Let E be a compact set in the complex plane C having connected and regular complement. For a nonentire function f analytic in the interior of E and continuous on E, we investigate the limiting distribution of the zeros of the sequence of polynomials {pn∗}1∞ of best uniform approximation to f on E. The zeros of best Lp polynomial approximants and best uniform rational approximants having a bounded number of free poles are also considered.

Automatic vehicle parallel parking design and its related concerns about safety improvement remain some of the heated problems for automatic land vehicular control. This paper presents the calculation process of a parallel parking car's path planning and the algorithm development for its motion design based on a fifthdegree polynomial curve. In addition to the proposed algorithm for automatic vehicle parking, the minimum horizontal distance allowed for parking between a car and a parking spot is also investigated. The preliminary results show that the fifth degree polynomial path planning and the algorithm are well applied to the automatic parallel parking problem.

Let f be a piecewise analytic (but not analytic) function in @[a, b], k > 0, and let p,* be the sequence of polynomials of best uniform approximation to f on [a, b]. It is well known that every point of [a, b] is a limit point of the zeros of the p,*. Let x E [a, b], and suppose that f is analytic at x and f(x) # 0. The main purpose of this paper is to show that there exists a constant y (which depends only on x) such that there is no zero of p,* within the circle of radius (y/n) log n centered at X, for all sufficiently large values of n.

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