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REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
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Communications of the Korean Mathematical Society
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Journal DOI :
The Korean Mathematical Society
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Volume & Issues
Volume 16, Issue 4 - Oct 2001
Volume 16, Issue 3 - Jul 2001
Volume 16, Issue 2 - Apr 2001
Volume 16, Issue 1 - Jan 2001
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역전도체 문제와 전기 임피던스 영상기법
Communications of the Korean Mathematical Society, volume 16, issue 3, 2001, Pages 333~369
APPLICATIONS OF THE REPRODUCING KERNEL THEORY TO INVERSE PROBLEMS
Saitoh, Saburou ;
Communications of the Korean Mathematical Society, volume 16, issue 3, 2001, Pages 371~383
In this survey article, we shall introduce the applications of the theory of reproducing kernels to inverse problems. At the same time, we shall present some operator versions of our fundamental general theory for linear transforms in the framework of Hilbert spaces.
DETERMINATION OF TEMPERATURE FILED FOR BACKWARD HEAT TRANSFER
Liu, Ji-Jun ;
Communications of the Korean Mathematical Society, volume 16, issue 3, 2001, Pages 385~397
Consider an inverse problem of determining of the 2-D temperature distribution from known temperature given at some time T>0. Our aim is to find the temperature for 0
PROPERTIES OF ELASTIC SYMBOLS AND CONSTRUCTION OF SOLUTIONS OF THE DIRICHLET PROBLEM
Kawashita, Mishio ; Soga, Hideo ;
Communications of the Korean Mathematical Society, volume 16, issue 3, 2001, Pages 399~404
We examine plane waves of the elastic reduced wave equation in the half-space, and show that linear combinations of them can cover all plane waves on the boundary. The proof is based on the complex analysis for the symbol in the (dual) variable in the normal direction to the boundary.
UNIQUENESS OF IDENTIFYING THE CONVECTION TERM
Cheng, Jin ; Gen Nakamura ; Erkki Somersalo ;
Communications of the Korean Mathematical Society, volume 16, issue 3, 2001, Pages 405~413
The inverse boundary value problem for the steady state heat equation with convection term is considered in a simply connected bounded domain with smooth boundary. Taking the Dirichlet to Neumann map which maps the temperature on the boundary to the that flux on the boundary as an observation data, the global uniqueness for identifying the convection term from the Dirichlet to Neumann map is proved.
DIRECT DETERMINATION OF THE DERIVATIVES OF CONDUCTIVITY AT THE BOUNDARY FROM THE LOCALIZED DIRICHLET TO NEUMANN MAP
Gen-Nakamura ; Kazumi-Tanuma ;
Communications of the Korean Mathematical Society, volume 16, issue 3, 2001, Pages 415~425
We consider the problem of determining conductivity of the medium from the measurements of the electric potential on the boundary and the corresponding current flux across the boundary. We give a formula for reconstructing the conductivity and its normal derivative at the point of the boundary simultaneously from the localized Diichlet to Neumann map around that point.
THE REFLECTION OF SOLUTIONS OF HELMHOLTZ EQUATION AND AN APPLICATION
Yun, Ki-Hyun ;
Communications of the Korean Mathematical Society, volume 16, issue 3, 2001, Pages 427~436
It is the purpose of this paper to study the reflection of solutions of Helmholtz equation with Neumann boundary data. In detail let u be a solution of Helmholtz equation in the exterior of a ball in R
with exterior Neumann data ∂(sub)νu = 0 on the boundary of the ball. We prove that u can be extended to R
except the center of the ball. As a corollary, we prove that a sound hard ball can be identified by the scattering amplitude corresponding to a single incident direction and as single frequency.
INVERSE PROBLEM FOR INTERIOR SPECTRAL DATA OF THE DIRAC OPERATOR
Mochizuki, Kiyoshi ; Trooshin, Igor ;
Communications of the Korean Mathematical Society, volume 16, issue 3, 2001, Pages 437~443
In this paper the inverse problems for the Dirac Operator are studied. A set of values of eigenfunctions in some internal point and spectrum are taken as a data. Uniqueness theorems are obtained. The approach that was used in the investigation of inverse problems for interior spectral data of the Sturm-Liouville operator is employed.
PROBLEMS IN INVERSE SCATTERING-ILLPOSEDNESS, RESOLUTION, LOCAL MINIMA, AND UNIQUENESSE
Ra, Jung-Woong ;
Communications of the Korean Mathematical Society, volume 16, issue 3, 2001, Pages 445~458
The shape and the distribution of material construction of the scatterer may be obtained from its scattered fields by the iterative inversion in the spectral domain. The illposedness, the resolution, and the uniqueness of the inversion are the key problems in the inversion and inter-related. The illposedness is shown to be caused by the evanescent modes which carries and amplifies exponentially the measurement errors in the back-propagation of the measured scattered fields. By filtering out all the evanescent modes in the cost functional defined as the squared difference between the measured and the calculated spatial spectrum of the scattered fields from the iteratively chosen medium parameters of the scatterer, one may regularize the illposedness of the inversion in the expense of the resolution. There exist many local minima of the cost functional for the inversion of the large and the high-contrast scatterer and the hybrid algorithm combining the genetic algorithm and the Levenberg-Marquardt algorithm is shown to find efficiently its global minimum. The resolution of reconstruction obtained by keeping all the propating modes and filtering out the evanescent modes for the regularization becomes 0.5 wavelength. The super resolution may be obtained by keeping the evanescent modes when the measurement error and instance, respectively, are small and near.
ELECTRICAL IMPEDANCE IMAGING FOR SEARCHING ANOMALIES
Ohin Kwon ; Seo, Jin-Keun ; Woo, Eung-Je ; Yoon, Jeong-Rock ;
Communications of the Korean Mathematical Society, volume 16, issue 3, 2001, Pages 459~485
The aim of EIT (electrical impedance tomography) system is to image cross-section conductivity distribution of a human body by means of both generating and sensing electrodes attached on to the surface of the body, where currents are injected and voltages are measured. EIT has been suffered from the severe ill-posedness which is caused by the inherent low sensitivity of boundary measurements to any changes of internal tissue conductivity values. With a limited set of current-to-voltage data, figuring out full structure of the conductivity distribution could be extremely difficult at present time, so it could be worthwhile to extract some necessary partial information of the internal conductivity. We try to extract some key patterns of current-to-voltage data that furnish some core information on the conductivity distribution such s location and size. This overview provides our recent observation on the location search and the size estimation.
A NUMERICAL METHOD FOR CAUCHY PROBLEM USING SINGULAR VALUE DECOMPOSITION
Lee, June-Yub ; Yoon, Jeong-Rock ;
Communications of the Korean Mathematical Society, volume 16, issue 3, 2001, Pages 487~508
We consider the Cauchy problem for Laplacian. Using the single layer representation, we obtain an equivalent system of boundary integral equations. We show the singular values of the ill-posed Cauchy operator decay exponentially, which means that a small error is exponentially amplified in the solution of the Cauchy problem. We show the decaying rate is dependent on the geometry of he domain, which provides the information on the choice of numerically meaningful modes. We suggest a pseudo-inverse regularization method based on singular value decomposition and present various numerical simulations.
A NUMERICAL METHOD FOR THE PROBLEM OF COEFFICIENT IDENTIFICATION OF THE WAVE EQUATION BASED ON A LOCAL OBSERVATION ON THE BOUNDARY
Shirota, Kenji ;
Communications of the Korean Mathematical Society, volume 16, issue 3, 2001, Pages 509~518
The purpose of this paper is to propose a numerical algorithm for the problem of coefficient identification of the scalar wave equation based on a local observation on the boundary: Determine the unknown coefficient function with the knowledge of simultaneous Dirichlet and Neumann boundary values on a part of boundary. To find the unknown coefficient function, the unknown Neumann boundary value is also identified. We recast our inverse problem to variational problem. The gradient method is applied to find the minimizing functions. We confirm the effectiveness of our algorithm by numerical experiments.
MAGNETIC RESONANCE ELECTRICAL IMPEDANCE TOMOGRAPHY
Kwon, Oh-In ; Seo, Jin-Keun ; Woo, Eung-Je ; Yoon, Jeong-Rock ;
Communications of the Korean Mathematical Society, volume 16, issue 3, 2001, Pages 519~541
Magnetic Resonance Electrical Impedance Tomography(MREIT) is a new medical imaging technique for the cross-sectional conductivity distribution of a human body using both EIT(Electrical Impedance Tomography) and MRI(Magnetic Resonance Imaging) system. MREIT system was designed to enhance EIT imaging system which has inherent low sensitivity of boundary measurements to any changes of internal tissue conductivity values. MREIT utilizes a recent CDI (Current Density Imaging) technique of measuring the internal current density by means of MRI technique. In this paper, a mathematical modeling for MREIT and image reconstruction method called the alternating J-substitution algorithm are presented. Computer simulations show that the alternating J-substitution algorithm provides accurate high-resolution conductivity images.