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Trained Hopfield neural networks need not be black-boxes (1999)
Presentation / Conference Contribution
Craddock, R., & Kambhampati, C. (1999, June). Trained Hopfield neural networks need not be black-boxes. Presented at Proceedings of the 1999 American Control Conference, San Diego, CA, USA

Displacement encoder using sine micro-window grating (1999)
Journal Article
Wang, C., Ma, X., Zhang, G., & Guo, S. (1999). Displacement encoder using sine micro-window grating. Acta Optica Sinica, 19(8), 1153-1157

A novel displacement encoder, employing a sine micro-window grating and featuring high quality signals free from harmonic errors, was developed. The sine micro-window grating is a special component composed of arrays of micro-elements with a sine win... Read More about Displacement encoder using sine micro-window grating.

Numerical computation and analysis of the Titchmarsh-Weyl mα(λ)  function for some simple potentials (1999)
Journal Article
Witwit, M. R. M., Gordon, N. A., & Killingbeck, J. (1999). Numerical computation and analysis of the Titchmarsh-Weyl mα(λ)  function for some simple potentials. Journal of Computational and Applied Mathematics, 106(1), 131-143. https://doi.org/10.1016/S0377-0427%2899%2900061-8

This article is concerned with the Titchmarsh-Weyl mα(λ) function for the differential equation d2y/dx2+[-q(x)]y=0. The test potential q(x)=x2, for which the relevant mα(λ) functions are meromorphic, having simple poles at the points =4k+1 and =4k+3,... Read More about Numerical computation and analysis of the Titchmarsh-Weyl mα(λ)  function for some simple potentials.

Deconstruction of fractals and its implications for cartographic education (1999)
Journal Article
Visvalingam, M. (1999). Deconstruction of fractals and its implications for cartographic education. The Cartographic journal, 36(1), 15-29. https://doi.org/10.1179/caj.1999.36.1.15

The research reported here was designed for two reasons: firstly, to involve anyone with an interest in cartographic visualization to participate in eliciting cartographic knowledge and to provide them with the opportunity to contribute their practic... Read More about Deconstruction of fractals and its implications for cartographic education.

Point transfer matrices for the Schrödinger equation: The algebraic theory (1999)
Journal Article
Gordon, N. A., & Pearson, D. B. (1999). Point transfer matrices for the Schrödinger equation: The algebraic theory. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 129(4), 717-732. https://doi.org/10.1017/S030821050001310X

This paper deals with the theory of point interactions for the one-dimensional Schrödinger equation. The familiar example of the δ5-potential V(x) = gδ(x - x 0 ), for which the transfer matrix across the singularity (point transfer matrix) is given b... Read More about Point transfer matrices for the Schrödinger equation: The algebraic theory.

Calculations for double-well potentials of perturbed oscillator type in three-dimensional systems using the Hill-determinant approach (1998)
Journal Article
Witwit, M., & Gordon, N. (1998). Calculations for double-well potentials of perturbed oscillator type in three-dimensional systems using the Hill-determinant approach. Canadian Journal of Physics, 76(8), 609-620. https://doi.org/10.1139/cjp-76-8-609

A determination of the eigenvalues for a three-dimensional system is made by expanding the potential functionV(x,y,z;Z2, λ,β)= ?Z2[x2+y2+z2]+λ {x4+y4+z4+2β[x2y2+x2z2+y2z2]}, around its minimum. In this paper the results of extensive numerical calcula... Read More about Calculations for double-well potentials of perturbed oscillator type in three-dimensional systems using the Hill-determinant approach.

Linear sections of GL(4, 2) (1998)
Journal Article
Gordon, N. A., Lunardon, G., & Shaw, R. (1998). Linear sections of GL(4, 2). Bulletin of the Belgian Mathematical Society, Simon Stevin, 5(2-3), 287-311. https://doi.org/10.36045/bbms/1103409012

For V = V (n; q); a linear section of GL(V ) = GL(n; q) is a vector subspace S of the n 2 -dimensional vector space End(V ) which is contained in GL(V ) [ f0g: We pose the problem, for given (n; q); of classifying the di erent kinds of maximal linear... Read More about Linear sections of GL(4, 2).

Calculating energy levels of a double-well potential in a two- dimensional system by expanding the potential function around its minimum (1997)
Journal Article
Witwit, M. R. M., & Gordon, N. A. (1997). Calculating energy levels of a double-well potential in a two- dimensional system by expanding the potential function around its minimum. Canadian Journal of Physics, 75(10), 705-714. https://doi.org/10.1139/p97-023

A determination of the eigenvalues for a three-dimensional system is made by expanding the potential functionV(x,y,z;Z2, λ,β)= ?Z2[x2+y2+z2]+λ {x4+y4+z4+2β[x2y2+x2z2+y2z2]}, around its minimum. In this paper the results of extensive numerical calcula... Read More about Calculating energy levels of a double-well potential in a two- dimensional system by expanding the potential function around its minimum.

Stable linearization using multilayer neural networks (1996)
Presentation / Conference Contribution
Delgado, A., Kambhampati, C., & Warwick, K. (1996, September). Stable linearization using multilayer neural networks. Presented at UKACC International Conference on Control. Control '96, Exeter, UK

The main limitation of linearization theory that prevents its application in practical problems is the need for an exact knowledge of the plant. This requirement is eliminated and it is shown that a multilayer network can synthesise the state feedbac... Read More about Stable linearization using multilayer neural networks.

A cognitive approach to road recognition with novel feature indicators (1996)
Journal Article
Varley, D., Visvalingam, M., & Wright, C. (1996). A cognitive approach to road recognition with novel feature indicators. Computer Journal, 39(9), 751-756. https://doi.org/10.1093/comjnl/39.9.751

This paper outlines a simple strategy for recognition of prototypical cases of urban roads from their outline forms alone. Two new form indicators, namely exits and occupancy, are used together with average width to label regions as roads. They prove... Read More about A cognitive approach to road recognition with novel feature indicators.

Mathematica and finite geometry (1995)
Presentation / Conference Contribution
Gordon, N. Mathematica and finite geometry. Presented at International Mathematica Symposium

We describe the use of Mathematica in the investigation of some aspects of finite geometry, in particular we look at an example of finding a single polynomial function corresponding to a set of polynomial functions, and an example of finding the PGL(... Read More about Mathematica and finite geometry.

Stable forward shooting for eigenvalues and expectation values (1995)
Journal Article
Killingbeck, J. P., Gordon, N. A., & Witwit, M. R. M. (1995). Stable forward shooting for eigenvalues and expectation values. Physics Letters A, 206(5-6), 279-282. https://doi.org/10.1016/0375-9601%2895%2900632-d

Internal differentiation techniques are used to produce a simple but highly accurate forwardsshootingmethod foreigenvaluesandexpectationvaluesof the Schrödinger equation. A multi-well potential is used as a test case.

Finite Geometry and Computer Algebra, with Applications (1994)
Thesis
Gordon, N. (1994). Finite Geometry and Computer Algebra, with Applications. (Thesis). University of Hull. https://hull-repository.worktribe.com/output/405456

The interaction between geometry and algebra is a diverse and fruitful area to explore. Of particular interest is the area of groups and geometry. In this work we will examine various aspects of this interplay, in particular looking at geometric cano... Read More about Finite Geometry and Computer Algebra, with Applications.

The relative order of a class of recurrent networks (1994)
Presentation / Conference Contribution
Manchanda, S., Kambhampati, C., Tham, M., & Green, G. (1994, March). The relative order of a class of recurrent networks. Presented at International Conference on Control '94, Coventry, UK

Three types of recurrent network configurations have been proposed since they enable adequate description of temporal behaviour. The concept of relative order has been introduced so as to provide a framework for analysing such network configurations.... Read More about The relative order of a class of recurrent networks.

Line generalisation by repeated elimination of points (1993)
Journal Article
Visvalingam, M., & Whyatt, J. D. (1993). Line generalisation by repeated elimination of points. The Cartographic journal, 30(1), 46-51. https://doi.org/10.1179/000870493786962263

This paper presents a new approach to line generalisation which uses the concept of ‘effective area’ for progressive simplification of a line by point elimination. Two coastlines are used to compare the performance of this, with that of the widely us... Read More about Line generalisation by repeated elimination of points.

Cartographic Algorithms: Problems of Implementation and Evaluation and the Impact of Digitising Errors (1991)
Journal Article
Whyatt, J. D., & Visvalingam, M. (1991). Cartographic Algorithms: Problems of Implementation and Evaluation and the Impact of Digitising Errors. Computer graphics forum : journal of the European Association for Computer Graphics, 10(3), 225-235. https://doi.org/10.1111/1467-8659.1030225

Cartographic generalisation remains one of the outstanding challenges in digital cartography and Geographical Information Systems (GIS). It is generally assumed that computerisation will lead to the removal of spurious variability introduced by the s... Read More about Cartographic Algorithms: Problems of Implementation and Evaluation and the Impact of Digitising Errors.