On Periodic Matrix-Valued Weyl-Titchmarsh Functions

We consider a certain class of Herglotz-Nevanlinna matrix-valued functions which can be realized as the Weyl-Titchmarsh matrix-valued function of some symmetric operator and its self-adjoint extension. New properties of Weyl -Titchmarsh matrix-valued functions as well as a new version of the functional model in such realizations are presented. In the case of periodic Herglotz-Nevanlinna matrix-valued functions we provide a complete characterization of their realizations in terms of the corresponding functional model. We also obtain properties of a symmetric operator and its self-adjoint extension generating periodic Weyl-Titchmarsh matrix-valued function. We study pairs of operators (a symmetric operator and its self-adjoint extension) with constant Weyl-Titchmarsh matrix-valued functions and establish connections between such pairs of operators and representations of the canonical commutation relations for unitary groups of operators in Weyl's form. As a consequence of such an approach we obtain the Stone-von Neumann theorem for two unitary groups of operators satisfying the commutation relations as well as some extension and refinement of the classical functional model for generators of those groups. Our examples include multiplication operators in weighted spaces, first and second order differential operators, as well as the Schr\"odinger operator with linear potential and its perturbation by bounded periodic potential

A mean-variance frontier in discrete and continuous time

The paper presents a mean-variance frontier based on dynamic frictionless investment strategies in continuous time. The result applies to a finite number of risky assets whose price process is given by multivariate geometric Brownian motion with deterministically varying coefficients. The derivation is based on the solution for the frontier in discrete time. Using the same multiperiod framework as Li and Ng (2000), I provide an alternative derivation and an alternative formulation of the solution. It allows for a nice asymptotic formulation of the efficient hyperbola and its underlying efficient processes that applies in continuous time.

I. African court on human and peoples’ rights, African commission on human and peoples’ rights v. Great socialist people’s Libyan Arab Jamahiriya, order for provisional measures, 25 March 2011

Africa has been struggling for years to establish a mechanism of human rights protection comparable to other international and regional mechanisms. Illiteracy and the low standards of economic development and social welfare, especially in rural areas, as well as the absence of financial resources were certainly not the best grounds to build on. Moreover, as Nmehielle notes, the creation of a human rights mechanism in Africa was equally hinged on other questions, more controversial ones, such as the existence of the concept of ‘law’ and ‘rights’ in pre-colonial Africa. In this respect, a Western-style mechanism of human rights protection would be naturally perceived with suspicion, as a form of foreign intervention

Reporting of Clinical Adverse Events Scale: a measure of doctor and nurse attitudes to adverse event reporting

Objective: To develop a validated measure of professionals' attitudes towards clinical adverse event reporting (CAER). Design: Cross-sectional survey with follow-up. Participants: 201 doctors and nurse/nurse-midwives undergoing postqualification training in Leeds, York and Hull Universities in 2003. Materials: A questionnaire which comprised 73 items extracted from interviews with professionals; a second, statistically reduced version of this questionnaire. Results: The analysis supported a 25-item questionnaire comprising five factors: blame as a consequence of reporting (six items); criteria for reporting (six items); colleagues' expectations (six items); perceived benefits of reporting events (five items); and clarity of reporting procedures (two items). The resulting questionnaire, the Reporting of Clinical Adverse Effects Scale (RoCAES), had satisfactory internal consistency (Cronbach's alpha = 0.83) and external reliability (Spearman's correlation = 0.65). The construct validity hypothesis -doctors have less positive attitudes towards CAER than nurses -was supported (t = 5.495; p < 0.0001). Conclusion: Initial development of an evidence-based, psychometrically rigorous measure of attitudes towards CAER has been reported. Following additional testing, RoCAES may be used to systematically elicit professionals' views about, and inform interventions to improve, reporting behaviour

Theoretical versus pragmatic design in qualitative research

For many years, discussions of the relative merits of generic and theoretical approaches to qualitative research have divided researchers while overshadowing the need to focus on addressing clinical questions. Drawing on the challenges of designing a study that explored parents’ experiences of living with children with hydrocephalus, the authors of this paper argue that over-adherence to, and deliberations about, the philosophical origins of qualitative methods is undermining the contributions qualitative research could make to evidence-based health care and suggest qualitative methods should stand alone