Planet 1894 AX

Edward Joseph Conway, 1894-1968

Ernest Basil Verney, 1894-1967.

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ON THE CONGRUENCE ax

We give bounds on the number of solutions to the Diophantine equation (X +1/x)(Y +1/y) = n as n tends to infinity. These bounds are related to the number of solutions to congruences of the form ax + by ≡ 1 modulo xy.

Sir James Paget (1814-1894).

Sir James Paget (Fig. 1) formed with William Fergusson (1808–1862) and Sir Benjamin Brodie (1783–1762) a triumvirate of surgical ‘greats’ in England in the nineteenth century w1x. Paget was born in Great Yarmouth, Norfolk, England, and until 20 yr of age had not ventured further than a few miles from his birthplace. His father, Samuel, was a prosperous businessman who unfortunately went bankrup...

Ax Grammars for Natural Languages

AAx Grammars over a Finite Lattice (agfls), a simple form of two-level grammars admitting quite eecient implementations, are proposed as a formalism to express the syntax of natural languages. In this paper the concepts and notation of agfls are described. A brief example is given of their use in describing a fragment of the English language, followed by a discussion of issues like parsing and ...