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The intelligent technology of CMM (2001)
Journal Article
Zhao, Y., Li, Z., Zhang, G., Liu, S., Wang, J., & Ma, X. (2001). The intelligent technology of CMM. Ji liang xue bao = Acta metrologica Sinica, 22(3), 164-167. https://doi.org/10.3321/j.issn%3A1000-1158.2001.03.002

The key technologies of intelligent CMM, including extracting the measuring information of a part from its CAD files, deciding measuring strategies, making algorithms of object-oriented error compensation, accuracy optimization, and collision-free me... Read More about The intelligent technology of CMM.

Numerical determination of the Titchmarsh-Weyl m-coefficient (2000)
Journal Article
(2000). Numerical determination of the Titchmarsh-Weyl m-coefficient. Computational Mathematics and Mathematical Physics / Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 40(1), 108-117

A numerical method for calculating the Titchmarsh-Weyl mα(λ)-coefficient for the differential equation d2y/dx2+ [1 - q(x)]y = 0 is tested for the cases q(x) = x and x2, for which mα(λ) has a known analytic form in terms of special functions. An indep... Read More about Numerical determination of the Titchmarsh-Weyl m-coefficient.

Iterative closest geometric objects registration (2000)
Journal Article
Li, Q., & Griffiths, J. G. (2000). Iterative closest geometric objects registration. Computers & mathematics with applications, 40(10-11), 1171-1188. https://doi.org/10.1016/s0898-1221%2800%2900230-3

In this paper, closed-form solutions are obtained for registering two sets of line segments, triangle patches, or even general simple geometric objects that are defined by a set of ordered points. Based on these new registration approaches, the itera... Read More about Iterative closest geometric objects registration.

Implementation of IGES-based CAD/CMM Automatic Workpiece Modelling (2000)
Journal Article
Zuo, Z., Ma, X., & Liu, S. (2000). Implementation of IGES-based CAD/CMM Automatic Workpiece Modelling. Aviation Precision Manufacturing Technology, 36(3), 28-33. https://doi.org/10.3969/j.issn.1003-5451.2000.03.007

In this paper,a CAD/CMM workpiece modelling system,which is based on IGES-files,is proposed.In this system,the CAD data of workpiece to be measured are extracted and recognized automatically,and the workpiece model is generated as a result of process... Read More about Implementation of IGES-based CAD/CMM Automatic Workpiece Modelling.

A stable one-step-ahead predictive control of non-linear systems (2000)
Journal Article
Kambhampati, C., Mason, J. D., & Warwick, K. (2000). A stable one-step-ahead predictive control of non-linear systems. Automatica : the journal of IFAC, the International Federation of Automatic Control, 36(4), 485-495. https://doi.org/10.1016/s0005-1098%2899%2900173-9

In this paper stability of one-step ahead predictive controllers based on non-linear models is established. It is shown that, under conditions which can be fulfilled by most industrial plants, the closed-loop system is robustly stable in the presence... Read More about A stable one-step-ahead predictive control of non-linear systems.

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.

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)
Conference Proceeding
Delgado, A., Kambhampati, C., & Warwick, K. (1996). Stable linearization using multilayer neural networks. . https://doi.org/10.1049/cp%3A19960551

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)
Conference Proceeding
Gordon, N. (1995). Mathematica and finite geometry. In V. Keranen, & P. Mitic (Eds.), Mathematics With Vision: Proceedings of the First International Mathematica Symposium (159 - 166)

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.