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.

Some results on solvability of ordinary linear differential equations in locally convex spaces

Let $\Gamma$ be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem $\dot x = Ax$, $x(0) = x_0$ with respect to functions $x: R\to E$. It is proved that if $E\in \Gamma$, then $E\times R^A$ is-an-element-of $\Gamma$ for an arbitrary set $A$. It is also proved that a topological product of infinitely many infinite-dimensional Frechet spaces, each not isomorphic to $\omega$, does not belong to $\Gamma$.

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.

Deficiencies of double-strand break repair factors and effects on mutagenesis in directly gamma-irradiated and medium-mediated bystander human lymphoblastoid cells

Using RNA interference techniques to knock down key proteins in two major double-strand break (DSB) repair pathways (DNA-PKcs for nonhomologous end joining, NHEJ, and Rad54 for homologous recombination, HR), we investigated the influence of DSB repair factors on radiation mutagenesis at the autosomal thymidine kinase (TK) locus both in directly irradiated cells and in unirradiated bystander cells. We also examined the role of p53 (TP53) in these processes by using cells of three human lymphoblastoid cell lines from the same donor but with differing p53 status (TK6 is p53 wild-type, NH32 is p53 null, and WTK1 is p53 mutant). Our results indicated that p53 status did not affect either the production of radiation bystander mutagenic signals or the response to these signals. In directly irradiated cells, knockdown of DNA-PKcs led to an increased mutant fraction in WTK1 cells and decreased mutant fractions in TK6 and NH32 cells. In contrast, knockdown of DNA-PKcs led to increased mutagenesis in bystander cells regardless of p53 status. In directly irradiated cells, knockdown of Rad54 led to increased induced mutant fractions in WTK1 and NH32 cells, but the knockdown did not affect mutagenesis in p53 wild-type TK6 cells. In all cell lines, Rad54 knockdown had no effect on the magnitude of bystander mutagenesis. Studies with extracellular catalase confirmed the involvement of H2O2 in bystander signaling. Our results demonstrate that DSB repair factors have different roles in mediating mutagenesis in irradiated and bystander cells. (C) 2008 by Radiation Research Society.

Gamma ray-induced bystander effect in tumour glioblastoma cells: a specific study on cell survival, cytokine release and cytokine receptors.

Recent experimental evidence has challenged the paradigm according to which radiation traversal through the nucleus of a cell is a prerequisite for producing genetic changes or biological responses. Thus, unexposed cells in the vicinity of directly irradiated cells or recipient cells of medium from irradiated cultures can also be affected. The aim of the present study was to evaluate, by means of the medium transfer technique, whether interleukin-8 and its receptor (CXCR1) may play a role in the bystander effect after gamma irradiation of T98G cells in vitro. In fact the cell specificity in inducing the bystander effect and in receiving the secreted signals that has been described suggests that not only the ability to release the cytokines but also the receptor profiles are likely to modulate the cell responses and the final outcome. The dose and time dependence of the cytokine release into the medium, quantified using an enzyme linked immunosorbent assay, showed that radiation causes alteration in the release of interleukin-8 from exposed cells in a dose-independent but time-dependent manner. The relative receptor expression was also affected in exposed and bystander cells.