**Department:** Mathematical Sciences

**Telephone:** +44 (0) 151 794 4023

**Fax:** +44 (0) 151 794 4061

**Office:** Room 423

**E-mail: doman@liv.ac.uk**

**Postal Address:**

Department of Mathematical Sciences, M&O Building, The University of
Liverpool,

Liverpool L69 3BX

**Interval Arithemetic:**I have produced an Ada package to perform arbitrary accuracy calculations which updates an error formed so that the result can be guaranteed to lie within a given error band. The package deals effectively with calculation up to about 300 decimal digits.

**Special Functions:**A collaborative project with NA software to produce a package to calculate accurate values of common special functions. The accurate calculations were performed in Ada using the above package. Near zeros of functions expansions ensure that the relative error is not reduced as the argument approaches the zero. The code for these special functions was in many cases generated automatically by specially designed Ada packages. Included among these are the Bessel Functions*J*and*Y*and the spherical bessel functions*js*and*ys*of orders up to 30 with the first 20 zeros of each function dealt with by a seperate piece of code.

**Quantum Dot:**Single electron wave functions in a magnetic field in an infinite or a finite square well potential expressed in terms of confluent hypergeometric functions.

*On the Use of Green Functions in the Theory of the Ising Ferrromagnet*, (with D. ter Haar), Phys. Lett. 2 (1962), 15-16.

*On the Use of Green Functions in the Theory of the Ising Ferromagnet*, (with R. A. Tahir-Kheli and D. ter Haar), Phys. Lett. 4 (1963), 5-7.

*An Exact Result for the Ising Ferromagnet*, Phys. Lett. 4 (1963), 156-7.

*The Thermal Conductivity of a Ferrodielectric*, J. Phys. Chem. Solids 27, (1966), 625-8.

*The de Haas-van Alphen Effect in the Presence of a Random Array of Scatterers*, J. Phys. Chem. Solids (1966), 1233-6.

*The Green Function Decoupling Procedure*, Proc. Phys. Soc. 90 (1967), 475-7.

*A Note on the RKKY Interaction*, Phys. Lett. 29A (1969), 349-50.

*A Note on the Correlation between the Spins of the Conduction Electrons and that of a Localised Magnetic Moment*, (with T. Gavan), Phys. Lett. 29A (1969), 623-4.

*A Note on the Equivalence of the Anderson and s-d Hamiltonians*, Phys. Lett. 31A (1970), 244-5.

*Electron Impurity Spin Correlations near T*, (with T. Gavan), Phys. Lett. 31A, (1970), 567-8._{K}

*A Green Function Approach to the Problem of Two Magnetic Impurities in a non-magnetic Metal*, (with T. Gavan), J. Phys. Chem. Solids 31, (1970), 2267-74.

*The Correlation Between the Spins of Conduction Electrons and that of a Magnetic Moment in a Superconductor*, (with T.Gavan), J. Phys. C 4 (1971), L31-3.

*Magnetic Polarisation of Electrons in Ferromagnetic Palladium*, J. Phys. F (1971), 920-4.

*The Application of Green's Functions to a System of Two Almost Magnetic Impurities*, (with R.B. Middleton) Phys. Stat. Solidi b 45, (1971), 611-8.

*Divergences in the RKKY Interaction*, J. Phys. F. 3 (1973), 30-8.

*Magnetic Stimulation of an Impurity by a Vacancy*, Phys. Lett 45A (1973), 384.

*Magnetic Field Effects on Positron Annihilation in Metals*, Phys. Lett 61A, (1977), 852-3.

*Localisation of Electrons in a Magnetic Field*, J. Phys. C 12 (1979), 1521-4.

*An Improved Molecular Field Approach to the Triangular Ising Antiferromagnet*, Phys. Stat. Solidi b92, (1979), 147-151.

*The Two Dimensional Wigner Crystal in a Magnetic Field*, J. Phys. C 12 (1979), 3757-60.

*Relativistic Energy Levels of Hydrogen in Strong Magnetic Fields*, J. Phys. B 13 (1980), 3335-40.

*Charge Density Waves in a Strong Magnetic Field*, J. Phys. C 14 (1981), 1457-61.

*The Ground State of an Impure Ising Antiferromagnet*, J. Phys. C 14 (1981), 1765-7.

*A Cluster Approach to the Ising Linear Chain with Long-range Interactions*, Phys. Stat. Solidi b 103 (1981), K168-71.

*A Relativistic Treatment of Positron Annihilation in a Strong Magnetic Field*, J. Phys. B 14, (1981), L405-7.

*Charge Density Waves in a Strong Magnetic Field II*, J. Phys. C 14 (1981), 3393-7.

*Fibonacci and Lucas Polynomials*, (with J.K. Williams), Math. Proc. Camb. Phil. Soc. 90 (1981), 385-7.

*Exciton Energy Levels in Thin Semiconductor Films*, J. Phys. C 15 (1982), 863-5.

*Low Temperature Properties of Frustrated Ising Chains*, (with J.K. Williams), J. Phys. C 15 (1982), 1693-1706.

*The Effect of a Strong Magnetic Field on Impurity Levels in Thin Semiconductor Films*, J. Phys C 15 (1982), 3031-5.

*Indirect Exchange Interaction in Thin Films of Hg*, Phys. Stat. Solidi b 111, (1982) K 43-4._{1-x}Mn_{x}Te

*Frustrated Ising Chains III*, J. Phys. C 15 (1982), 5641-8.

*Charge Density Waves in a Strong Magnetic Field III*, J. Phys. C 16 (1983), 2069-74.

*Frustrated Ising Chains IV*, (with M.A.Z. Habeeb), J. Phys. C 15 (1983), 2591-2601.

*Electron Energy Levels in a Thin Wire in a Magnetic Field*, Phys. Stat. Solidi. b 120 (1983) K79-82.

*A Mean Field Treatment of Charge Density Waves in a Strong Magnetic Field*, Essays in Theoretical Physics in Honour of Dirk ter Haar (1984), Pergamon Press, Oxford.

*Travelling Charge Density Waves: A Mean Field Treatment*, Charge Density Waves in Solids Conference Proceedings Budapest, eds. G Hutiray and J Solyom (1984), Springer (1985).

*The Design of a Generic Quadrature Library in Ada*, (with L.M. Delves), Numerical Integration, NATO ASI Series Mathematical and Physical Sciences 203, eds. P.Keast and G. Fairweather, Halifax (1986), Riedel(1987).

*A Set of Ada Packages for High Precision Calculations*, (with C.J. Pursglove and W.M. Coen) ACM Trans. Math. Software 21 (1995), 416-431.

*An Asymptotic Expansion for the Incomplete Beta Function*, Math. Comp. 65 (1996), 1283-1288.

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