2. Existence of solutions of differential equations in Banach space, Bulletin of the American Mathematical Society, vol. 80, no. 1, 1974, pp. 148-149; (announcement of results published in detail in the following paper).
3. Solutions of differential equations in B-spaces, Duke Mathematics Journal, vol. 41, no. 2, 1974, pp. 437-442.
4. Counterexample to a theorem on differential equations in Hilbert space, Proceedings of the American Mathematical Society, vol. 51, no. 2, 1975, pp. 378-380.
This paper gave me a small notoriety among researchers in the area of differential equations in abstract spaces. It showed that a well-known and frequently cited theorem by the president of the American Mathematical Society was false.
5. Convergence and divergence of p-series, with Teresa Cohen, Mathematics Magazine, vol. 52, no. 3, 1979, p.178.
This decidedly minor piece of work contains a simple, elegant proof that I found for the divergence of the "harmonic infinite series". The remainder of the note was supplied by my 84 year old collaborator and shows that my technique can be modified to prove convergence of series similar to the harmonic series.
6. Functions with zero right derivatives are constant, American Mathematical Monthly, vol. 87, no. 8, 1980, pp. 657-658.
The goal of several of my papers has been to show that certain mathematical theorems that were thought to require graduate level mathematics can in fact be proved by much more elementary means. This paper belongs to that group (as do items 5 and 7).
7. A strong inverse function theorem, American Mathematical Monthly, vol. 95, no. 7, 1988, pp. 648-651.
I am particularly fond of this paper because it shows how one of the most important theorems of undergraduate mathematical analysis can be strengthened by using an elementary technique. Heretofore it had been thought that my strong form of the theorem could be obtained only by first developing a more advanced theory of differentiation.
8. Search in an ordered array having variable probe cost, Society for Industrial and Applied Mathematics Journal of Computation, vol. 17, no. 6, 1988, pp. 1203-1214.
I consider this to be the best piece of work I have done. It settled a conjecture by Professor Kenneth Steiglitz of Princeton University concerning searches in arrays.
2. Search in an Ordered Array Having Variable Probe Cost, Master's Thesis, 1986, U. of Illinois, Urbana; directed by Edward M. Reingold.
In connection with this manuscript, I was pleased to get a letter from N. J. A. Sloane of Bell Labs, who is the author of a well-known reference book, "Handbook of Integer Sequences", for researchers in various mathematically based disciplines. He is interested in determining whether some of the sequences we generate in this paper are suitable for inclusion in the forthcoming revision of his book.