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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 王振男(Jenn-Nan Wang) | |
| dc.contributor.author | Mei-Chu Hung | en |
| dc.contributor.author | 洪美珠 | zh_TW |
| dc.date.accessioned | 2021-06-08T06:59:54Z | - |
| dc.date.copyright | 2009-06-30 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-06-23 | |
| dc.identifier.citation | [1a] Edward B. Curtis and James A.Morrow, Chapter 3.1 Conductivities
on Graphs, Inverse Problems for Electrical Networks, Mathematics Department University of Washing ton, Seattle USA, (2000), 27-29. [1b] Edward B. Curtis and James A.Morrow, Chapter 3.2 The Response Mtrix, Inverse Problems for Electrical Networks, Mathematics Department University of Washing ton, Seattle USA, (2000), 32-33. [1c] Edward B. Curtis and James A.Morrow, Chapter 3.3 The Kirchho Ma- trix, Inverse Problems for Electrical Networks, Mathematics Department University of Washing ton, Seattle USA, (2000), 33-35. [1d] Edward B. Curtis and James A.Morrow, Chapter 3.4 The Dirichlet Norm, Inverse Problems for Electrical Networks, Mathematics Department University of Washing ton, Seattle USA, (2000), 35-38. [1e] Edward B. Curtis and James A.Morrow, Chapter 3.5 The Schur Com- plement, Inverse Problems for Electrical Networks, Mathematics Department University of Washing ton, Seattle USA, (2000), 40-47. [1f] Edward B. Curtis and James A.Morrow, Chapter 3.6 Sub-matrices of Response Matrix, Inverse Problems for Electrical Networks, Mathematics Department University of Washing ton, Seattle USA, (2000), 47-48. [1g] Edward B. Curtis and James A.Morrow, Chapter 3.7 Connections and Determinations, Inverse Problems for Electrical Networks, Mathematics Department University of Washing ton, Seattle USA, (2000), 52-55. [1h] Edward B. Curtis and James A.Morrow, Chapter 3.8 Recovery of Con- ductance, Inverse Problems for Electrical Networks, Mathematics Department University of Washing ton, Seattle USA, (2000), 55-58. [2a] Edward B. Curtis and James A.Morrow, Chapter 4.1 Harmonic Con- tinuation, Inverse Problems for Electrical Networks, Mathematics Department University of Washing ton, Seattle USA, (2000), 59-62. [2b] Edward B. Curtis and James A.Morrow, Chapter 4.2 Recovering Con- ductances from , Inverse Problems for Electrical Networks, Mathematics Department University of Washing ton, Seattle USA, (2000), 62-67. [2c] Edward B. Curtis and James A.Morrow, Chapter 4.3 Special Functions on Networks , Chapter 4.4 Special Functions onG4m+3 , Inverse Problems for Electrical Networks, Mathematics Department University of Washing ton, Seattle USA, (2000), 67-73. [2d] Edward B. Curtis and James A.Morrow, Chapter 4.6 The Di eren- tial of L, Inverse Problems for Electrical Networks, Mathematics Department University of Washing ton, Seattle USA, (2000), 77-80. [3] D. Crabtree and E. Haynsworth, An Identity for the Schur complement of a mtrix, Proc. Amer. Math Soc. 22 (1969) 364-366.. [4] C. L. Dodgson, Condensation of determinants, Proc. Royal Society of London, vol. 15 (1866) 15-155. [5] K. JbilouA. Messaoudib and K. Tabaâc, Some Schur complement identi- ties and applications to matrix extrapolation methods, Laboratoire de Mathematiques Appliquees, Université du Littoral, Zone Universitaire de la Mi-voix, Batiment H. Poincarré, 50 rue F. Buisson, BP 699, F-62280 Calais Cedex, France , Ecole Normale Supérieure Takaddoum, Département d'Informatique, B.P. 5118, Av. Oued Akreuch, Takaddoum, Rabat, Morocco, Département de Mathématiques, Faculté des Sciences de Rabat, Agdal, Rabat, Morocco, (2004) . [6] Zhang, Fuzhen, The Schur Complement and Its Applications Series: Nu- merical Methods and Algorithms , Vol. 4 , XVI, 296 p., Hardcover (2005). [7] Nathaniel D. Blair-Stahn; David B. Wilson , Electrical response matrix of a regular -gon, Proc. Amer. Math. Soc. 137 (2009), 2015-2025. [8] Lawrence C. Evans, Partial Di erential Equations, Department of Mathematics University of California, Berkeley, Vol. 19, (1998), 42-44. [9] P Hahner, An Inverse Problemin the Electrostatics, Inverse Problem, 15, (1999), 961-975. [10] G. Alessandrini, Stable Deteminationof Conductivity by Boundary Mea- surements, Applicable Anal.,27 (1988), 153-172. [11] G. Alessandrini, Examples of instability in inverse boundary value prob- lems, Inverse Problems, 13 (1997), 887 897. [12] G. Alessandrini, V. Isakov, and J. Powell, Local uniqueness in the inverse conductivity problem with one measurement, Trans. Amer. Math. Soc., 347 (1995), 3031 3041. [13] G. Alessandrini, A. Morassi, and E. Rosset, Detecting cavities by elec- trostatic boundary measurements, Inverse Problem s, 18 (2002), 1333 1353. [14] H. Ammari and H. Kang, High-order terms in the asymptotic expan- sions of the steady-state voltage potentials in the presence of conductivity inho- mogeneities of small diameter, SIAM J. Math. Anal., 34 (2003), 1152 1166. [15] A. El Badia and T. Ha-Duong, An inverse source problem in potential analysis, Inverse Problems, 16 (2000), 651 663. [16] G. Bao, F. Ma, and Y. Chen, An error estimate for recursive lineariza- tion of the inverse scattering problems, J. Math. Anal. Appl., 247 (2000), 255 271. [17] E. Beretta, E. Francini, and M.S. Vogelius, Asymptotic formulas for steady state voltage potentials in the presence of thin inhomogeneities. A rigor- ous error analysis, J. Math. Pures Appl., 82 (2003), 1277 1301. [18] M. Br¨uhl, Explicit characterization of inclusions in electrical impedance tomography, SIAM J. Math. Anal., 32 (2001), 1327 1341. [19] M. Cheney, D. Isaacson, and J.C. Newell, Electrical impedance tomo- graphy, SIAM Rev., 41 (1999), 85 101. [20] D.C. Dobson and F. Santosa, Resolution and stability analysis of an inverse problem in electrical impedance tomography: dependence of the input current patterns, SIAM J. Appl. Math., 54 (1994), 1542 1560. [21] E. Fabes, H. Kang, and J.K. Seo, Inverse conductivity problem with one measurement: Error estimates and approximate identi cation for perturbed disks, SIAM J. Math. Anal., 30 (1999), 699 720. [22] J. Jossinet, E. Marry, and A. Montalibet, Electrical impedance endoto- mography: imaging tissue from inside, IEEE Trans. Medical Imag., 21 (2002), 560 565. [23] J. Jossinet, E. Marry, and A. Matias, Electrical impedance endo-tomography, Phys. Med. Biol., 47 (2002), 2189 2202. [24] H. Kang, J.K. Seo, and D. Sheen, The inverse conductivity problem with one measurement: stability and estimation of size, SIAM J. Math. Anal., 28 (1997), 1389 1405. [25] A. Kirsch, An Introduction to the Mathematical Theory of Inverse Prob- lems, Applied Mathematical Sciences 120, Springer-Verlag, New York, 1996. [26] R.V. Kohn and M.S. Vogelius, Determining conductivity by boundary measurements, Comm. Pure Appl. Math., 37 (1984), 289 298. [27] J.K. Seo, A uniqueness result on inverse conductivity problem with two measurements, J. Fourier Anal. Appl., 2 (1996), 227 235. [28] C.W. Therrien, Discrete Random Signals and Statistical Signal Process- ing, Englewood Cli s, NJ, Prentice-Hall, 1992. [29] C.F. Tolmasky and A. Wiegmann, Recovery of small perturbations of an interface for an elliptic inverse problem via linearization, Inverse Problems, 15 (1999), 465 487. [30] Developments in inverse problems since Calder´on's foundational paper, Chapter 19 in Harmonic Analysis and Partial Di erential Equations , 295 345, edited by M. Christ, C. Kenig, and C. Sadosky, University of Chicago Press, 1999. [31] T. Yorkey, J. Webster, and W. Tompkins, Comparing reconstruction algorithms for electrical impedance tomography, IEEE Trans. Biomed. Engr., 34 (1987), 843 852. [32] Curtis, E. B., Ingerman, D., Morrow, J. A., Circular planar graphs and resistor networks. Linear Algebra Appl. 283 (1998), no. 1-3, 115 150 [33] Curtis, E. B., Ingerman, D., Morrow, J. A., Circular planar graphs and resistor networks. Linear Algebra Appl. 283 (1998), no. 1-3, 115 150. [34] Borcea, L., Druskin, V. and Vasquez, F. G., Electrical impedance tomog- raphy with resistor networks, Inverse Problems, 24 (2008), 035013. [35]Borcea, L., Electrical impedance tomography. Inverse Problems 18 (2002), no. 6, R99 R136. [36] Russell Brown, Department of Mathematics University of Kentucky Lexington, Kentucky,Imaging with electricity: the mathematics of electrical impedance tomography, 2002. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/26085 | - |
| dc.description.abstract | 這篇論文主要是針對離散型反問題來作討論，我們會以簡單電路圖來介紹在離散情形對於導電係數和圖形圈數的關係，並進一步利用線性化來探討導電係數的穩定狀況。有別於連續型的反問題處理，我們首先將以對照方式介紹在離散情形的電壓、電流與導電係數的代表函數，在利用電路學上歐姆定律定義出數學上的諧和函數，利用這樣的函數可以幫助我們找到特有的電路圖與導電性的關係，甚至給予線性化方式來討論圖形由內而外的穩定狀態，這是我們這篇論文將要陳述的事與相關證明。 | zh_TW |
| dc.description.provenance | Made available in DSpace on 2021-06-08T06:59:54Z (GMT). No. of bitstreams: 1 ntu-98-R96221011-1.pdf: 724301 bytes, checksum: 349fa3ab68b0fa74b621a4a4c87c0e28 (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | 論文口試委員審定書 i
謝辭 ii 中文摘要 iii 英文摘要 iv 第一章 Introduction 1-1 Continuous Case. 1 1-2 Discrete Case on the Resistor Network 1 第二章 Properties of the Resistor Network 2-1 Response Matrix 4 2-2 Kirchhoff Matrix 5 2-3 Schur Complement 6 2-4 Dirichlet Norm 16 2-5 Sub-matrices of Response Matrix and Connections and Determinations 24 2-6 Recovery of Conductance 30 第三章 Harmonic Functions 3-1 Harmonic Continuation 36. 3-2 Recovering Conductance from Response Matrix 40 3-3 Harmonic Functions 46 3-4 Linearization and Stability 49 參考文獻 76 | |
| dc.language.iso | en | |
| dc.subject | 科綺沃夫矩陣 | zh_TW |
| dc.subject | 調和函數 | zh_TW |
| dc.subject | 歐姆定律 | zh_TW |
| dc.subject | 離散型反問題 | zh_TW |
| dc.subject | 電流感應矩陣 | zh_TW |
| dc.subject | Inverse Problems for resistor network | en |
| dc.subject | Kirchhoff matrix | en |
| dc.subject | Schur complement | en |
| dc.subject | response matrix | en |
| dc.title | 離散型電流阻抗掃描 | zh_TW |
| dc.title | Discrete Electrical Impedance Tomography | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳俊全(Chun-chuan Chen),林景隆(Ching-Lung Lin) | |
| dc.subject.keyword | 歐姆定律,電流感應矩陣,科綺沃夫矩陣,離散型反問題,調和函數, | zh_TW |
| dc.subject.keyword | Inverse Problems for resistor network,response matrix,Kirchhoff matrix,Schur complement,, | en |
| dc.relation.page | 78 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2009-06-24 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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| ntu-98-1.pdf 未授權公開取用 | 707.33 kB | Adobe PDF |
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