310 = 59.68%, Subject Category : Mathematics)
  21. Y.H. Cheng, C.K. Law*, W.C. Lian and W.C. Wang, 2015/8, An inverse nodal problem and Ambarzumyan problem for the periodic p-Laplacian operator with integrable potentials, Taiwanese Journal of Mathematics, Vol. 19, No. 4, 1305-1316. (SCI, 2015 Impact Factor : 0.617, Ranking : 154/312 = 49.4%, Subject Category : Mathematics)
  22. Y.H. Cheng and W.C. Wang*, 2016/5, Inverse nodal problems for the p-Laplacian with eigenparameter dependent energy functions, Boundary Value Problems, 2016(1), 1-15. (SCIE, 2016 Impact Factor : 0.819, Ranking : 98/310 = 31.6%, Subject Category : Mathematics. 2016 SJR:0.570, Q3)
  23. Y.H. Cheng, K.C. Hung, and S.H. Wang, 2016/7, Classification and evolution of bifurcation curves for a one-dimensional prescribed mean curvature problem, Differential and Integral Equations, Vol. 29, No. 7-8, 631-664. (SCIE, 2016 Impact Factor : 0.565, Ranking : 183/310 = 59.0%, Subject Category : Mathematics. 2016 SJR:1.045, Q2)
  24. Y.H. Cheng*, K.C. Hung and S.H. Wang, 2016/11, On the classification and evolution of bifurcation curves for a one-dimensional prescribed curvature problem with nonlinearity , Nonlinear Analysis: Theory, Methods and Applications, Vol. 146, 161-184. (SCI, 2016 Impact Factor :1.192, Ranking : 41/310 = 13.2%, Subject Category : Mathematics. 2016 SJR:1.520, Q1)
  25. Y.H. Cheng and Wei-Chuan Wang*, 2017/3, On some nodal properties for a p-Laplacian system, Electronic Journal of Differential Equations, Vol. 2017 (2017), No. 87, 1-8. (SCIE, 2016 Impact Factor :0.954, Ranking : 70/310 = 22.6%, Subject Category : Mathematics. 2017 SJR:0.538, Q3)
  26. W.C. Wang and Y.H. Cheng*, 2017/6, Sign-changing solutions to a class of nonlinear equations involving p-Laplacian, Rocky Mountain Journal of Mathematics, Vol. 47, No. 3, 971-996. (SCIE, 2016 Impact Factor : 0.250, Ranking : 303/310 = 97.7%, Subject Category : Mathematics. 2017 SJR:0.398, Q3)
  27. Y.H. Cheng and W.C. Wang*, 2020/1, Some remarks on a nonhomogeneous eigenvalue problem related to generalized trigonometric functions, Nonlinear Analysis: Theory, Methods and Applications, Vol. 190, 111614. (SCI. 2019 SJR:1.848, Q1)
  28. Wei-Chua Chen and Y.H. Cheng*, 2020/7, Remarks on the one-dimensional sloshing problem involving the p-Laplacian operator, Turkish Journal of Mathematics, Vol. 44, No. 4, 1376-1387. (SCIE. 2019 SJR:0.408, Q3)
  29. Y.H. Cheng*, 2020/11, Reconstruction and stability of inverse nodal problems for energy-dependent p-Laplacian equations, Journal of Mathematical Analysis and Applications, Volume 491, Issue 2, Article 124388. (SCI. 2019 SJR:1.021, Q1)
  30. Y.H. Cheng*, 2020, On the Neumann eigenvalues for second-order Sturm-Liouville difference equations, Advances in Difference Equations, accepted(SCIE)
 

研討會論文
  1. 鄭彥修(2000)Remarks on a new inverse nodal problem,論文發表於 2000年國際數學與統計研討會暨第34屆中華民國數學會年會,淡江大學,台北縣。
  2. Y.H. Cheng (2002). A vectorial inverse nodal problem. Paper Presented at International Conference on Inverse Problems - Recent Developments in Theories and Numerics, City University of Hong Kong, Hong Kong.
  3. 鄭彥修 (2003)On the nodal map of the inverse Sturm-Liouville problem,論文發表於2003年數學學術研討會暨第37屆中華民國數學年會,國立中央大學,中壢市。
  4. Y.H. Cheng (2004). The quasinodal map and the inverse nodal problem. Paper Presented at The 2nd International Conference on Inverse Problems - Recent Theoretical Development and Numerical Approaches, Fudan University, Shanghai, China.
  5. 鄭彥修(2008)Inverse problem for the first instability interval in Schrödinger equation。論文發表於2008年數學學術研討會暨中華民國數學會年會,國立清華大學,新竹市。
  6. 鄭彥修 (2009)Reconstructing potentials using nodal points in Schrödinger equation,論文發表於第十七屆微分方程研討會,國立高雄大學應用數學系,高雄市。
  7. 鄭彥修 (2010)The gap of the first two eigenvalues for the p-Laplacian,論文發表於2010年數學學術研討會暨中華民國數學會年會,國立彰化師範大學,彰化市。
  8. 鄭彥修 (2009)Inverse problems for the p-Laplacian operator,論文發表於2009年非線性分析與應用研討會,國立高雄師範大學數學系,高雄市。
  9. Y.H. Cheng (2010). Reconstructing potentials from zeros of one eigenfunction. Paper Presented at 2010 SIAM Annual Meeting, University of Pittsburgh, USA.
  10. Y.H. Cheng (2011). The Tikhonov regularization method on inverse nodal problems. Paper Presented at The 4th Mathematical Society of Japan, Seasonal Institute - Nonlinear Dynamics in Partial Differential Equations, Kyushu University, Japan.
  11. 鄭彥修 (2011)An inverse spectral problem for p-Laplacian,論文發表於2011 年數學學術研討會暨中華民國數學會年會,中原大學,中壢市。
  12. 鄭彥修 (2012)The generalized sine function of the p-Laplacian problem,論文發表於2012分析與微分方程研討會,國立新竹教育大學,新竹市。
  13. 鄭彥修 (2012)The nodal problems for the p-Laplacian eigenvalue problem,論文發表於The 3rd Taiwan-Japan Joint Workshop for Young Scholars in Applied Mathematics,國立台灣大學,台北市。
  14. Y.H. Cheng (2014). On the first instability interval of the string equation. Paper Presented at SEOUL ICM 2014 International Congress of Mathematicians, Seoul, Korea.
  15. Y.H. Cheng (2016). Eigenvalue estimates for the Sturm-Liouville equation. Paper Presented at The 22nd International Conference on Difference Equations and Applications (ICDEA2016), Osaka Prefecture University, Japan.
  16. 鄭彥修 (2016)Some inverse problems on the p-Laplacian,論文發表於Workshop on Spectral Analysis of Differential Operators and Related Topics,淡江大學,新北市。
  17. 鄭彥修 (2017)The order of eigenvalues for the Sturm-Liouville equation with the Dirichlet/Neumann boundary conditions,論文發表於2017暑期海峽兩岸微分算子譜反演問題研討會,南京理工大學,中華人民共和國。
  18. Y.H. Cheng (2018). Some properties on the generalized sine function. Paper Posted at The Role of Metrics in the Theory of Partial Differential Equations (MSJ-SI), Hokkaido University, Japan.
  19. 鄭彥修 (2019)On the eigenvalue gap/ratio of Sturm-Liouville equations with eigenparameter dependent boundary conditions,論文發表於第二屆海峽兩岸反譜問題與相關課題暨慶祝淡江大學數學系創系60週年學術研討會,淡江大學,新北市。
 歷年科技部計畫
  1. 97學年度,圖上的奇異函數之節點反演問題,NSC 97-2115-M-110 -01097/10/01 98/07/31
  2. 98學年度,週期 p-Laplacain 算子上的Ambarzumyan 定理及節點反演問題,NSC 98-2115-M-110 -00698/08/01 99/07/31
  3. 102學年度,p-Laplacian 上的固有值反演問題,NSC 102-2115-M-152 -002102/08/01 103/07/31
  4. 103學年度,能量函數倚賴能階之 p-Laplacian 的節點反演問題,MOST 103-2115-M-152 -002103/08/01 104/07/31
  5. 104學年度,p-Laplacian 之非齊次特徵值問題的節點反演問題,MOST 104-2115-M-152-002104/08/01 105/07/31
  6. 105學年度,擬線性橢圓系統上的 Prufer 變換之研究,MOST 105-2115-M-152-002105/08/01 106/07/31
  7. 106學年度,離散型Sturm-Liouville問題的Neumann固有值之研究,MOST 106-2115-M-152-001106/08/01 107/07/31
  8. 107學年度,Sturm-Liouville 方程伴隨固有值參數在邊界條件上的固有值間距/比值問題之研究,MOST 107-2115-M-152-002107/08/01 108/07/31
  9. 108學年度,Tikhonov 正則法應用在特徵參數伴隨能量函數之p-Laplacian方程的研究MOST 108-2115-M-152-002108/08/01 109/07/31
  10. 109學年度,四階微分方程上的節點反演問題和固有值間距問題MOST 109-2115-M-152-001109/08/01 110/07/31