Properties of a method of fundamental solutions for the parabolic heat equation

We show that a set of fundamental solutions to the parabolic heat equation, with each element in the set corresponding to a point source located on a given surface with the number of source points being dense on this surface, constitute a linearly independent and dense set with respect to the standard inner product of square integrable functions, both on lateral- and time-boundaries. This result leads naturally to a method of numerically approximating solutions to the parabolic heat equation denoted a method of fundamental solutions (MFS). A discussion around convergence of such an approximation is included.

Assessing the impact of management concerns in e-business requirements planning in manufacturing organizations

This paper describes the application of a model, initially developed for determining the e-business requirements of a manufacturing organization, to assess the impact of management concerns on the functions generated. The model has been tested on 13 case studies in small, medium and large organizations. This research shows that the incorporation of concerns for generating the requirements for e-business functions improves the results, because they expose issues that are of relevance to the decision making process relating to e-business. Running the model with both and without concerns, and then presenting the reasons for major variances, can expose the issues and enable them to be studied in detail at the individual function/ reason level. © IFIP International Federation for Information Processing 2013.

Successful development and testing of a Method for Aggregating The Reporting of Interventions in Complex Studies (MATRICS)

Objectives: To develop a tool for the accurate reporting and aggregation of findings from each of the multiple methods used in a complex evaluation in an unbiased way. Study Design and Setting: We developed a Method for Aggregating The Reporting of Interventions in Complex Studies (MATRICS) within a gastroenterology study [Evaluating New Innovations in (the delivery and organisation of) Gastrointestinal (GI) endoscopy services by the NHS Modernisation Agency (ENIGMA)]. We subsequently tested it on a different gastroenterology trial [Multi-Institutional Nurse Endoscopy Trial (MINuET)]. We created three layers to define the effects, methods, and findings from ENIGMA. We assigned numbers to each effect in layer 1 and letters to each method in layer 2. We used an alphanumeric code based on layers 1 and 2 to every finding in layer 3 to link the aims, methods, and findings. We illustrated analogous findings by assigning more than one alphanumeric code to a finding. We also showed that more than one effect or method could report the same finding. We presented contradictory findings by listing them in adjacent rows of the MATRICS. Results: MATRICS was useful for the effective synthesis and presentation of findings of the multiple methods from ENIGMA. We subsequently successfully tested it by applying it to the MINuET trial. Conclusion: MATRICS is effective for synthesizing the findings of complex, multiple-method studies.