1,463 research outputs found

    A new approach to hyperbolic inverse problems II (Global step)

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    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

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    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

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    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

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    We study the inverse boundary value problems for the Schr\"{o}dinger equations with Yang-Mills potentials in a bounded domain Ω0⊂Rn\Omega_0\subset\R^n containing finite number of smooth obstacles Ωj,1≤j≤r\Omega_j,1\leq j \leq r. We prove that the Dirichlet-to-Neumann operator on ∂Ω0\partial\Omega_0 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 ∂Ω0\partial\Omega_0.Comment: 15 page

    Right-angled billiards and volumes of moduli spaces of quadratic differentials on CP¹

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    Optical Aharonov-Bohm effect: an inverse hyperbolic problems approach

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    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

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    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

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    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/

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    Environmental temperature effects on EKG of squirrel monkey - animal study of heart rate and T-wave amplitud
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