On weak and strong Peano theorems

We say that the Peano theorem holds for a topological vector space $E$ if, for any continuous mapping $f : {\Bbb R}\times E \to E$ and any $(t(0), x(0))$ is an element of ${\Bbb R}\times E$, the Cauchy problem $\dot x(t) = f(t,x(t))$, $x(t(0)) = x(0)$, has a solution in some neighborhood of $t(0)$. We say that the weak version of Peano theorem holds for $E$ if, for any continuous map $f : {\Bbb R}\times E \to E$, the equation $\dot x(t) = f (t, x(t))$ has a solution on some interval. We construct an example (answering a question posed by S. G. Lobanov) of a Hausdorff locally convex topological vector space E for which the weak version of Peano theorem holds and the Peano theorem fails to hold. We also construct a Hausdorff locally convex topological vector space E for which the Peano theorem holds and any barrel in E is neither compact nor sequentially compact.

Thermodynamics of trajectories and local fluctuation theorems for harmonic quantum networks

We present a general method to undertake a thorough analysis of the thermodynamics of the quantum jump trajectories followed by an arbitrary quantum harmonic network undergoing linear and bilinear dynamics. The approach is based on the phase-space representation of the state of a harmonic network. The large deviation function associated with this system encodes the full counting statistics of exchange and also allows one to deduce for fluctuation theorems obeyed by the dynamics. We illustrate the method showing the validity of a local fluctuation theorem about the exchange of excitations between a restricted part of the environment (i.e., a local bath) and a harmonic network coupled with different schemes.

Trauma and Family Therapy: Reflections on September 11 from Northern Ireland

This article draws on the author's experience of living and working in Belfast, Northern Ireland. Connections between the traumatic events of September 11 and the situation in the north of Ireland of ongoing civil conflict and violence are developed and aspects of therapeutic practice are described. Coping with the effects of trauma presents systemic therapists with multiple and complex challenges in whatever sociopolitical context they practice. A therapist stance that combines flexibility and openness of attitude with the creative use of therapeutic practices, including those from other modalities, will assist systemic therapists in rising to these challenges.

Cryopreservation of human semen and prepared sperm: effects on motility parameters and DNA integrity

Objective: To investigate effects of cryopreservation on sperm motility and DNA integrity. Design: Pre-cryopreservation and post-cryopreservation analysis of motility and DNA integrity of semen and prepared sperm samples. Setting: A hospital andrology laboratory. Patient(s): Forty men attending the Regional Fertility Centre, Belfast, Northern Ireland. Intervention(s): Each sample was divided, and an aliquot was frozen unprepared. Remaining aliquots were prepared by Percoll density centrifugation (95.0:47.5) or direct swim-up procedure and divided into aliquots to allow direct comparison of fresh and frozen semen and prepared sperm (frozen with or without the addition of seminal plasma) from the same ejaculate. Samples were frozen by static-phase vapor cooling and being plunged into liquid nitrogen. Thawing was carried out at room temperature. Main Outcome Measure(s): Sperm DNA integrity was determined using a modified alkaline single cell gel electrophoresis (comet) assay, and motility was determined using computer-assisted semen analysis. Result(s): Sperm frozen unprepared in seminal fluid appeared more resistant to freezing damage than frozen prepared sperm. Further improvements can be achieved by selecting out the subpopulation of sperm with best motility and DNA integrity and freezing these sperm in seminal plasma, making this the optimal procedure. Conclusion(s): Freezing sperm in seminal plasma improves postthaw motility and DNA integrity.