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Reconstruction Of Partially Conductive Cracks Using Boundary Data, David Mccune, Janine Haugh
Reconstruction Of Partially Conductive Cracks Using Boundary Data, David Mccune, Janine Haugh
Mathematical Sciences Technical Reports (MSTR)
This paper develops an algorithm for finding one or more non-insulated, pair-wise disjoint, linear cracks in a two dimensional region using boundary measurements.
The Birational Isomorphism Types Of Smooth Real Elliptic Curves, Sean A. Broughton
The Birational Isomorphism Types Of Smooth Real Elliptic Curves, Sean A. Broughton
Mathematical Sciences Technical Reports (MSTR)
In this note we determine all birational isomorphism types of real elliptic curves and show that it is the same as the orbit space of smooth cubic real curves in real projective space under linear projective equivalence. There are two families, each depending polynomially on a real parameter in a open subinterval of R. We further show that the complexification of a real elliptic curve has exactly two real forms. Thus the real elliptic curves come in pairs which are isomorphic over C. Finally, the map taking a real elliptic curve to its j-invariant maps the two families …
Reconstruction Of An Unknown Boundary Portion From Cauchy Data In N-Dimensions, Kurt M. Bryan, Lester Caudill
Reconstruction Of An Unknown Boundary Portion From Cauchy Data In N-Dimensions, Kurt M. Bryan, Lester Caudill
Mathematical Sciences Technical Reports (MSTR)
We consider the inverse problem of determining the shape of some inacces sible portion of the boundary of a region in n dimensions from Cauchy data for the heat equation on an accessible portion of the boundary. The inverse problem is quite ill-posed, and nonlinear. We develop a Newton-like algorithm for solving the problem, with a simple and efficient means for computing the required derivatives, develop methods for regularizing the process, and provide computational examples
Determining The Length Of A One-Dimensional Bar, Natalya Yarlikina, Holly Walrath
Determining The Length Of A One-Dimensional Bar, Natalya Yarlikina, Holly Walrath
Mathematical Sciences Technical Reports (MSTR)
In this paper we examine the inverse problem of determining the length of a one-dimensional bar from thermal measurements (temperature and heat flux) at one end of the bar (the "accessible" end); the other inaccessible end of the bar is assumed to be moving. We develop two different approaches to estimating the length of the bar, and show how one approach can also be adapted to find unknown boundary conditions at the inaccessible end of the bar.