For given $\epsilon>0$ and $b\in \mathbb {R}^m$, we say that a real $m\times n$ matrix A is $\epsilon $-badly approximable for the target b if

$$ \begin{align*}\liminf_{q\in\mathbb{Z}^n, \|q\|\to\infty} \|q\|^n \langle Aq-b\rangle^m \geq \epsilon,\end{align*} $$

$\langle \cdot \rangle $

$\epsilon $

$\epsilon $

$\epsilon $

We prove an effective estimate with a power saving error term for the number of square-tiled surfaces in a connected component of a stratum of quadratic differentials whose vertical and horizontal foliations belong to prescribed mapping class group orbits and which have at most L squares. This result strengthens asymptotic counting formulas in the work of Delecroix, Goujard, Zograf, Zorich, and the author.

Increasing interest from stakeholders has brought about a new emphasis on risk regulation in the oil and gas industry. Our basis for this work is the offshore oil and gas industry, which is composed of major operators, entrepreneurs and contractors working globally, but we focus on Norwegian and US activities. The fundamental strategies, institutions, legal traditions and explanations of regulation are reviewed and, together with empirical data, a novel model with the means of identifying “effective” regulation has been developed. The model presented here incorporates three dimensions: the industry’s intentions; their resources and expertise and trust in the regulator (and vice versa: the regulator’s trust in the industry); and the space where functional respective normative rules are deemed most effective.

Literature pertaining to cognitive behavioural therapy (CBT) supervision is limited, particularly about CBT supervision during training. This exploratory study outlines the thoughts of supervisors and supervisees in a training context about which elements make supervision effective. Four supervisees and four experienced CBT supervisors (all from a CBT training programme and independent of one another) were interviewed and asked to consider what makes CBT supervision during training effective. Their responses were evaluated using thematic analysis (TA) and key themes identified. The fit with existing literature was considered via the use of an adapted Delphi poll. Two main themes, containing seven subthemes, were identified from the thematic analysis: ‘supervision as structured learning’ and ‘supervisory relations and process’. The adapted Delphi poll was divided into six categories denoting important characteristics of CBT supervision: (1) the supervisory relationship, (2) ethical factors, (3) generic supervisory skills, (4) mirroring the CBT approach, (5) the supervisor’s knowledge and (6) addressing difficulties. There was a good fit between the TA themes and the Delphi categories. For those engaging in CBT supervision, establishing a structure that mirrors a CBT session, alongside a supportive supervisory alliance, may promote effective CBT supervision during training.

This is a summary of the presentations and discussion of Panel 2.1 of the Conference, Health Aspects of the Tsunami Disaster in Asia, convened by the World Health Organization (WHO) in Phuket, Thailand, 04–06 May 2005. The topics discussed included issues related to assessing needs and measuring impact as pertaining to the responses to the damage created by the Tsunami. It is presented in the following major sections: (1) key questions; (2) assessing needs; (3) measuring impact; and (4) lessons learned and recommendations.

We examine how the use of typical techniques from non-convex vector variational problems can help in understanding optimal design problems in conductivity. After describing the main ideas of the underlying analysis and providing some standard material in an attempt to make the exposition self-contained, we show how those ideas apply to a typical optimal desing problem with two different conducting materials. Then we examine the equivalent relaxed formulation to end up with a new problem whose numerical simulation leads to approximated optimal configurations. We include several such simulations in 2d and 3d.

Given $E$, an elliptic curve defined over $K$, a field of positive characteristic, provided that $j$, the Weierstrass $j$-invariant, is not an element of $K^p$, we construct explicitly, that is, we give by a closed form formula, a non-trivial homomorphism, $\mu:E(K) \rightarrow K^+$, from the group of $K$-rational points of $E$ to $K^+$, the additive group of $K$. In the course of our analysis we discover a canonical differential, $\omega_q \in \Omega; K|{\bb F}_p$, associated to $E$ and we relate it to the differential $dq/q$ associated to the Tate curve. If the transcendence degree of $K$ over ${\bb F}_p$ is equal to one, as for example is the case for function fields in one variable, then $\mu$ is a $p$-descent map, that is, its kernel is equal to $pE(K)$ and the explicit formula for $\mu$ can be used to provide effective proofs of analogues of classical theorems on elliptic curves. For example, in the author's thesis at The University of Texas at Austin the analogue of Siegel's Theorem on the finiteness of integral points of $E(K)$ is proved effectively.