New results on a classical operator

It is remarkable how the classical Volterra integral operator, which was one of the first operators which attracted mathematicians' attention, is still worth of being studied. In this essentially survey work, by collecting some of the very recent results related to the Volterra operator, we show that there are new (and not so new) concepts that are becoming known only at the present days. Discovering whether the Volterra operator satisfies or not a given operator property leads to new methods and ideas that are useful in the setting of Concrete Operator Theory as well as the one of General Operator Theory. In particular, a wide variety of techniques like summability kernels, theory of entire functions, Gaussian cylindrical measures, approximation theory, Laguerre and Legendre polynomials are needed to analyze different properties of the Volterra operator. We also include a characterization of the commutator of the Volterra operator acting on L-P[0, 1], 1

Remarks on common hypercyclic vectors

We treat the question of existence of common hypercyclic vectors for families of continuous linear operators. It is shown that for any continuous linear operator T on a complex Fréchet space X and a set ? ? R+ × C which is not of zero three-dimensional Lebesgue measure, the family {a T + b I : (a, b) ? ?} has no common hypercyclic vectors. This allows to answer negatively questions raised by Godefroy and Shapiro and by Aron. We also prove a sufficient condition for a family of scalar multiples of a given operator on a complex Fréchet space to have a common hypercyclic vector. It allows to show that if D = {z ? C : | z | < 1} and f ? H8 (D) is non-constant, then the family {z Mf{star operator} : b- 1 < | z | < a- 1} has a common hypercyclic vector, where Mf : H2 (D) ? H2 (D), Mf f = f f, a = inf {| f (z) | : z ? D} and b = sup {| f (z) | : | z | ? D}, providing an affirmative answer to a question by Bayart and Grivaux. Finally, extending a result of Costakis and Sambarino, we prove that the family {a Tb : a, b ? C {set minus} {0}} has a common hypercyclic vector, where Tb f (z) = f (z - b) acts on the Fréchet space H (C) of entire functions on one complex variable.

On the set of hypercyclic vectors for the differentiation

Let D be the differentiation operator Df = f' acting on the Fréchet space H of all entire functions in one variable with the standard (compact-open) topology. It is known since the 1950’s that the set H(D) of hypercyclic vectors for the operator D is non-empty. We treat two questions raised by Aron, Conejero, Peris and Seoane-Sepúlveda whether the set H(D) contains (up to the zero function) a non-trivial subalgebra of H or an infinite-dimensional closed linear subspace of H. In the present article both questions are answered affirmatively.

Disjoint mixing operators

Chan and Shapiro showed that each (non-trivial) translation operator acting on the Fréchet space of entire functions endowed with the topology of locally uniform convergence supports a universal function of exponential type zero. We show the existence of d-universal functions of exponential type zero for arbitrary finite tuples of pairwise distinct translation operators. We also show that every separable infinite-dimensional Fréchet space supports an arbitrarily large finite and commuting disjoint mixing collection of operators. When this space is a Banach space, it supports an arbitrarily large finite disjoint mixing collection of C0-semigroups. We also provide an easy proof of the result of Salas that every infinite-dimensional Banach space supports arbitrarily large tuples of dual d-hypercyclic operators, and construct an example of a mixing Hilbert space operator T so that (T,T2) is not d-mixing.

Cognitive inhibition and interference in dissociative indentity disorder: the effects of anxiety on specific executive functions:The effects of anxiety on specific executive functions

Using an experimentally based, computer-presented task, this study assessed cognitive inhibition and interference in individuals from the dissociative identity disorder (DID; n=12), generalized anxiety disorder (GAD; n=12) and non-clinical (n=12) populations. Participants were assessed in a neutral and emotionally negative (anxiety provoking) context, manipulated by experimental instructions and word stimuli. The DID sample displayed effective cognitive inhibition in the neutral but not the anxious context. The GAD sample displayed the opposite findings. However, the interaction between group and context failed to reach significance. There was no indication of an attentional bias to non-schema specific negative words in any sample. Results are discussed in terms of the potential benefit of weakened cognitive inhibition during anxious arousal in dissociative individuals.

BRCA1 Functions as a Differential Modulator of Chemotherapy-induced Apoptosis

We have evaluated the role played by BRCA1 in mediating the phenotypic response to a range of chemotherapeutic agents commonly used in cancer treatment. Here we provide evidence that BRCA1 functions as a differential mediator of chemotherapy-induced apoptosis. Specifically, we demonstrate that BRCA1 mediates sensitivity to apoptosis induced by antimicrotubule agents but conversely induces resistance to DNA-damaging agents. These data are supported by a variety of experimental models including cells with inducible expression of BRCA1, siRNA-mediated inactivation of endogenous BRCA1, and reconstitution of BRCA1-deficient cells with wild-type BRCA1. Most notably we demonstrate that BRCA1 induces a 10–1000-fold increase in resistance to a range of DNA-damaging agents, in particular those that give rise to double-strand breaks such as etoposide or bleomycin. In contrast, BRCA1 induces a >1000-fold increase in sensitivity to the spindle poisons, paclitaxel and vinorelbine. Fluorescence-activated cell sorter analysis demonstrated that BRCA1 mediates G2/M arrest in response to both antimicrotubule and DNA-damaging agents. However, poly(ADP-ribose) polymerase and caspase-3 cleavage assays indicate that the differential effect mediated by BRCA1 in response to these agents occurs through the inhibition or induction of apoptosis. Therefore, our data suggest that BRCA1 acts as a differential modulator of apoptosis depending on the nature of the cellular insult.