The resonance spectrum of the cusp map in the space of analytic functions

We prove that the Frobenius-Perron operator $U$ of the cusp map $F:[-1,1]\to [-1,1]$, $F(x)=1-2 x^{1/2}$ (which is an approximation of the Poincare section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any $q\in (0,1)$ the spectrum of $U$ in the Hardy space in the disk $\{z\in C:|z-q|

On effective linearly ordered sets of comparison functions

Both the existence and the non-existence of a linearly ordered (by certain natural order relations) effective set of comparison functions (=dense comparison classes) are compatible with the ZFC axioms of set theory.

Analysis procedure for calculation of electron energy distribution functions from incoherent Thomson scattering spectra

Incoherent Thomson scattering (ITS) provides a nonintrusive diagnostic for the determination of one-dimensional (1D) electron velocity distribution in plasmas. When the ITS spectrum is Gaussian its interpretation as a three-dimensional (3D) Maxwellian velocity distribution is straightforward. For more complex ITS line shapes derivation of the corresponding 3D velocity distribution and electron energy probability distribution function is more difficult. This article reviews current techniques and proposes an approach to making the transformation between a 1D velocity distribution and the corresponding 3D energy distribution. Previous approaches have either transformed the ITS spectra directly from a 1D distribution to a 3D or fitted two Gaussians assuming a Maxwellian or bi-Maxwellian distribution. Here, the measured ITS spectrum transformed into a 1D velocity distribution and the probability of finding a particle with speed within 0 and given value v is calculated. The differentiation of this probability function is shown to be the normalized electron velocity distribution function. (C) 2003 American Institute of Physics.

Selective catalytic reduction of O-2 with excess H-2 in the presence of C2H4 or C3H6

The selective reduction of molecular oxygen with excess H-2 in the presence of alkenes was achieved successfully for the first time: silver supported on alumina catalysts exhibited full conversion of O-2 at temperature as low as 50 degrees C, while the conversion of ethene or propene remained essentially zero up to 250 degrees C.

Hierarchical synthesis of complex DSP functions on FPGAs

SoC systems are now being increasingly constructed using a hierarchy of subsystems or silicon Intellectual Property (IP) cores. The key challenge is to use these cores in a highly efficient manner which can be difficult as the internal core structure may not be known. A design methodology based on synthesizing hierarchical circuit descriptions is presented. The paper employs the MARS synthesis scheduling algorithm within the existing IRIS synthesis flow and details how it can be enhanced to allow for design exploration of IP cores. It is shown that by accessing parameterised expressions for the datapath latencies in the cores, highly efficient FPGA solutions can be achieved. Hardware sharing at both the hierarchical and flattened levels is explored for a normalized lattice filter and results are presented.