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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.

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.

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. 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.

The lines of PG(4, 2) are the points on a quintic in PG(9,2) (1994)
Journal Article
Shaw, R., & Gordon, N. A. (1994). The lines of PG(4, 2) are the points on a quintic in PG(9,2). Journal of Combinatorial Theory, Series A, 68(1), 226-231. https://doi.org/10.1016/0097-3165%2894%2990102-3

Let V denote a 5-dimensional vector space over a field, and let (bij) denote the 10 independent components of a bivectorb?Λ2Vrelative to a choice of product basis {eiΛej: 1 ≤i<j≤ 5} forΛ2V. It is well known thatb(≠ 0) is decomposable (pure, simple) i...

Application of artificial intelligence techniques to probeless fault diagnosis of printed circuit boards (1994)
Thesis
Arslan, T. S. Application of artificial intelligence techniques to probeless fault diagnosis of printed circuit boards. (Thesis). University of Hull. https://hull-repository.worktribe.com/output/4223811

This thesis describes investigations which led to the development of a failure diagnosis expert system for printed circuit boards which exploits functional test data. The boards considered are highly complex mixed signal (analogue and digital) system... Read More about Application of artificial intelligence techniques to probeless fault diagnosis of printed circuit boards.

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.

Approaches to the optimizing control problem (1988)
Journal Article
Ellis, J. E., Kambhampati, C., Sheng, G., & Roberts, P. D. (1988). Approaches to the optimizing control problem. International Journal of Systems Science, 19(10), 1969-1985. https://doi.org/10.1080/00207728808964092

The selection of the steady-state controls which enable a system to operate in an optimum manner is the optimizing control problem. An examination of direct and adaptive model-based approaches to this problem is made. In the direct approach, system m... Read More about Approaches to the optimizing control problem.

The signed Chi-score measure for the classification and mapping of polychotomous data (1981)
Journal Article
Visvalingam, M. (1981). The signed Chi-score measure for the classification and mapping of polychotomous data. The Cartographic journal, 18(1), 32-43. https://doi.org/10.1179/caj.1981.18.1.32

Several polychotomous characteristics, when expressed in chi-score form, exhibit distributions in property space which deviate from the inherent assumptions of the more commonly used methods of cluster analysis. This paper suggests a novel approach t... Read More about The signed Chi-score measure for the classification and mapping of polychotomous data.