CONTENTS -- Foreword -- Section I : Surveys -- Recovery of Small Electromagnetic Inhomogeneities H. Ammari -- 1 The Helmholtz Equation -- 1.1 Problem Formulation -- 1.2 Identification Reconstruction Procedure from Complete Boundary Measurements -- 1.3 Incomplete Boundary Measurements -- 2 The Wave Equation -- 2.1 Complete Dynamic Boundary Measurements -- 2.2 Incomplete Dynamic Boundary Measurements -- 3 Discussion -- References -- Investigation of Inverse and Other Nonclassical Problems in the Russian Far East D. S. Anikonov, A. E. Kovtanuyk, D. D. Konovalova, V.G. Nazarene and I. V. Prothorax -- 1 Introduction -- 2 Short Review of Various Investigations -- 3 Radiation Tomography -- 4 Final Remark -- Acknowledgments -- References -- Incorporation of Uncertainty in Inverse Problem H. T. Banks -- 1 Introduction -- 2 Examples -- 2.1 PBPK Models for TCE an Fat Cells -- 2.2 Thermally Conductive Composite Adhesives -- 2.3 Electromagnetic Imaging of Dielectric Materials -- 2.4 Modelling of the HIV Infection Pathway -- 3 A Theoretical Framework -- 4 Concluding Remarks -- Acknowledgements -- References -- Inverse and Optimal Design Problems in Diffractive Optics G. Bao -- 1 Introduction -- 2 The Diffraction Problem -- 3 Uniqueness for the Inverse Problem -- 4 Stability for the Inverse Problem -- 5 Optimal Design -- 6 Future Directions -- Acknowledgments -- References -- The Inverse Problem of Option Pricing V. Isakov -- 1 The Black-Schools Equation -- 2 Uniqueness and Stability Results -- 3 The Linearized Inverse Option Pricing Problem -- 4 Numerical Algorithm and its Testing -- 5 Open Problems and Future Research -- Acknowledgment -- References -- An Outline of Adaptive Wavelet Galerkin Methods for Tikhonov Regularization of Inverse Parabolic Problems S. Dahlke and Peter Maa -- 1 Introduction -- 2 A model problem.

3 A framework for adaptive Tikhonov regularization -- 4 Wavelet Galerkin methods for operator equations -- Acknowledgments -- References -- Estimation of Discontinuous Solutions of Ill-posed Problems by Regularization for Surface Representations: Numerical Realization via Moving Grids A. Neubauer -- 1 Introduction -- 2 Moving Grids: The Deformation Method -- 3 Numerical Realization -- 4 Numerical Results -- Acknowledgments -- References -- Inverse Theory: Solving or Understanding Models? P. C. Sabatier -- 1 Introduction -- 2 Relation between inverse problems analysis and the mathematical model. -- 3 Putting Physical Information into the Model. -- 4 Representation of Information in the Model -- 5 What about Algorithms and Their Own Modelling ? -- 6 Cases Where Data Sets That Can Be Collected Do Not Determine the Model. -- 7 An Extreme Case of Modelling : Inverse Transforms and Applications -- 8 Extreme opposite case : inverse problem solved by a physical device. -- 9 Conclusions -- References -- Section II: Theoretical Aspects -- Inverse Boundary Value Problems for Systems of Partial Differential Equations G. Eskin and J. Ralston -- 1 The Schrodinger Equation with an External Yang-Mills Potential. -- 2 Construction of Complex Exponential Solutions. -- 3 The Equations of Isotropic Elasticity. -- References -- Uniqueness in the Two-Dimensional Inverse Gravimetry Problem: Case of Variable Coefficient S. Kim and M. Yamamoto -- 1 Introduction -- 2 Main results -- 3 Non-existence of an H2- solution to a Cauchy problem -- 4 Proof of Theorem 1 -- References -- Inversion of Discontinuous Anisotropic Conductivities D. Lesnic -- 1 Introduction -- 2 Mathematical Formulation -- 3 Size Estimation of the Inclusion -- 4 Boundary Integral Formulation -- 5 Conclusions -- References -- On Stability Estimate for a Backward Heat Transfer Problem J-J. Liu -- 1 Introduction.

2 Conditional Stability -- 3 Regularization and Convergence Analysis -- Acknowledgments -- References -- An Existence for an Inverse Problem from Combustion Theory and its Numerical Simulation Y-Ch. Ma, Q. Chen, G-J. Ying and G-Sh. Li -- 1 Introduction -- 2 Assumptions -- 3 Lemmas and the Estimations -- 4 Existence of the Inverse Problem -- 5 The Proof of the Theorem 1 and Theorem 2 -- 6 Numerical Simulation -- References -- Identification and Control of Strongly Damped Nonlinear Hyperbolic Problems with Applications S. Migorski -- 1 Introduction -- 2 Motivating Example -- 3 Existence Result -- 4 Optimal Control for Hemivariational Inequalities -- 4.1 Bolza Type Optimal Control Problem -- 4.2 The Identification Problem -- Acknowledgments -- References -- Estimation of All Mathematical Model Parameters and Experiment Informativeness M. R. Romanovski -- 1 Introduction -- 2 Violation of One-to-one Correspondence -- 3 Simultaneous Identification of Model Coefficients and Boundary Conditions -- References -- Scattering of Elastic Waves in the Half-space and Relation between the Lax-Phillips Theory and the Wilcox Theory M. Kawashita, W. Kawashita and H. Soga -- 1 Introduction -- 2 Reflection of the Plane Waves -- 3 The Generalized Fourier Transformation -- 4 Relation Between The Wilcox and Lax-Phillips Theories -- 5 Expressions in the Free Space -- Acknowledgments -- References -- Formulas for Reconstructing Conductivity and its Normal Derivative at the Boundary from the Localized Dirichlet to Neumann Map G. Nakamura and K. Tanuma -- 1 Introduction -- 2 Reconstruction Formulas -- 3 Estimate of Convergence -- Acknowledgments -- References -- Hochstadt-Lieberman Type Theorem for a Non-symmetric System of First-order Ordinary Differential Operators I. Trooshin and M. Yamamoto -- 1 Introduction and the Main Result -- 2 Proof of the Main Theorem.

Acknowledgments -- References -- Solving the MKDV Hierarchy with Integral Type of Source by Inverse Scattering Transformation Y-B. Zeng and S. Ye -- 1 Introduction -- 2 The mKdV Hierarchy with Integral Type of Source -- 3 The Lax Representation -- 4 Evolution Equation for the Reflection Coefficients -- References -- Section III: Numerical Methods -- Numerical Differentiation on the Nonuniform Grid and its Error Estimate J. Cheng, X-Zh. Jia and Y-B. Wang -- 1 Introduction -- 2 The formulation of the problem and main results -- 3 Proofs of Main Results -- 3.1 Preliminaries -- 3.2 Proof of Theorem I -- 4 Numerical Examples -- 5 Conclusions -- Acknowledgments -- References -- Wavelet Methods for the Sideways Heat Equation Ch-L. Fu, Ch-Y. Qiu and Y-B. Zhu -- 1 Introduction -- 2 Wavelets Regularization and Error Estimate -- Acknowledgments -- References -- Direct Simulation of an Integral Equation of the First Kind H. Imai and T. Takeuchi -- 1 Introduction -- 2 Application of IPNS -- 2.1 Infinite-Precision Numerical Simulation -- 2.2 The Way of Application -- 3 Numerical Results -- 4 Conclusion -- Acknowledgments -- References -- Inverse Problem of Reconstructing the Parabolic Equation's Initial Value and the Heat Radiative Coefficient Y-J. Tan and Ch-X. Jia -- 1 Introduction -- 2 Minimizing the cost function by quasi-Newton method -- 3 the calculation of cost function and its gradient -- 3.1 RBF method -- 3.2 Finite difference method -- 4 numerical result -- 4.1 Assume that p is a constant -- 4.2 Assume that p(x) is a function -- 5 Conclusion -- References -- Numerical Reconstruction of Piecewise Constant Potential for One Dimensional Helmholtz Equation F-M. Ma and F-F. Sun -- 1 Problem -- 2 Discussion on Impedance Functions -- 3 Numerical Reconstruction of Potential q ( x ) -- Acknowledgments -- References.

Algebraic Solution for the Inverse Source Problem of the Poisson Equation T. Nara and S. Ando -- 1 Introduction -- 2 Relation Between the Source Parameters and the Boundary Data Via Multipole Expansion Coefficients -- 3 Direct Representation of the Source Parameters -- 3.1 Explicit Expression of Positions and Strength -- 3.2 Estimation of the Number N -- 4 Stability -- 5 Numerical Simulation -- 6 Conclusion -- References -- Identifying Parameters of Linear Stochastic Differential Equations from Incomplete Noisy Measurements I. V. Semoushin -- 1 Problem Statement -- 2 Discrete-time Model -- 3 Adaptive Filter-Identifier, AFI -- 4 Application Problem -- 4.1 Extended Inertial Navigation System Error Model, EINSEM -- 4.2 Real Data Mathematical Model, RDMM -- 4.3 Filter INS Error Model, FINSEM -- 5 Computational Experiments -- 6 Conclusions -- References -- A Meshless Scheme for Solving Inverse Problems of Laplace Equation Y.C. Hon and T. Wei -- 1 Introduction -- 2 Meshless Method -- 3 Numerical Experiments -- 3.1 Numerical Tests for Two-dimensional Problem 1 and Problem 2 -- 3.2 Three-dimensional Test Case. -- 4 Conclusion and Future Directions -- References -- Stabilized Solution and Numerical Simulation for a Two-Dimensional Hausdorff Moment Problem D-H. Xu and Z- W. Wang -- 1 Hausdorff Moment Problems -- 2 Local Conditional Stability and Tikhonov Regularization Algorithm for the One-Dimensional HMP -- 3 Local Conditional Stability for the Two-Dimensional HMP -- 4 Stabilized Algorithm for the Two-Dimensional HMP -- 5 Numerical Examples -- 6 SomeRemarks -- Acknowledgments -- References -- A Novel Hybrid Genetic Algorithm and its application to Inverse Problems in MEMs Y.G. Xu, G.R. Liu and H. Ohtsubo -- 1 Introduction -- 2 Hybrid Genetic Algorithm (nhGA) -- 2.1 Algorithm Description -- 2.2 Performance Tests -- 3 Inverse Problem Solving.

3.1 Parameter Identification of the Value-less Micropumps.