Inverse Problems in Applied Sciences—towards breakthrough

Jin Cheng, Yuusuke Iso, Gen Nakamura, Masahiro Yamamoto
2007 Journal of Physics, Conference Series  
Preface The purpose of this conference is to establish the collaboration links among the researchers in Asia and worldwide leading researchers in inverse problems. The conference will address both theoretical (Mathematics), applied (Engineering) and development aspects on inverse problems. The proposed conference is intended to nurture Asian-American-European collaborations in this evolving interdisciplinary area. It is envisioned that the conference will lead to a long-term commitment and
more » ... boration among the participated countries and researchers. Additionally, newcomers to the subject matter will be encouraged to participate through (i) the attendance of tutorial sessions, serial lectures and panel discussion, and (ii) the availability of a practical information on the application of inverse problems to engineering disciplines to enter the study of inverse problem. We propose a new direction for future Electrical Impedance Tomography (EIT) research, for mainly biomedical applications. Our technique is based on simultaneous measure of an electric current and of acoustic vibrations induced by ultrasound waves. This technique can provide high resolutions images, while conserving the most important merits of EIT. This work is joint with EThe talk is an attempt to inscribe the BC-method in the scope of model theory that is a branch of functional analysis dealing with representation of the abstractly given operators in the form of the operators acting in functional spaces. We show that determination of the Riemannian manifold Ω from its boundary spectral or dynamical data by the BC-method is equivalent to construction of a canonical functional model of the minimal Beltrami-Laplace operator Δ 0 acting in L 2 (Ω). The basic element of this construction is a metric spaceΩ built of the increasing families (nests) of subspaces formed by waves produced by boundary sources. Such nests, parametrized by the action time of sources, play the role of points of the space whereas the distance between two points inΩ is introduced as the "interaction time" equal to the (doubled) value of the parameter at which the subspaces of two nests begin to intersect. By its construction, the spaceΩ turns out to be isometric to the original Ω whereas the corresponding Beltrami-Laplace operatorΔ 0 is unitary equivalent to Δ 0 . The construction ofΩ can be interpreted in terms of the Spectral Theorem for the von Neumann algebras. Such a philosophy gives a unified look at a rather wide class of inverse problems; in particular, it gives a procedure of time-optimal reconstruction of the Riemannian manifold from dynamical electromagnetic boundary data. The last result generalizes the ones on determination of parameters of the Maxwell system from its response operator (Belishev, Glasman, Isakov, Pestov, Sharafutdinov 1997-2001. A priori information. Let 0 < a, b < 1, 0 < κ < 1, L > 0, M > 0, and ρ 0 > 0 be fixed numbers. (1) Assume that F j 's satisfy
doi:10.1088/1742-6596/73/1/011001 fatcat:4mwyip2gdzeaffk7zgk62cvtvm