Inverting Onto Functions and Polynomial Hierarchy

In this paper we construct an oracle under which the polynomial hierarchy is infinite but there are non-invertible polynomial time computable multivalued onto functions

Electromechanical Simulation of Actively Controlled Rotordynamic Systems with Piezoelectric Actuators

Theories and tests for incorporating piezoelectric pushers as actuator devices for active vibration control are discussed. It started from a simple model with the assumption of ideal pusher characteristics and progressed to electromechanical models with nonideal pushers. Effects on system stability due to the nonideal characteristics of piezoelectric pushers and other elements in the control loop were investigated

Measurement of the transverse spatial quantum state of light at the single-photon level

We present an experimental method to measure the transverse spatial quantum state of an optical field in coordinate space at the single-photon level. The continuous-variable measurements are made with a photon-counting, parity-inverting Sagnac interferometer based on all-reflecting optics. The technique provides a large numerical aperture without distorting the shape of the wave front, does not introduce astigmatism, and allows for characterization of fully or partially coherent optical fields at the single-photon level. Measurements of the transverse spatial Wigner functions for highly attenuated coherent beams are presented and compared to theoretical predictions.Comment: 3 pages, 2 figure

Inversion of the star transform

We define the star transform as a generalization of the broken ray transform introduced by us in previous work. The advantages of using the star transform include the possibility to reconstruct the absorption and the scattering coefficients of the medium separately and simultaneously (from the same data) and the possibility to utilize scattered radiation which, in the case of the conventional X-ray tomography, is discarded. In this paper, we derive the star transform from physical principles, discuss its mathematical properties and analyze numerical stability of inversion. In particular, it is shown that stable inversion of the star transform can be obtained only for configurations involving odd number of rays. Several computationally-efficient inversion algorithms are derived and tested numerically.Comment: Accepted to Inverse Problems in this for