Faculty Publications - Department of Mathematics and Statistics
https://hdl.handle.net/20.500.11919/37
Mon, 23 Sep 2019 05:35:32 GMT2019-09-23T05:35:32ZInfluence of Phosphate Source on Vesicular-Arbuscular Mycorrhizae of Bouteloua-Gracilis
https://hdl.handle.net/20.500.11919/1570
Influence of Phosphate Source on Vesicular-Arbuscular Mycorrhizae of Bouteloua-Gracilis
Allen, Michael F.; Sexton, J. C.; Moore, J. C.; Christensen, M.
https://hdl.handle.net/20.500.11919/1570Comparative Water Relations and Photosynthesis of Mycorrhizal and Non-Mycorrhizal Bouteloua-Gracilis HBK Lag Ex Steud
https://hdl.handle.net/20.500.11919/1569
Comparative Water Relations and Photosynthesis of Mycorrhizal and Non-Mycorrhizal Bouteloua-Gracilis HBK Lag Ex Steud
Allen, Michael F.; Smith, W. K.; Moore, T. S.; Christensen, M.
https://hdl.handle.net/20.500.11919/1569Set of All MXN Rectangular Real Matrices of Rank-R Is Connected by Analytic Regular Arcs, The
https://hdl.handle.net/20.500.11919/1578
Set of All MXN Rectangular Real Matrices of Rank-R Is Connected by Analytic Regular Arcs, The
Evard, J. C.; Jafari, Farhad
It is well known that the set of all square invertible real matrices has two connected components. The set of all m x n rectangular real matrices of rank r has only one connected component when m ≠ n or r < m = n. We show that all these connected components are connected by analytic regular arcs. We apply this result to establish the existence of p-times differentiable bases of the kernel and the image of a rectangular real matrix function of several real variables.
https://hdl.handle.net/20.500.11919/1578Reconstruction of a Spherically Symmetrical Speed of Sound
https://hdl.handle.net/20.500.11919/1582
Reconstruction of a Spherically Symmetrical Speed of Sound
McLaughlin, J. R.; Polyakov, Peter; Sacks, P. E.
Consider the inverse acoustic scattering problem for a spherically symmetric inhomogeneity of compact support that arises, among other places, in nondestructive testing. Define the corresponding homogeneous and inhomogeneous interior transmission problems, see, e.g., [D. Colton and P. Monk, Quart. J. Mech. Math., 41 (1988), pp. 97-125]. Here the authors study the subset of transmission' eigenvalues corresponding to spherically symmetric eigenfunctions of the homogeneous interior transmission problem. It is shown in McLaughlin and Polyakov [J. Differential Equations, to appear] that these eigenvalues are the zeros of an average of the scattering amplitude, and a uniqueness theorem for the inverse acoustic scattering problem is presented where these eigenvalues are the given data. In the present paper an algorithm for finding the solution of the inverse acoustic scattering problem from this subset of transmission eigenvalues is developed and implemented. The method given here completely determines the sound speed when the size, measured by an integral, satisfies a particular bound. The algorithm is based on the Gelfand-Levitan integral equation method.
I. M. Gelfand and B. M. Levitan, Amer. Math. Sec. Trans., 1(1951), pp. 253-304, W. Rundell and P. E. Sacks, Inverse Problems, 8 (1992), pp. 457-482.
https://hdl.handle.net/20.500.11919/1582