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Recovering quantum graphs from their Bloch spectrum

Ralf Rueckriemen (2013)

Annales de l’institut Fourier

We define the Bloch spectrum of a quantum graph to be the map that assigns to each element in the deRham cohomology the spectrum of an associated magnetic Schrödinger operator. We show that the Bloch spectrum determines the Albanese torus, the block structure and the planarity of the graph. It determines a geometric dual of a planar graph. This enables us to show that the Bloch spectrum indentifies and completely determines planar 3 -connected quantum graphs.

Recovering the total singularity of a conormal potential from backscattering data

Mark S. Joshi (1998)

Annales de l'institut Fourier

The problem of recovering the singularities of a potential from backscattering data is studied. Let Ω be a smooth precompact domain in ℝ n which is convex (or normally accessible). Suppose V i = v + w i with v ∈ C c ∞ ( ℝ n ) and w i conormal to the boundary of Ω and supported inside Ω ‾ then if the backscattering data of V 1 and V 2 are equal up to smoothing, we show that w 1 - w 2 is smooth.

Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems

Philippe Moireau, Dominique Chapelle (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We propose a general reduced-order filtering strategy adapted to Unscented Kalman Filtering for any choice of sampling points distribution. This provides tractable filtering algorithms which can be used with large-dimensional systems when the uncertainty space is of reduced size, and these algorithms only invoke the original dynamical and observation operators, namely, they do not require tangent operator computations, which of course is of considerable benefit when nonlinear operators are considered....

Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems

Philippe Moireau, Dominique Chapelle (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We propose a general reduced-order filtering strategy adapted to Unscented Kalman Filtering for any choice of sampling points distribution. This provides tractable filtering algorithms which can be used with large-dimensional systems when the uncertainty space is of reduced size, and these algorithms only invoke the original dynamical and observation operators, namely, they do not require tangent operator computations, which of course is of considerable benefit when nonlinear operators are considered....

Reliable solutions of problems in the deformation theory of plasticity with respect to uncertain material function

Ivan Hlaváček (1996)

Applications of Mathematics

Maximization problems are formulated for a class of quasistatic problems in the deformation theory of plasticity with respect to an uncertainty in the material function. Approximate problems are introduced on the basis of cubic Hermite splines and finite elements. The solvability of both continuous and approximate problems is proved and some convergence analysis presented.

Remarks on Carleman estimates and exact controllability of the Lamé system

Oleg Yu. Imanuvilov, Masahiro Yamamoto (2002)

Journées équations aux dérivées partielles

In this paper we established the Carleman estimate for the two dimensional Lamé system with the zero Dirichlet boundary conditions. Using this estimate we proved the exact controllability result for the Lamé system with with a control locally distributed over a subdomain which satisfies to a certain type of nontrapping conditions.

Currently displaying 201 – 220 of 355