A short proof of existence of disjoint hypercyclic operators

We give a short proof of existence of disjoint hypercyclic tuples of operators of any given length on any separable infinite dimensional Fr\'echet space. Similar argument provides disjoint dual hypercyclic tuples of operators of any length on any infinite dimensional Banach space with separable dual.

Operators, commuting with the Volterra operator, are not weakly supercyclic

We prove that any bounded linear operator on $L_p[0,1]$ for $1\leq p

Utility, Caller, and Patient Profile of a Novel Chemotherapy Telephone Helpline Service Within a Regional Cancer Centre in Northern Ireland

Background: The telephone is an accepted and useful means of communication for the management of patient care. The Chemotherapy Telephone Helpline (CTH) service, located in a large inner-city Trust within the United Kingdom, is a unique nurse-led service within Northern Ireland.

Objective: The objective of the study was to investigate the utility, caller, and patient profile of a novel CTH.

Methods: This was a retrospective study of telephone contacts during 2007 to the CTH. Calls were categorized by caller and patient characteristics, reason for call, and subsequent action.

Results: A total of 7498 calls were made to the CTH during 2007. Of these, 25.6% occurred outside 8AM-4PM. Callers included patients (45.8%), lay carers (31%), and health care professionals (20.5%); 35.2% of calls concerned patients with polysymptomatic problems; 36.8% of calls led directly to patients being medically assessed.

Conclusions: The utility of the CTH service confirms the need of this nurse-led service. This service facilitates access to specialist advice and support for patients, their families, and allied health care professionals.

Implications for Practice: The international significance of these findings for practice includes its demonstration of the multifaceted symptom experience of patients receiving chemotherapy and highlights the importance of rapid access to specialist cancer services for patients and their lay and professional carers. In addition, it demonstrates the capacity of helplines to identify gaps in professional skills and training.

Telephone survey evaluation of the educational impact of a distance learning course

The educational impact of a distance learning (DL) course entitled ''Health Screening for Health Promotion, was investigated using a telephone questionnaire survey. An introduction to the DL course was distributed to all community pharmacists in England (16,400); the main body of the course, on which pharmacists were examined, was distributed free of charge to all pharmacists who requested it (1,485). Pharmacists participating in the survey (868) were organized by random selection into groups and stratified according to age, sex and postcode. A matched control group was randomly drawn from those pharmacists who had not participated in the course. The DL course improved pharmacists' knowledge about health screening/health promotion issues (e.g., mean score of 66 percent achieved by a group who had completed the course; 51 percent achieved by the control group; P<0.001). Factors influencing score achieved included sex and year of registration. Males performed better than females (P<0.008) while performance decreased with number of years on the register (P<0.001).

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.

Mixing operators on spaces with weak topology

We prove that a continuous linear operator T on a topological vector space X with weak topology is mixing if and only if the dual operator T' has no finite dimensional invariant subspaces. This result implies the characterization of hypercyclic operators on the space $\omega$ due to Herzog and Lemmert and implies the result of Bayart and Matheron, who proved that for any hypercyclic operator T on $\omega$, $T\oplus T$ is also hypercyclic.

On supercyclicity of operators from a supercyclic semigroup

We show that for every supercyclic strongly continuous operator
semigroup $\{T_t\}_{t\geq 0}$ acting on a complex $\F$-space, every
$T_t$ with $t>0$ is supercyclic. Moreover, the set of supercyclic
vectors of $T_t$ does not depend on the choice of $t>0$.

Cyclic behaviour of Volterra composition operators

We determine the cyclic behaviour of Volterra composition operators, which are defined as $(V_\phif)(x) =\int_0^{\phi(x)}f(t) dt$, $f ? L^p[0, 1]$, 1\leq p <\infty$,
where $?$ is a measurable self-map of [0, 1]. The cyclic behaviour of $V_\phi$ is essentially determined by the behaviour of the inducing symbol $\phi$ at 0 and at 1. As a particular result, we provide new examples of quasinilpotent supercyclic operators, which extend and complement previous ones of Hector Salas.

Hypercyclic tuples of operators on $C^n$ and $R^n$

A tuple $(T_1,\dots,T_n)$ of continuous linear operators on a topological vector space $X$ is called hypercyclic if there is $x\in X$ such that the the orbit of $x$ under the action of the semigroup generated by $T_1,\dots,T_n$ is dense in $X$. This concept was introduced by N.~Feldman, who have raised 7 questions on hypercyclic tuples. We answer those 4 of them, which can be dealt with on the level of operators on finite dimensional spaces. In
particular, we prove that the minimal cardinality of a hypercyclic tuple of operators on $\C^n$ (respectively, on $\R^n$) is $n+1$ (respectively, $\frac n2+\frac{5+(-1)^n}{4}$), that there are non-diagonalizable tuples of operators on $\R^2$ which possess an orbit being neither dense nor nowhere dense and construct a hypercyclic 6-tuple of operators on $\C^3$ such that every operator commuting with each member of the tuple is non-cyclic.

Hypercyclic operators on countably dimensional spaces

According to Grivaux, the group GL(X) of invertible linear operators on a separable infinite dimensional Banach space X acts transitively on the set s (X) of countable dense linearly independent subsets of X. As a consequence, each A? s (X) is an orbit of a hypercyclic operator on X. Furthermore, every countably dimensional normed space supports a hypercyclic operator. Recently Albanese extended this result to Fréchet spaces supporting a continuous norm. We show that for a separable infinite dimensional Fréchet space X, GL(X) acts transitively on s (X) if and only if X possesses a continuous norm. We also prove that every countably dimensional metrizable locally convex space supports a hypercyclic operator.

Responding to crisis: When the telephone fails

The world is changing. Advances in telecommunications have meant that the world is shrinking – data can be moved across continents in the time it takes to send an email or access the cloud. Although developments such as these highlight the extent of scientific and technological evolution, in terms of legal liability, questions must be asked as to the capacity of our legal structures to evolve accordingly.

This article looks at how emergency telephone provision and any shift to VoIP systems might fit with existing tort liability and associated duty implications. It does so by analysing the technology through the principles that signpost UK tort law. This article recognises that as an emerging area, the legal liability implications have not yet been discussed in any great detail. The aim of this article therefore is to introduce the area, encourage debate and consider the issues that may become increasingly relevant as these types of technologies become industrial standards.

Self-reported use of natural health products:A cross-sectional telephone survey in older Ontarians

Background: The self-reported use of natural health products (NHPs) (herbal products and vitamin and mineral supplements) has increased over the past decade in Canada. Because the elderly population might have comorbidities and concurrently administered medications, there is a need to explore the perceptions and behaviors associated with NHPs in this age group. Objective: The goal of this study was to assess the use of NHPs in a cohort of older Canadian residents and the characteristics, perceptions, and behaviors associated with NHP use. Methods: Survey participants aged =60 years were randomly selected from telephone listings in the area of greater Hamilton, Ontario, Canada. Data were collected using a standardized computer-assisted telephone interview system. Self-reported data covering 7 domains were collected: (1) demographics; (2) self-reported 12-month NHP use; (3) reasons for NHP use; (4) self-reported 12-month prescription medication use; (5) expenditures on NHPs; (6) patient-reported adverse events and drug-NHP interactions; and (7) perceptions of physicians' attitudes regarding NHPs. Descriptive statistics were used to compare the characteristics of NHP users with those of nonusers and to assess the characteristics of NHP users across these 7 domains. Multivariate regression analysis was conducted to determine the demographic variables that might be associated with NHP user status. Results: Of 2528 persons identified as age =60 years, 1206 (48%) completed the telephone interview. Six hundred sixteen of these respondents (51%) reported the use of =1 NHP during the previous 12 months. On the initial univariate analysis, younger age and higher income were significantly associated with reporting NHP use (mean age, users vs nonusers, 71.1 vs 72.7 years, respectively; 95% CI, 1.02-1.06; P <0.001; income more than Can $26,000 was 28% and 22% in users and nonusers, respectively; P = 0.028). One hundred seventy of 616 users (28%) used an NHP to treat the same condition for which they were concurrently receiving a prescription medication, and 43 (25%) had not informed their physicians about their NHP use. Patients' characteristics such as sex, education, smoking status, and self-reported health status did not differ significantly between users and nonusers. In individuals who regularly spent money to purchase NHPs (n = 394), the mean cost was $20.38/mo. NHP expenditure was not significantly associated with age, sex, or income. Conclusion: Based on these findings, a substantial proportion of those Ontarians aged =60 years reported NHP use, and there is a need for greater communication with physicians to avoid potential drug-NHP interactions. © 2009 Excerpta Medica Inc. All rights reserved.