1,473 research outputs found
A new approach to hyperbolic inverse problems II (Global step)
We study the inverse problem for the second order self-adjoint hyperbolic
equation with the boundary data given on a part of the boundary. This paper is
the continuation of the author's paper [E]. In [E] we presented the crucial
local step of the proof. In this paper we prove the global step. Our method is
a modification of the BC-method with some new ideas. In particular, the way of
the determination of the metric is new.Comment: 21 pages, 2 figure
A new approach to hyperbolic inverse problems
We present a modification of the BC-method in the inverse hyperbolic
problems. The main novelty is the study of the restrictions of the solutions to
the characteristic surfaces instead of the fixed time hyperplanes. The main
result is that the time-dependent Dirichlet-to-Neumann operator prescribed on a
part of the boundary uniquely determines the coefficients of the self-adjoint
hyperbolic operator up to a diffeomorphism and a gauge transformation. In this
paper we prove the crucial local step. The global step of the proof will be
presented in the forthcoming paper.Comment: We corrected the proof of the main Lemma 2.1 by assuming that
potentials A(x),V(x) are real value
Strong wavefront lemma and counting lattice points in sectors
We compute the asymptotics of the number of integral quadratic forms with
prescribed orthogonal decompositions and, more generally, the asymptotics of
the number of lattice points lying in sectors of affine symmetric spaces. A new
key ingredient in this article is the strong wavefront lemma, which shows that
the generalized Cartan decomposition associated to a symmetric space is
uniformly Lipschitz
Inverse problems for Schrodinger equations with Yang-Mills potentials in domains with obstacles and the Aharonov-Bohm effect
We study the inverse boundary value problems for the Schr\"{o}dinger
equations with Yang-Mills potentials in a bounded domain
containing finite number of smooth obstacles . We
prove that the Dirichlet-to-Neumann operator on determines
the gauge equivalence class of the Yang-Mills potentials. We also prove that
the metric tensor can be recovered up to a diffeomorphism that is identity on
.Comment: 15 page
Optical Aharonov-Bohm effect: an inverse hyperbolic problems approach
We describe the general setting for the optical Aharonov-Bohm effect based on
the inverse problem of the identification of the coefficients of the governing
hyperbolic equation by the boundary measurements. We interpret the inverse
problem result as a possibility in principle to detect the optical
Aharonov-Bohm effect by the boundary measurements.Comment: 34 pages. Minor changes, references adde
Inverse hyperbolic problems and optical black holes
In this paper we give a more geometrical formulation of the main theorem in
[E1] on the inverse problem for the second order hyperbolic equation of general
form with coefficients independent of the time variable. We apply this theorem
to the inverse problem for the equation of the propagation of light in a moving
medium (the Gordon equation). Then we study the existence of black and white
holes for the general hyperbolic and for the Gordon equation and we discuss the
impact of this phenomenon on the inverse problems
Triangulations and volume form on moduli spaces of flat surfaces
In this paper, we are interested in flat metric structures with conical
singularities on surfaces which are obtained by deforming translation surface
structures. The moduli space of such flat metric structures can be viewed as
some deformation of the moduli space of translation surfaces. Using geodesic
triangulations, we define a volume form on this moduli space, and show that, in
the well-known cases, this volume form agrees with usual ones, up to a
multiplicative constant.Comment: 42 page
The effects of environmental temperature changes on the EKG of the squirrel monkey /Saimiri sciureus/
Environmental temperature effects on EKG of squirrel monkey - animal study of heart rate and T-wave amplitud
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