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Abstract-A method is presented for computing an orthonormal set of eigenvectors for the discrete Fourier transform (DFT). The technique is based on a detailed analysis of the eigenstructure of a special matrix which commutes with the DFT. It is also shown how fractional powers of the DFT can be efficiently computed, and possible applications to multiplexing and transform coding are suggested.

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Absiraci-Fixed step size random search for minimization of functions of several parameters is described and compared with the k e d step size gradient method for a particular surface. A theoretical technique, using the optimum step size at each step, is analyzed. A practical adaptive step size random search algorithm is then proposed, and experimental experience is reported that shows the superiority of random search over other methods for sufllciently high dimension.T

We prove that time-gated Manakov (1+1)-dimensional spatial solitons can perform arbitrary computation in a homogeneous medium with beams entering only at one boundary.

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We study auctions where bidders have independent private values but attach a disutility to the surplus of rivals, and derive symmetric equilibria for first-price, second-price, English, and Dutch auctions. We find that equilibrium bidding is more aggressive than standard predictions. Indeed, in second-price auctions it is optimal to bid above one's valuation; that is, bidding "frenzies" can arise in equilibrium. Further, revenue equivalence between second-price and first-price auctions breaks down, with second-price outperforming first-price. We also find that strategic equivalence between second-price and English auctions no longer holds, although they remain revenue equivalent. We conclude that spiteful bidding rationalizes anomalies observed in laboratory experiments across the four auction forms better than the leading alternatives.