143,265 research outputs found

    Fixed Parameter Undecidability for Wang Tilesets

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    Deciding if a given set of Wang tiles admits a tiling of the plane is decidable if the number of Wang tiles (or the number of colors) is bounded, for a trivial reason, as there are only finitely many such tilesets. We prove however that the tiling problem remains undecidable if the difference between the number of tiles and the number of colors is bounded by 43. One of the main new tool is the concept of Wang bars, which are equivalently inflated Wang tiles or thin polyominoes.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249

    On the qq-log-convexity conjecture of Sun

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    In his study of Ramanujan-Sato type series for 1/π1/\pi, Sun introduced a sequence of polynomials Sn(q)S_n(q) as given by Sn(q)=k=0n(nk)(2kk)(2(nk)nk)qk,S_n(q)=\sum\limits_{k=0}^n{n\choose k}{2k\choose k}{2(n-k)\choose n-k}q^k, and he conjectured that the polynomials Sn(q)S_n(q) are qq-log-convex. By imitating a result of Liu and Wang on generating new qq-log-convex sequences of polynomials from old ones, we obtain a sufficient condition for determining the qq-log-convexity of self-reciprocal polynomials. Based on this criterion, we then give an affirmative answer to Sun's conjecture

    On the characterization of Wang's class of premium principles.

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    A premium principle is an economic decision rule used by the insurer in order to determine the amount of the net premium for each risk in his portfolio. In this paper we investigate the problem of determining the premium principle to be used. First, we discuss some desirable properties of a premium principle. We prove that the only premium principles that possess these properties belong to a class of premium principles introduced by Wang (1996). Similar results ccan be found in Wang, Young & Panjer (1997)..Principles;

    Replies

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    This paper responds to the contributions by Alexander Bird, Nathan Wildman, David Yates, Jennifer McKitrick, Giacomo Giannini & Matthew Tugby, and Jennifer Wang. I react to their comments on my 2015 book Potentiality: From Dispositions to Modality, and in doing so expands on some of the arguments and ideas of the book

    Array multiplier

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    Digital array multiplier consisting of any number of identical digital adder cells in a repetitive planar configuration functions as a modular multiplier for use in computer applications of airborne vehicles. The modular multiplier utilizes large scale integration and metal oxide semiconductors
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