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Abstract: In [l] and [2], two algorithms have been proposed to calculate the output probability of Boolean functions represented by OBDDs, assuming that the input variables are equiprobable and each variable is statistically independent from others. In this paper, we point out that under these assumptions, the output probability calculation is equivalent to counting the number of minterms of the corresponding Boolean functions. An algorithm is proposed to compute the output probability using simple integer arithmetic as opposed to floating point arithmetic involved in [1,2]. To compute output probability of Boolean functions represented by shared OBDI)s and OBDDs with edge negation, we further propose a generalized algorithm. [Copyright &y& Elsevier]

In the paper, we show a law of the iterated logarithm for rescaled R/S statistics without second moment. [Copyright &y& Elsevier]

Most collision detection algorithms are ones of a discrete type which utilize convexity and local coherence to verify the closest points. However, the incremental algorithms have such critical drawbacks like failure to detect high-speed collisions and dependence on the time complexity on the time step size of animation. In this paper, in order to find a new method which can resolve the drawbacks, we are concerned with a more restricted but nontrivial version of the problem: given a fixed infinite plane H and a moving convex polyhedron P, compute their collision time. Our algorithm utilizes the spherical extreme vertex diagram that is the embedding of the dual graph P onto the Gauss sphere. Exploiting the diagram, we are able to efficiently compute the sequence of the extreme vertices vis, i = 1, …, m and find the time interval [ti, ti+1] during which vi is the extreme vertex of P. With the sequences of the consecutive time intervals and extreme vertices, we construct a distance function between P and H. Hence, we can compute their collision time within a given tolerance by applying the interval Newton method to the distance function. Moreover, the total time complexity is independent of the time step size of animation. [Copyright &y& Elsevier]

This paper presents some new techniques in designing finite-difference domain decomposition algorithm for the heat equation. The basic procedure is to define the finite-difference schemes at the interface grid points with smaller time step Δt = SHAPE="SOL" ALIGN="C" STYLE="S">Δtm (m is a positive integer) by Saul''yev asymmetric schemes. The algorithm can increase the stability bounds of the classical explicit method by 2m times, and the prior error estimates for the numerical solutions are obtained for some algorithms when m = 2 or m = 3. Numerical experiments on stability and accuracy are also presented. [Copyright &y& Elsevier]