Visiting Fellows

Dr David Branson

Staff positionVisiting Fellow
Emailbrand@essex.ac.uk
Telephone01206 874294
Room5.519
Biography

I obtained my B.A. and Ph.D. degrees at the University of Cambridge. I subsequently carried out research at the University of California at Berkeley, at Princeton University and at the University of Cambridge before coming to Essex in 1968. My early research was in the area of elementary particle theory, an interest that led to my spending a period at the CERN laboratory in Geneva. I later changed my research field to probability and combinatorics. I have written papers on the distribution of genetic characteristics in a population and other properties of populations subject to time-varying rates of birth, death and immigration. More recently I have written several papers on the properties of Stirling numbers. 

Research interests

Applied probability and stochastic processes – birth-death models and population genetics; properties and applications of Stirling numbers.

Publications

D. Branson, P.V. Landshoff and J.C. Taylor. 'Derivation of partial amplitudes and the validity of dispersion relations for production processes', Physical Review, Vol.132, 902-912, 1963.

D. Branson. 'Time and the S-matrix', Physical Review, Vol.135, B1255-1262, 1964.

D. Branson. 'Three particle singularities in scattering amplitudes', Annals of Physics, Vol.35, 351-372, 1965.

D. Branson. 'The cross-discontinuity condition in S-matrix theory', Il Nuovo Cimento, Vol.44, 1081-1090, 1966.

D. Branson, S. Nussinov, S.B. Treiman and W.I. Weisberger. 'Contribution of Regge cuts to forward nucleon-nucleon scattering', Physics Letters, Vol.25B, 141-143, 1967.

D. Branson. 'Physical sheet properties of second-type singularities', Il Nuovo Cimento, Vol.51B, 239-240, 1967.

D. Branson. 'Singularity properties of the bubble diagrams of S-matrix theory', Il Nuovo Cimento, Vol.54A, 217-233, 1968.

D. Branson. 'Signature of Regge cuts coupled to spinning particles', Physical Review, Vol.179, 1608-1616, 1969.

D. Branson. 'A colliding pole and branch point as a model for a self-consistent Pomeranchuk singularity', Il Nuovo Cimento, Vol.3A, 271-286, 1971.

D. Branson. 'Hard Regge cuts consistent with elastic unitarity', Il Nuovo Cimento, Vol.15A, 217-226, 1973.

D. Branson and E.L. Berger. 'Particle production at large transverse momentum', Physics Letters, Vol.45B, 57-62, 1973.

D. Branson. 'Continuity conditions on Schrödinger wave functions at discontinuities of the potential', American Journal of Physics, Vol.47, 1000-1003, 1979.

D. Branson. 'The correspondence principle and scattering from potential steps', American Journal of Physics, Vol.47, 1101-1102, 1979.

D. Branson. 'Binomial aspects of failure rate analysis', American Journal of Physics, Vol.53, 174-175, 1985.

D. Branson. 'Times of flight', The Mathematical Gazette, Vol.75, 202-203, 1991.

D. Branson. 'Inhomogeneous birth-death and birth-death-immigration processes and the logarithmic series distribution', Stochastic Processes and their Applications, Vol.39, 131-137, 1991.

D. Branson. 'An urn model and the coalescent in neutral infinite-alleles genetic processes', in I.V. Basawa and R.L. Taylor (eds.) Selected Proceedings of the Sheffield Symposium on Applied Probability, 1989, Institute of Mathematical Statistics Lecture Notes - Monograph Series Vol.18, 174-192, Institute of Mathematical Statistics, Hayward, California, 1991.

D. Branson. 'Sequences obtained from tossing a coin', The Mathematical Gazette, Vol. 76, 401-402, 1992.

D. Branson. 'Moments of discrete probability distributions derived using a differential operator', The American Statistician, Vol. 47, 83-84, 1993.

D. Branson. 'An extension of Stirling numbers', The Fibonacci Quarterly, Vol. 34, 213-223, 1996.

D. Branson. 'Oscillations in random walks', Sankhyã: The Indian Journal of Statistics, Vol. 59, 1-9, 1997.

D. Branson. 'Inhomogeneous birth-death and birth-death-immigration processes and the logarithmic series distribution. Part 2', Stochastic Processes and their Applications, Vol. 86, 183-191, 2000.

D. Branson. 'Stirling numbers and Bell numbers: their role in combinatorics and probability' The Mathematical Scientist, Vol. 25, 1-31, 2000.

D Branson. 'A combinatorial interpretation of identities involving Stirling numbers and their generalizations', The Fibonacci Quarterly, Vol. 44, 131-140, 2006.

D. Branson, 'Stirling number representations', Discrete Mathematics, Vol. 306, 478-494, 2006. 

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