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An inequality on the variation of the product of two functions of bounded variation and some applications in numerical solution of certain class of parabolic partial diierential equations by low-discrepancy sequences are given.
In this paper, we study the geometric generation of the (0; m; 2)-nets. Based on some combinatorial methods, a generation property on (0; m; 2)-nets with an applications to a Sobol' sequence and the number of the (0; m; 2)-nets in equivalent sense are given. We also present some symmetry properties of the Sobol' sequence and the Roth-Zaremba sequence.
In this paper, we estimate the star-diaphony and the diaphony of the Roth sequence and the Zaremba sequence using their L 2-discrepancy formula given by Halton and Zaremba (see 3]), and White (see 17]). The optimal estimates and the exact asymptotic behaviours of the star-diaphony and the diaphony of both sequences are given. Moreover, the exact asymptotic… (More)
In this paper, we introduce the notion of volume-discrepancy (and of isotropic volume-discrepancy) of a sequences of points and we establish some of their basic properties. This notion is illustrated by an application to a reliability problem.