3,076 research outputs found
Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential
For the Schrodinger equation at fixed energy with a potential supported in a
bounded domain we give formulas and equations for finding scattering data from
the Dirichlet-to-Neumann map with nonzero background potential. For the case of
zero background potential these results were obtained in [R.G.Novikov,
Multidimensional inverse spectral problem for the equation
-\Delta\psi+(v(x)-Eu(x))\psi=0, Funkt. Anal. i Ego Prilozhen 22(4), pp.11-22,
(1988)]
New global stability estimates for the Gel'fand-Calderon inverse problem
We prove new global stability estimates for the Gel'fand-Calderon inverse
problem in 3D. For sufficiently regular potentials this result of the present
work is a principal improvement of the result of [G. Alessandrini, Stable
determination of conductivity by boundary measurements, Appl. Anal. 27 (1988),
153-172]
A convergent algorithm for the hybrid problem of reconstructing conductivity from minimal interior data
We consider the hybrid problem of reconstructing the isotropic electric
conductivity of a body from interior Current Density Imaging data
obtainable using MRI measurements. We only require knowledge of the magnitude
of one current generated by a given voltage on the boundary
. As previously shown, the corresponding voltage potential u in
is a minimizer of the weighted least gradient problem
with . In this paper we present an
alternating split Bregman algorithm for treating such least gradient problems,
for non-negative and . We
give a detailed convergence proof by focusing to a large extent on the dual
problem. This leads naturally to the alternating split Bregman algorithm. The
dual problem also turns out to yield a novel method to recover the full vector
field from knowledge of its magnitude, and of the voltage on the
boundary. We then present several numerical experiments that illustrate the
convergence behavior of the proposed algorithm
Inverse problems with partial data for a magnetic Schr\"odinger operator in an infinite slab and on a bounded domain
In this paper we study inverse boundary value problems with partial data for
the magnetic Schr\"odinger operator. In the case of an infinite slab in ,
, we establish that the magnetic field and the electric potential can
be determined uniquely, when the Dirichlet and Neumann data are given either on
the different boundary hyperplanes of the slab or on the same hyperplane. This
is a generalization of the results of [41], obtained for the Schr\"odinger
operator without magnetic potentials. In the case of a bounded domain in ,
, extending the results of [2], we show the unique determination of the
magnetic field and electric potential from the Dirichlet and Neumann data,
given on two arbitrary open subsets of the boundary, provided that the magnetic
and electric potentials are known in a neighborhood of the boundary.
Generalizing the results of [31], we also obtain uniqueness results for the
magnetic Schr\"odinger operator, when the Dirichlet and Neumann data are known
on the same part of the boundary, assuming that the inaccessible part of the
boundary is a part of a hyperplane
Evidence for Pervasive Adaptive Protein Evolution in Wild Mice
The relative contributions of neutral and adaptive substitutions to molecular evolution has been one of the most controversial issues in evolutionary biology for more than 40 years. The analysis of within-species nucleotide polymorphism and between-species divergence data supports a widespread role for adaptive protein evolution in certain taxa. For example, estimates of the proportion of adaptive amino acid substitutions (alpha) are 50% or more in enteric bacteria and Drosophila. In contrast, recent estimates of alpha for hominids have been at most 13%. Here, we estimate alpha for protein sequences of murid rodents based on nucleotide polymorphism data from multiple genes in a population of the house mouse subspecies Mus musculus castaneus, which inhabits the ancestral range of the Mus species complex and nucleotide divergence between M. m. castaneus and M. famulus or the rat. We estimate that 57% of amino acid substitutions in murids have been driven by positive selection. Hominids, therefore, are exceptional in having low apparent levels of adaptive protein evolution. The high frequency of adaptive amino acid substitutions in wild mice is consistent with their large effective population size, leading to effective natural selection at the molecular level. Effective natural selection also manifests itself as a paucity of effectively neutral nonsynonymous mutations in M. m. castaneus compared to humans
Inverse medium problem for a singular contrast
We consider an inverse medium problem in two- and three-dimensional cases. Namely, we investigate the problem of reconstruction of unknown compactly supported refractive index (contrast) from L-2 with a fixed positive wave number. The proof is based on the new estimates for the Green-Faddeev function in L-infinity space. The main goal of this work is to prove a uniqueness result in the two- and three-dimensional cases and to discuss some possible constructive methods for solving the problem. Finally, we present some numerical examples to demonstrate the results in two dimensions. Published under license by AIP Publishing.Peer reviewe
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