Generalized characteristic functions for a single-mode radiation field

We derive simple formulas for the higher-order moments of the quadrature operators operators of a two-field superposition by introducing a new generalized characteristic function depending on two complex variables. Using this formalism we investigate the preservation of higher-order squeezing during weak thermalization of an even coherent state.     

A characterization theorem for certain unions of two starshaped sets in R 2

Let S be a compact set in R ². For S simply connected, S is a union of two starshaped sets if and only if for every F finite, F bdry S, there exist a set G bdry S arbitrarily close to F and points s, t depending on G such that each point of G is clearly visible via S from one of s, t. In the case where S has at most finitely many components, the necessity of the condition still holds while the sufficiency fails.     

A search for sonoluminescence in vivo in the human cheek

In a previous experiment, sonoluminescence was observed in aerated water, especially at the pressure antinodes in the standing-wave field of a physiotherapeutic ultrasound device (Therasonic 1030). Mammalian cells in vitro showed growth inhibition when placed at the pressure antinodes but not at adjacent pressure nodes. In the light of these results, we looked for sonoluminescence in vivo when a similar standing-wave field was set up. To detect luminescence, a light guide was held against the inner surface of the human cheek. This would channel any luminescence photons to a cooled, red-sensitive photomultiplier which would quantify the light. Direct insonation of the cheek produced no detectable luminescence. Similarly when a water bag was placed against the outer surface of the cheek, and the latter was insonated through the bag, no luminescence was detected. Sonoluminescence from the water bag was, however, detected when the bag was placed against the inner surface of the cheek, showing that absorption of sound by the cheek tissue was not preventing cavitation. Further analysis showed that if cavitation had been occurring in the cheek without detection using the system employed, then the resulting sonoluminescence would have to be at most 0.025 times as intense as that produced by an equivalent volume of aerated water.     

A PDE approach to image restoration problem with observation on a meager domain

We present here a new nonlinear PDE approach to image restoration (the inpainting problem) using a meager blurred image or a finite number of observation points. To this end, one uses a least square approach with the H⁻¹ distributional metric. Some important theoretical and numerical results are provided in this paper.     

Solving chemical master equations by adaptive wavelet compression

Solving chemical master equations numerically on a large state space is known to be a difficult problem because the huge number of unknowns is far beyond the capacity of traditional methods. We present an adaptive method which compresses the problem very efficiently by representing the solution in a sparse wavelet basis that is updated in each step. The step-size is chosen adaptively according to estimates of the temporal and spatial approximation errors. Numerical examples demonstrate the reliability of the error estimation and show that the method can solve large problems with bimodal solution profiles.     

On a new chaotic system

In this paper, a novel 3D nonlinear system with chaotic behavior is considered. Our proposed system is a generalized Lorenz‐like system, with no reflections about coordinates axes. Although the considered system depends on seven real parameters, its stability is completely analyzed. Also, the presence of Hopf bifurcation is pointed out. Copyright © 2014 John Wiley & Sons, Ltd.