By Q. Ho-Kim, X. Pham

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The motions also need not be truly n-dimensional unless the A, are independent over the rationals. REFERENCE [1] A. M. FINK, Almost periodic differential equations, Springer-Verlag Lecture Notes, vol. 377, Springer-Verlag, New York. Editorial note. For other related results, see the forthcoming paper-of the proposer and C. PISOT, Extremwn problems for the motions of a billiard ball. Problem 59-7 (Corrected), A Minimum Time Path, by D. J. NEWMAN (Yeshiva University). Determine the minimal time path of a jet plane from take-off to a given point in space.

Two heights were tested (1 and 2 x h). The double height (2 x A) was obtained by taping two dominoes together. Testing was conducted on a flat surface, the dominoes («=100) being equally spaced in a straight row. Timing was done by hand utilizing a stopwatch: the timing start and stop was based on the initial impulse (provided by hand) and the fall of the last domino in the row. 13 MECHANICS The experimental results are shown in Fig. 2, where the normalized wave speed is plotted as a function of relative spacing.

Then so that where 22 PROBLEMS IN APPLIED MATHEMATICS Suppose that Then for any positive finite F 0 , there exists a unique positive finite value £ such that The kinetic energy E, and hence the velocity v, vanishes when x = £. Since the acceleration x is always negative (the air density p(x) is assumed to be nonnegative) it follows that £ is the maximum value attained by x and that the missile falls back to earth after reaching the height £. If, on the other hand, the integral 7 is finite, and the initial velocity F0 is not less than 71/2, then it follows from (1) that E > 0, and hence that v > 0, throughout the missile trajectory.