We give a sharp upper estimate for the response of boundary current-voltage measurements to perturbations of the admittivity in a body that are localized in space and frequency. We calculate the differential of the measurement mapping and study the$Gabor symbol$of this operator.

We consider Fourier integral operators with symbols in modulation spaces and non-smooth phase functions whose second orders of derivatives belong to certain types of modulation space. We prove continuity and Schatten–von Neumann properties of such operators when acting on$L$^{2}.

We compute the open Gromov-Witten invariants for every compact semi-Fano toric surface, i.e. a toric surface X with nef anticanonical bundle. Unlike the Fano case, this involves non-trivial obstructions in the corresponding moduli problem. As an application, an explicit expression of the superpotential W for the mirror of X is obtained, which in turn gives an explicit ring presentation of the small quantum cohomology of X. We also give a computational verification of the natural ring isomorphism between the small quantum cohomology of X and the Jacobian ring of W.

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