The aim of the paper is to summarize some work by the author on the theory of sugar boiling. The boiling of sugar in vacuum pans has been modelled with a set of interconnected differential and integral equations. The model equations are solved numerically on a computer. Simulation results are compared with actual plant data.
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kernel of a certain triangular derivation of the polynomial ring k[x1, x2, x3, x4, x5] is shown to be non-finitely generated over k (a field of characteristic zero), thus giving a new counterexample to Hilbert's Fourteenth Problem, in the lowest dimension to date.
We analyse Cook's Nike Free Shoes Toronto
equation for spinodal decomposition and compare its predictions with computer-simulation data to conclude its formal consistency with the observations at early times. We thus provide a simple reference for the analysis of experiments at early, observable times and for the development of theory at late times.
Given any solution triple of natural numbers to the Markoff equation a2+b2+c2=3abc, an old problem asks whether the largest number determines the triple uniquely. We show this to be true in a range of cases by considering the factorisation of ideals in certain quadratic number fields, but also exhibit a counterexample for this approach when the question is widened to other numbers.