Lie systems: theory, generalisations, and applications

Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of mapping: the so-called superposition rule. Apart from this fundamental property, Lie systems enjoy many other geometrical features and they appear in multiple branches of Mathematics and Physics, which strongly motivates their study. These facts, together with the authors' recent findings in the theory of Lie systems, led to the redaction of this essay, which aims to describe such new achievements within a self-contained guide to the whole theory of Lie systems, their generalisations, and applications.Comment: 161 pages, 2 figure

Experimental Verification of the Number Relation at Room and Elevated Temperatures

The accuracy of the Neuber equation for predicting notch root stress-strain behavior at room temperature and at 650 C was experimentally investigated. Strains on notched specimens were measured with a non-contacting, interferometric technique and stresses were simulated with smooth specimens. Predictions of notch root stress-strain response were made from the Neuber Equation and smooth specimen behavior. Neuber predictions gave very accurate results at room temperature. However, the predicted interaction of creep and stress relaxation differed from experimentally measured behavior at 650 C

Patient perceptions of epinephrine auto-injectors: Exploring barriers to use

Background: In recent years, government initiatives have proposed that patient self-care should serve as a key resource in response to the anticipated increase in global demand for health care. However, if patients are to be empowered as self-carers, barriers to engagement must be identified and overcome. Anaphylaxis is an increasingly common life threatening allergic reaction. Patients at risk of anaphylaxis are prescribed epinephrine auto-injectors and play a crucial role in delivering their own care and management of this condition. One key recommendation is that patients routinely carry an epinephrine auto-injector with them, and deploy the device when needed. However, only a small proportion of patients that require epinephrine actually receive it. Objective: To explore the reasons why patients who have been prescribed epinephrine auto-injectors fail to adhere to self-care and management recommendations. Methods: In-depth interviews with 15 adults who have been prescribed epinephrine auto-injectors were carried out to explore the barriers that exist in the provision of effective self-care and management of anaphylaxis. Results: Inconsistent health professional advice, perceived stigma of carrying a ‘weapon-like’ device, poor device design and limited patient training were identified as barriers to carriage or use. Patients were reluctant to carry devices in public because of perceived and observed stigma and suspicion. They were happy to ignore expiry dates and some participants were confident that the emergency services would provide them with the appropriate care they needed, and therefore did not carry the device in urban areas. Conclusions and clinical implications: Improved training of patients, the public and health professionals around both the carriage and use of auto-injectors are areas for urgent attention if improved levels of self-care are to be attained. The design of epinephrine auto-injectors should also receive attention as patients often fail to carry them due to size and aesthetics. Key words: Adherence, allergy, anaphylaxis, empowerment, epinephrine, self-care, self-management, patient perspectivesThis study was funded by grant number Ref: GR/S29874/01 from the Engineering and Physical Sciences Research Council