By Peter G. Anderson (auth.), Professor Gerald E. Bergum, Professor Andreas N. Philippou, Professor Alwyn F. Horadam (eds.)

This booklet includes forty three papers shape one of the fifty five papers provided on the 6th foreign convention on Fibonacci Numbers and Their functions which was once held at Washington nation college, Pullman, Washington, from July 18-22, 1994. those papers were chosen after a cautious overview via popular referees within the box, they usually diversity from simple quantity thought to likelihood and information. The Fibonacci numbers and recurrence family are their unifying bond. it really is expected that this e-book, like its 5 predecessors, could be necessary to analyze employees and graduate scholars drawn to the Fibonacci numbers and their purposes. October 30, 1995 The Editors Gerald E. Bergum South Dakota kingdom collage Brookings, South Dakota, U.S.A. Alwyn F. Horadam college of latest England Armidale, N.S.W., Australia Andreas N. Philippou 26 Atlantis highway Aglangia, Nicosia Cyprus xxi THE ORGANIZING COMMITTEES neighborhood COMMITTEE foreign COMMITTEE lengthy, Calvin T., Co-Chair Horadam, A.F. (Australia), Co-Chair Webb, William A., Co-Chair Philippou, A.N. (Cyprus), Co-Chair Burke, John Ando, S. (Japan) DeTemple, Duane W.

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Extra info for Applications of Fibonacci Numbers: Volume 6 Proceedings of ‘The Sixth International Research Conference on Fibonacci Numbers and Their Applications’, Washington State University, Pullman, Washington, U.S.A., July 18–22, 1994

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Then, pW I rn since where the summation is taken over i E M. Since q is the largest prime power that divides rn by the definition, we have pW ~ q and Aif(i),R E S(f) for R v(Y) ~ veX) for Y = A[f(I),R. , R. Since v(kf(I) = pW. (k f (I) - R + l)X/(k[ + l)(k[ + 2)···(k[ + R» ~ veX). and the proof is completed. 4. ), we can state now the criterion to decide whether a star S covers its center or not. t. ). Proof: Sufficiency is given by previous lemmas. We will show the necessity. Let S be a center covering star.

First, We can find an integer s such that Q = p8 length of rays in S. = pU, where p is a prime. Now, notice that v(q) = vern) = u > o. > max{pU, r m}, where r m denotes the maximum 27 MINIMAL CENTER COVERING STARS WITH RESPECT TO LCM... e. i or t or j) is zero, and c =1 otherwise. (kh + r) I ,r < Q, where h, j E M, h 1= i, and h 1= t if j =i. The case (T t ):v(k;-A)=v(k t +A+2) for A=O,"',r-l and v(k;-r+l)

Given a natural or synthetic image, how can the appropriate palette be chosen? A very good but very time-consuming method performs a statistical clustering analysis of the actual color usage. A quick and dirty approach is to start with an empty palette, and then render the image, pixel by pixel, using an existing palette color if the right color is already on the palette, add the new desired color to the palette if the palette is not yet full, and use the closest palette color when the palette is full If the pixel rendering is by row order, a terrible picture will result.

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