John D. Dixon

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A method is described for computing the exact rational solution to a regular system Ax=b of linear equations with integer coefficients. The method involves: (i) computing the inverse (modp) of A for some prime p; (ii) using successive refinements to compute an integer vector ~ such that A,2-b (modp") for a suitably large integer m; and (iii) deducing the(More)
iv iv Expanding the Measure of Wealth 4.1 The simple economics of win-win subsidy reform 42 4.2 Price reform problems in transition economies 47 4.3 Energy in Russia: what lies ahead? 50 4.4 China: subsidy reform in the coal sector 50 4.5 Electricity subsidies 51 4.6 Removing pesticide subsidies in Bangladesh 54 4.7 Removing pesticide subsidies in Indonesia(More)
The paper describes a "probabilistic algorithm" for finding a factor of any large composite integer n (the required input is the integer n together with an auxiliary sequence of random numbers). It is proved that the expected number of operations which will be required is 0(exp{ /ftln n In In n)1/2}) for some constant ß > 0. Asymptotically, this algorithm(More)
Let w be a non-trivial word in two variables. We prove that the probability that two randomly chosen elements x, y of a nonabelian finite simple group S satisfy w(x, y) = 1 tends to 0 as |S| → ∞. As a consequence, we obtain a new short proof of a well-known conjecture of Magnus concerning free groups, as well as some applications to profinite groups.(More)
Acknowledgments This Handbook is the product of a team effort. Jock Anderson contributed to the chapter on risk analysis, Howard Barnum to the chapter on the assessment of health projects, John Dixon to the chapter on environmental externalities, and Jee-Peng Tan to the chapter on the assessment of education projects. George Psacharopoulos provided very(More)
Detecting the environmental impacts of human activities on natural communities is a central problem in applied ecology. It is a difficult problem because one must separate human perturbations from the considerable natural temporal variability displayed by most populations. In addition, most human perturbations are generally unique and thus unreplicated.(More)
The probability that a random pair of elements from the alternating group An generates all of An is shown to have an asymptotic expansion of the form 1¡1/n¡ 1/n2¡4/n3¡23/n4¡171/n5¡ ... . This same asymptotic expansion is valid for the probability that a random pair of elements from the symmetric group Sn generates either An or Sn. Similar results hold for(More)