Iterative solutions to classical second-order ordinary differential equations (2019)
Journal Article
Robin, W. (2019). Iterative solutions to classical second-order ordinary differential equations. Journal of Innovative Technology and Education, 6(1), 1-12

An elementary scheme is detailed for introducing certain basic concepts in the solution of (especially) the basic second-order ordinary differential equations of classical mathematical physics. The method proposed, an integration/iteration process, a... Read More about Iterative solutions to classical second-order ordinary differential equations.

BayesPiles: Visualisation Support for Bayesian Network Structure Learning (2018)
Journal Article
Vogogias, A., Kennedy, J., Archambault, D., Bach, B., Smith, V. A., & Currant, H. (2018). BayesPiles: Visualisation Support for Bayesian Network Structure Learning. ACM transactions on intelligent systems and technology, 10(1), Article 5. https://doi.org/10.1145/3230623

We address the problem of exploring, combining and comparing large collections of scored, directed networks for understanding inferred Bayesian networks used in biology. In this feld, heuristic algorithms explore the space of possible network solutio... Read More about BayesPiles: Visualisation Support for Bayesian Network Structure Learning.

Exploring the relationship between metacognitive and collaborative talk during group mathematical problem-solving – what do we mean by collaborative metacognition? (2018)
Journal Article
Smith, J. M., & Mancy, R. (2018). Exploring the relationship between metacognitive and collaborative talk during group mathematical problem-solving – what do we mean by collaborative metacognition?. Research in Mathematics Education, 1-23. https://doi.org/10.1080/14794802.2017.1410215

The purpose of this study was to enhance our understanding of the relationship between collaborative talk and metacognitive talk during group mathematical problem-solving. Research suggests that collaborative talk may mediate the use of metacognitive... Read More about Exploring the relationship between metacognitive and collaborative talk during group mathematical problem-solving – what do we mean by collaborative metacognition?.

On the comparison of initialisation strategies in differential evolution for large scale optimisation (2017)
Journal Article
Segredo, E., Paechter, B., Segura, C., & González-Vila, C. I. (2018). On the comparison of initialisation strategies in differential evolution for large scale optimisation. Optimization Letters, 12(1), 221-234. https://doi.org/10.1007/s11590-017-1107-z

Differential Evolution (DE) has shown to be a promising global opimisation solver for continuous problems, even for those with a large dimensionality. Different previous works have studied the effects that a population initialisation strategy has on... Read More about On the comparison of initialisation strategies in differential evolution for large scale optimisation.

Some new uniform approximate analytical representations of the Blasius function. (2015)
Journal Article
Robin, W. (2015). Some new uniform approximate analytical representations of the Blasius function. Global Journal of Mathematics, 2, 150-155

New uniform approximations of the Blasius velocity profile and Blasius function are developed from existing rational approximations of the Blasius velocity profile and of the Blasius function itself. Essentially, the existing rational approximations... Read More about Some new uniform approximate analytical representations of the Blasius function..

On compact uniform analytical approximations to the Blasius Velocity profile. (2015)
Journal Article
Robin, W. (2015). On compact uniform analytical approximations to the Blasius Velocity profile. International Mathematical Forum, 10, 311-322. https://doi.org/10.12988/imf.2015.514

It is shown that approximate analytical representations of the Blasius function may be developed by using the error function, erf (ax), for positive constant a, as a basic compact approximate form for the derivative of the Blasius function, that is,... Read More about On compact uniform analytical approximations to the Blasius Velocity profile..

On the use of inclusion structure in fuzzy clustering algorithm in case of Gaussian membership functions (2015)
Journal Article
Nefti-Meziani, S., Oussalah, M., & Soufian, M. (2015). On the use of inclusion structure in fuzzy clustering algorithm in case of Gaussian membership functions. Journal of Intelligent and Fuzzy Systems, 28(4), 1477-1493. https://doi.org/10.3233/IFS-141407

This article addresses the problem of incorporating an inclusion structure in the general class of fuzzy c-means algorithms. Conventionally, all the classes of fuzzy clustering algorithms involve a distance structure as the main tool to compute the i... Read More about On the use of inclusion structure in fuzzy clustering algorithm in case of Gaussian membership functions.

Experiences of using Audio Feedback in Engineering Mathematics Modules. (2015)
Presentation / Conference Contribution
Durkacz, K., & Mowat, E. (2015, June). Experiences of using Audio Feedback in Engineering Mathematics Modules. Presented at Barriers and Enablers to Learning Maths: Enhancing Learning and Teaching for All Learners

The main purpose of the Engineering Mathematics modules at Edinburgh Napier University is to explain the underpinning mathematical techniques, in areas such as calculus, series and vectors, which are required by the engineering modules. These modules... Read More about Experiences of using Audio Feedback in Engineering Mathematics Modules..

The Engineering Peer Tutors. (2015)
Presentation / Conference Contribution
Durkacz, K. (2015, June). The Engineering Peer Tutors. Paper presented at Scottish Maths Support Network meeting

Series Solution of Second-Order Linear Homogeneous Ordinary Differential Equations via Complex Integration (2014)
Journal Article
Robin, W. (2014). Series Solution of Second-Order Linear Homogeneous Ordinary Differential Equations via Complex Integration. International Mathematical Forum, 9, 967-976. https://doi.org/10.12988/imf.2014.4492

A method is presented, with standard examples, based on an elementary complex integral expression, for developing, in particular, series solutions for second-order linear homogeneous ordinary differential equations. Straightforward to apply, the meth... Read More about Series Solution of Second-Order Linear Homogeneous Ordinary Differential Equations via Complex Integration.

On the procedure for the series solution of certain general-order homogeneous linear differential equations via the complex integration method. (2014)
Journal Article
Robin, W. (2014). On the procedure for the series solution of certain general-order homogeneous linear differential equations via the complex integration method. Nonlinear Analysis and Differential Equations, 2, 155-171. https://doi.org/10.12988/nade.2014.4712

The theory of series solutions for two important classes of the general higher-order linear homogeneous ordinary differential equation is developed ab initio, using an elementary complex integral expression derived and applied in previous papers [10,... Read More about On the procedure for the series solution of certain general-order homogeneous linear differential equations via the complex integration method..

Ladder-Operator Factorization and the Bessel Differential Equations (2014)
Journal Article
Robin, W. (2014). Ladder-Operator Factorization and the Bessel Differential Equations. International Mathematical Forum, 9, 71-80. https://doi.org/10.12988/imf.2014.311214

We present an alternative approach to the discussion of Bessel equations and Bessel functions, through an elementary factorization method. The various Bessel equations are represented by a single parameterized form and, after a standard transformatio... Read More about Ladder-Operator Factorization and the Bessel Differential Equations.

Frobenius Series Solution of Fuchs Second-Order Ordinary Differential Equations via Complex Integration (2014)
Journal Article
Robin, W. (2014). Frobenius Series Solution of Fuchs Second-Order Ordinary Differential Equations via Complex Integration. International Mathematical Forum, 9, 953-965. https://doi.org/10.12988/imf.2014.4491

A method is presented (with standard examples) based on an elementary complex integral expression, for developing Frobenius series solutions for second-order linear homogeneous ordinary Fuchs differential equations. The method reduces the task of fin... Read More about Frobenius Series Solution of Fuchs Second-Order Ordinary Differential Equations via Complex Integration.

On the procedure for the series solution of second-order homogeneous linear differential equation via the complex integration method (2014)
Journal Article
Robin, W. (2014). On the procedure for the series solution of second-order homogeneous linear differential equation via the complex integration method. Nonlinear Analysis and Differential Equations, 2(4), 173-188. https://doi.org/10.12988/nade.2014.4713

The theory of series solutions for second-order linear homogeneous ordinary differential equation is developed ab initio, using an elementary complex integral expression (based on Herrera’ work [3]) derived and applied in previous papers [8, 9]. As w... Read More about On the procedure for the series solution of second-order homogeneous linear differential equation via the complex integration method.

On the Rodrigues Formula Solution of the Hypergeometric-Type Differential Equation (2013)
Journal Article
Robin, W. (2013). On the Rodrigues Formula Solution of the Hypergeometric-Type Differential Equation. International Mathematical Forum, 8, 1455-1466. https://doi.org/10.12988/imf.2013.37133

In this paper, we present a new systematic approach to the solution of the hypergeometric-like differential equation and its associated equation. The method produces, tout court, the general solution of these equations in the form of a combination of... Read More about On the Rodrigues Formula Solution of the Hypergeometric-Type Differential Equation.

Some Remarks on the Homotopy-Analysis Method and Series Solutions to the Blasius Equation (2013)
Journal Article
Robin, W. (2013). Some Remarks on the Homotopy-Analysis Method and Series Solutions to the Blasius Equation. International Mathematical Forum, 8, 1205-1213. https://doi.org/10.12988/imf.2013.3478

We present an new angle on the introduction of the homotopy-analysis method of Liao [6]. The homotopy-analysis method is then applied to produce a series solution of the Blasius problem in two different ways and comparison made with the work of Wang... Read More about Some Remarks on the Homotopy-Analysis Method and Series Solutions to the Blasius Equation.

Sharing Assessment across Institutions and VLEs. (2013)
Presentation / Conference Contribution
Milne, S., McVey, M., Barr, N., Davis, M., Mason, J., Greenhalgh, R., Barnes, S., Durkacz, K., & Fletcher, L. (2013, September). Sharing Assessment across Institutions and VLEs. Paper presented at CETL-MSOR Conference 2013

IMS Question and Test Interoperability version 2.1 (QTI 2.1) provides
a flexible and powerful way of specifying computer delivered assessment
questions and tests in an XML format that can be used by different
delivery systems, including Moodle. Th... Read More about Sharing Assessment across Institutions and VLEs..

Optical fibre-based sensor technology for humidity and moisture measurement: Review of recent progress (2013)
Journal Article
Alwis, L., Sun, T., & Grattan, K. (2013). Optical fibre-based sensor technology for humidity and moisture measurement: Review of recent progress. Measurement : journal of the International Measurement Confederation, 46(10), 4052-4074. https://doi.org/10.1016/j.measurement.2013.07.030

Humidity and moisture sensing is becoming increasingly important in industry and through a wide spectrum of applications and a review of research activity in the field across a range of technologies was presented previously by some of the authors. Re... Read More about Optical fibre-based sensor technology for humidity and moisture measurement: Review of recent progress.

The Scottish Mathematics Support Network (2012)
Journal Article
Ahmed, S., & Durkacz, K. (2012). The Scottish Mathematics Support Network. MSOR Connections, 12, 42-44. https://doi.org/10.11120/msor.2012.12020042

The preliminary meeting of the Scottish Mathematics Support Network was held at the University of St Andrews on 18 July 2008. The aim of the meeting was to initialise a support network for people working in Scottish Universities and Colleges who were... Read More about The Scottish Mathematics Support Network.

On the Rodrigues’ Formula Approach to Operator Factorization (2012)
Journal Article
Robin, W. (2012). On the Rodrigues’ Formula Approach to Operator Factorization. International Mathematical Forum, 7(45-48), 2333-2351

In this paper, we derive general formulae that reproduce well-known instances of recurrence relations for the classical orthogonal polynomials as special cases. These recurrence relations are derived, using only elementary mathematics, directly from... Read More about On the Rodrigues’ Formula Approach to Operator Factorization.