80j:68051 68E05 Gates, William H.; Papadimitriou, Christos H. Bounds for sorting by prefix reversal. (English) Discrete Math. 27 (1979), no. 1, 47--57. _________________________________________________________________ The authors study the problem of sorting a sequence of distinct numbers by prefix reversal -- reversing a subsequence of adjacent numbers which always contains the first number of the current sequence. Let f(n) denote the smallest number of prefix reversals which is sufficient to sort n numbers in any ordering. The authors prove that f(n) <= (5n+5)/3 by demonstrating an algorithm which never needs more prefix reversals. They also prove that f(n) >= 17n/16 whenever n is a multiple of 16. The sequences which achieve this bound are periodic extensions of the basic sequence 1, 7, 5, 3, 6, 4, 2, 8, 16, 10, 12, 14, 11, 13, 15, 9. If, furthermore, each integer is required to participate in an even number of prefix reversals, the corresponding function g(n) is shown to satisfy 3n/2 - 1 <= g(n) <= 2n+3. Reviewed by Frank K. Hwang ============================================================================== 40 #1591 30.62 Kaczynski, T. J. The set of curvilinear convergence of a continuous function defined in the interior of a cube. (English) Proc. Amer. Math. Soc. 23 1969 323--327. Reviewed by J. E. McMillan _________________________________________________________________ 39 #4402 30.62 Kaczynski, T. J. Boundary functions and sets of curvilinear convergence for continuous functions. (English) Trans. Amer. Math. Soc. 141 1969 107--125. Reviewed by J. E. McMillan _________________________________________________________________ 38 #4689 30.62 31.00 Kaczynski, T. J. Boundary functions for bounded harmonic functions. (English) Trans. Amer. Math. Soc. 137 1969 203--209. Reviewed by J. E. McMillan _________________________________________________________________ 37 #3990 10.05 Kaczynski, T. J. Note on a problem of Alan Sutcliffe. (English) Math. Mag. 41 1968 84--86. Reviewed by B. M. Stewart _________________________________________________________________ 35 #1785 30.62 Kaczynski, T. J. On a boundary property of continuous functions. (English) Michigan Math. J. 13 1966 313--320. Reviewed by D. C. Rung _________________________________________________________________ 31 #355 30.62 Kaczynski, T. J. Boundary functions for function defined in a disk. (English) J. Math. Mech. 14 1965 589--612. Reviewed by C. Tanaka ============================================================================== 20 #1365 Fagen, R. E.; Lehrer, T. A. Random walks with restraining barrier as applied to the biased binary counter. J. Soc. Indust. Appl. Math. 6 1958 1--14. (Reviewer: R. W. Hamming) 60.00 19,936a Austin, T.; Fagen, R.; Lehrer, T.; Penney, W. The distribution of the number of locally maximal elements in a random sample. Ann. Math. Statist. 28 (1957), 786--790. (Reviewer: A. Sade) 05.0X At http://php.indiana.edu/~jbmorris/FAQ/lehrer.bio.html we read: >He majored in math at Harvard, earning a BA in 1946 and an MA in >1947. (No, he is not "Professor Lehrer," nor is he "Dr. Lehrer." >"Mr. Lehrer" will suffice, as will "The Almighty.") He remained at >Harvard as a graduate student until 1953. (The Christian Science Monitor writes, "He graduated from Harvard with a BA in mathematics at age 18 and earned an MA a year later. (Mr. Lehrer has completed all the work for a PhD except his dissertation.)" which is a very forgiving description of an ABD!) ============================================================================== I don't know whether this is the (American) Football star Frank Ryan; parts of the data seem consistent with what I know of him, but this certainly seems like too much academic work for a person with that other career! 49 #9215 Ryan, Frank B. A counterexample in asymptotic behavior of holomorphic functions. Math. Systems Theory 7 (1973), 12--13. (Reviewer: J. E. McMillan) 30A72 47 #5260 Ryan, Frank B. On the asymptotic behavior of functions holomorphic in the unit disc. Michigan Math. J. 19 (1972), 381--382. (Reviewer: J. E. McMillan) 30A72 45 #7033 Lohwater, A. J.; Ryan, Frank A distortion theorem for a class of conformal mappings. Mathematical essays dedicated to A. J. Macintyre, pp. 257--262. Ohio Univ. Press, Athens, Ohio, 1970. (Reviewer: E. C. Schlesinger) 30A30 43 #2221 Ryan, F. B. On the Poisson-Stieltjes representation for functions with bounded real part. Michigan Math. J. 17 1970 301--310. (Reviewer: S. Fisher) 30.65 42 #529 Bruckner, A. M.; Lohwater, A. J.; Ryan, Frank Some non-negativity theorems for harmonic functions. Ann. Acad. Sci. Fenn. Ser. A I No. 452 1969 8 pp. (Reviewer: D. C. Rung) 31.10 (30.00) 36 #391 Ryan, Frank B.; Barth, Karl F. Asymptotic values of functions holomorphic in the unit disk. Math. Z. 100 1967 414--415. (Reviewer: G. Piranian) 30.62 34 #2894 Ryan, Frank B. A characterization of the set of asymptotic values of a function holomorphic in the unit disc. Duke Math. J. 33 1966 485--493. (Reviewer: Edward F. Collingwood) 30.62 34 #2893 Ryan, Frank B. The set of asymptotic values of a bounded holomorphic function. Duke Math. J. 33 1966 477--484. (Reviewer: Edward F. Collingwood) 30.62 26 #2615 MacLane, G. R.; Ryan, F. B. On the radial limits of Blaschke products. Pacific J. Math. 12 1962 993--998. (Reviewer: K. Noshiro) 30.65 © Copyright American Mathematical Society 2000 ============================================================================== There is a web page of "famous nonmathematicians" http://stcloudstate.edu/~dbuske/famousnonmathematicians.html