本論文旨在針對反算法於化學反應問題之研究，其中兩個章節探討的內容如下。
在第一章中問題的物理模型主要是在探討藉由量測自由擴散濃度與固定濃度來預測反應速率函數與溶質濃度，我們是利用反算法中的共軛梯度法來進行反算分析工作，我們假設兩個隨時間變化的反應速率函數以及溶質濃度，其隨時間變化的函數型態並不知道，必須藉著量測得的資料來反求之，我們將此類的反算問題歸類為“函數預測法”(Function Estimation)。
在第二章中問題的物理模型主要是在探討藉由量測纖維酸與鹽的濃度值來預測酸與鹽的擴散係數，我們同樣是利用反算法中的共軛梯度法來進行反算分析工作，我們假設兩個隨(x,)變化的酸與鹽的擴散係數，其隨(x,)變化的函數型態並不知道，必須藉著量測得的資料來反求之，本章的反算問題亦可歸類為“函數預測法”(Function Estimation)。

The inverse chemical reaction problems are studied in this thesis and the following two topics were examined.
In the first chapter, the main concern is to estimate two reaction rate functions and solute concentration based on the concentration measurements with time. The conjugate gradient algorithm is utilized to perform the inverse analysis. It is assumed that the functional forms for two time-dependent reaction rate functions and solute concentration are all unknown, and they must be recasted by using the measurement data. This kind of inverse problem is classified as “Function Estimation” algorithm.
In the second chapter, the main purpose is to estimate the acid and salt diffusivities by utilizing the measured concentrations of acid and salt, respectively. Again, the functional forms for acid and salt diffusivities are both unknown and it is also defined as the “Function Estimation” in the category of inverse problems.

第一章

1. S. M. Katz, E. T. Kubu, and J. H. Wakelin, The Chemical Attack on Polymeric Materials as Modified by Diffusion, Text Res. J., (1950) 754-760.
2. A. Petropoulos and P. P. Roussis, Organic Solid State Chemistry (G. Adler, Ed.), Gordon and Breach, London, 1969.
3. J. Crank, The Mathematics of Diffusion, 2nd ed., Clarendon Press, London, 1975.
4. P. Nicolson and F. J. W. Roughton, A Theoretical Study of Influence of Diffusion and Chemical Reaction Velocity on the Rate of Exchange of Carbon Monoxide and Oxygen between the Red Blood Corpuscle and the Surrounding Fluid, Proc. R. Soc. (B), 138, (1951), 241-264.
5. M. D. Mikhailov and M. N. Ozisik, in: Unified Analysis and Solutions of Heat and Mass Diffusion, Wiley, New York, 1984.
6. V. B. Storozhev, Estimation of the Contribution of Heterogeneous Reactions on the Surface of Aerosol Particles to the Chemistry of the Atmosphere, Journal of Aerosol Science, 26 (1995) 1179-1184.
7. G. Cartry, L. Magne and G. Cernogora, Atomic Oxygen Recombination on Fused Silica: Modeling and Comparison to Low-Temperature Experiments (300 K), Journal of Physics D-Applied Physics, 33 (2000) 1303-1314.
8. R. M. Harrison and G. M. Collins, Measurements of Reaction Coefficients of NO2 and HONO on Aerosol Particles, Journal of Atmospheric Chemistry, 30 (1998) 397-406.
9. O. M. Alifanov, Inverse Heat Transfer Problem, Springer-Verlag, Berlin, 1994.
10. H. R. B. Orlande and M. N. Ozisik, Determination of the Reaction Function in a Reaction-Diffusion Parabolic Problem, J. Heat Transfer, 116 (1994) 1041-1044.
11. B. Jin, Conjugate Gradient Method for the Robin Inverse Problem Associated with the Laplace Equation, Int. J. Numerical Methods in Engineering, 71 (2007) 433–453.
12. M. Prud’homme and T. H. Nguyen, Fourier Analysis of Conjugate Gradient Method Applied to Inverse Heat Conduction Problems, Int. J. Heat and Mass Transfer, 42 (1999) 4447-4460.
13. C. H. Huang and S. P. Wang, A Three-Dimensional Inverse Heat Conduction Problem in Estimating Surface Heat Flux by Conjugate Gradient Method, Int. J. Heat and Mass Transfer, 42 (1999) 3387-3403.
14. C. H. Huang, A Nonlinear Inverse Vibration Problem of Estimating the External Forces for A System with Displacement-Dependent Parameters, J. Sound and Vibration, 248 (2001) 789-807.
15. C. H. Huang and S. Kim, An Inverse Problem for Estimating the Time-Dependent Reaction Coefficient in an Autocatalytic Reaction Pathway, Chemical Engineering Science, 60 (2005) 447-457.
16. C. H. Huang and K.Y. Chen, An Inverse Phonon Radiative Transport Problem in Estimating the Boundary Temperatures for A Double-Layer Nanoscale Thin-Film, Numerical Heat Transfer, Part A---Applications, 52 (2007) 43-70.
17. C. H. Huang and C.Y. Lin, An Iterative Regularization Method in Estimating the Unknown Energy Source by Laser Pulses with a Dual-Phase-Lag Model, Int. J. Numerical Methods in Engineering, 76 (2008) 108–126.
18. C. H. Huang, C. C. Shih and Sin Kim, An Inverse Vibration Problem in Estimating the Spatial and Temporal-Dependent External Forces for Cutting Tools, Applied Mathematical Modelling, 33 (2009) 2683–2698.
19. C. H. Huang and Y. L. Chung, An Optimal Fin Design Problem in Estimating the Shapes of Longitudinal and Spine Fully Wet Fins, CMES-Computer Modeling in Engineering & Sciences, 44 (2009) 249-279.
20. M. D. Mikhailov and M. N. Ozisik, A General Solution of Solute Diffusion with Reversible Reaction, Int. J. Heat and Mass Transfer, 24 (1981) 81-87.
21. IMSL Library Edition 10.0. User's Manual: Math Library Version 1.0, IMSL, Houston, TX, 1987.

第二章

1. S. G. Li, G. H. Koops, M. H. V. Mulder, T. van den Boomgaard and C. A. Smolders, Wet Spinning of Integrally Skinned Hollow Fiber Membranes by A Modified Dual-Bath Coagulation Method Using A Triple Orifice Spinneret, Journal of Membrane Science, 94 (1994) 329-340.
2. C. C. Pereira, R. Nobrega and C. P. Borges, Spinning Process Variables and Polymer Solution Effects in the Die-Swell Phenomenon During Hollow Fiber Membranes Formation, Braz. J. Chem. Eng., 17 (2000) 599-606.
3. J. F. V. Vasconcellos, A. N. J. Silva Neto and C. S. C. Santana, An Inverse Mass Transfer Problem in Solid–Liquid Adsorption Systems, Inverse Problems in Science and Engineering, 11 (2003) 391–408.
4. A. Memmedov, G.I. Kelbaliyev and G.T. Alisoy, Solution of An Inverse Problem for Mass Transfer in a Drying Process in a Magnetic Field, Inverse Problems in Science and Engineering, 18 (2010) 723–736.
5. C. H. Huang, C. Y. Yeh and Helcio R. B. Orlande, A Non-Linear Inverse Problem in Simultaneously Estimating the Heat and Mass Production Rates for A Chemically Reacting Fluid, Chemical Engineering Science, 58 (2003) 3741-3752.
6. H. R. B. Orlande and M. N. Ozisik, Determination of the Reaction Function in a Reaction-Diffusion Parabolic Problem, J. Heat Transfer, 116 (1994) 1041-1044.
7. C. H. Huang and S. P. Wang, A Three-Dimensional Inverse Heat Conduction Problem in Estimating Surface Heat Flux by Conjugate Gradient Method, Int. J. Heat and Mass Transfer, 42 (1999) 3387-3403.
8. C. H. Huang, A Nonlinear Inverse Vibration Problem of Estimating the External Forces for A System with Displacement-Dependent Parameters, J. Sound and Vibration, 248 (2001) 789-807.
9. B. Jin, Conjugate Gradient Method for the Robin Inverse Problem Associated with the Laplace Equation, Int. J. Numer. Meth. Engng, 71 (2007) 433–453.
10. M. Prud’homme and T. H. Nguyen, Fourier Analysis of Conjugate Gradient Method Applied to Inverse Heat Conduction Problems, Int. J. Heat and Mass Transfer, 42 (1999) 4447-4460.
11. C. H. Huang and Y. L. Chung, An Optimal Fin Design Problem in Estimating the Shapes of Longitudinal and Spine Fully Wet Fins, CMES-Computer Modeling in Engineering & Sciences, 44 (2009) 249-279.
12. O. M. Alifanov, Inverse Heat Transfer Problem, Springer-Verlag, Berlin, 1994.
13. M. E. Davis, Numerical Methods and Modeling for Chemical Engineering, John Wily & Sons, Inc., New York, 1984.
14. C. H. Huang and J. Y. Yan, An Inverse Problem in Simultaneously Measuring Temperature Dependent Thermal Conductivity and Heat Capacity, Int. J. Heat and Mass Transfer, 38 (1995) 3433-3441.
15. IMSL Library Edition 10.0. User's Manual: Math Library Version 1.0, IMSL, Houston, TX, 1987.