Simultaneous Continuation of Infinitely Many Sinks Near a Quadratic Homoclinic Tangency

We prove that the $C^3$ diffeomorphisms on surfaces, exhibiting infinitely many sinksnear the generic unfolding of a quadratic homoclinic tangency of a dissipative saddle, can be perturbed along an infinite dimensional manifold of $C^3$ diffeomorphisms such that infinitely many sinks persist simultaneously. On the other hand, if they are perturbed along one-parameter families that unfold generically the quadratic tangencies, then at most a finite number of those sinks have continuation

Deconvolution Processing for Flaw Signatures

The ultimate resolution of all ultrasonic flaw detection systems is limited by transducer response. Although the system output contains detailed information about the target structure, these details are masked by the system characteristics. Since the output can be described as the convolution of the target response and the impulse response of the system, it should- in principle - be possible to reverse this operation and extract the target response. In practice, it is found that the presence of even relatively small amounts of noise make the deconvolution process impossible. If, however, the flaw detection system has an extremely high output signal-to-noise ratio it is possible to use estimation techniques in the deconvolution process to achieve a good approximation to the actual target response. Results are presented that demonstrate these techniques applied to both simulated and experimental data. Coupling deconvolution processing with feature extraction is shown to yield an order of magnitude increase in range resolution

On stochastic sea of the standard map

Consider a generic one-parameter unfolding of a homoclinic tangency of an area preserving surface diffeomorphism. We show that for many parameters (residual subset in an open set approaching the critical value) the corresponding diffeomorphism has a transitive invariant set $\Omega$ of full Hausdorff dimension. The set $\Omega$ is a topological limit of hyperbolic sets and is accumulated by elliptic islands. As an application we prove that stochastic sea of the standard map has full Hausdorff dimension for sufficiently large topologically generic parameters.Comment: 36 pages, 5 figure

Use of the TIDier checklist to describe an online structured education programme for type 2 diabetes

Objectives: The aim of structured education for type 2 diabetes is to improve knowledge, skills and confidence in self-management. It is recommended in the UK for everyone who is newly diagnosed with type 2 diabetes. We developed an on-line programme called HeLP-Diabetes: Starting Out to address poor uptake of face-to-face structured education. The aim of this paper is to describe the intervention in line with the Template for Intervention Description and Replication guide, which calls for better reporting of interventions. Methods: The Template for Intervention Description and Replication guide provided the item headings for the description. These included the theoretical underpinning, materials, procedures, providers, and mode of delivery. Results: The programme was developed to meet NICE requirements for structured education and therefore followed a structured curriculum with four sessions covering content such as what diabetes is and how it is treated, possible complications, and how lifestyle changes can improve health. Content was delivered in text, images and video, and behaviour change techniques, self-assessment and feedback were used to help people target key health behaviours. The programme was delivered entirely online, but the team were available for support via telephone. Email feedback and reminders were sent. Conclusions: The TIDieR checklist allowed us to provide a clear structure for the description of the intervention. However, it could not capture the full complexity of the programme, and intervention developers considering using it in the future may find that it needs to be adapted to make it more specific to their intervention