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Search Results for Collection: Computing and Mathematical Sciences Papers
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(University of Waterloo, 2012)We study integers n > 1 satisfying the relation σ(n) = γ(n) ² , where σ(n) and γ(n) are the sum of divisors and the product of distinct primes dividing n, respectively. We show that the only solution n with at most four ... -
(IOP Publishing, 2010)We describe a method for determining a complete set of integrals for a classical Hamiltonian that separates in orthogonal subgroup coordinates. As examples, we use it to determine complete sets of integrals, polynomial in ...
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(Society for Industrial and Applied Mathematics, 2003)It is known that the generating vector of a rank-1 lattice rule can be constructed component-by-component to achieve strong tractability error bounds in both weighted Korobov spaces and weighted Sobolev spaces. Since the ... -
(Springer Netherlands, 2006)The continuing and widespread use of lattice rules for high-dimensional numerical quadrature is driving the development of a rich and detailed theory. Part of this theory is devoted to computer searches for rules, appropriate ... -
(2005)Lame and Heun functions arise via separation of the Laplace equation in general Jacobi ellipsoidal or conical coordinates. In contrast to hypergeometric functions that also arise via variable separation in the Laplace ... -
(Springer, Berlin, 2006)The ‘goodness’ of a set of quadrature points in [0, 1]d may be measured by the weighted star discrepancy. If the weights for the weighted star discrepancy are summable, then we show that for n prime there exist n-point ... -
(2010)In this paper we examine the problem of decomposing the lexicographic product of a cycle with an empty graph into cycles of uniform length. We determine necessary and sufficient conditions for a solution to this problem ... -
(John Wiley & Sons, Ltd., 2008)Smoothed particle hydrodynamics (SPH) is becoming increasingly common in the numerical simulation of complex fluid flows and an understanding of the errors is necessary. Recent advances have established techniques for ...
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(2005)The unsteady axisymmetric withdrawal from a fluid with a free surface through a point sink is considered. Results both with and without surface tension are included and placed in context with previous work. The results ... -
(World Scientific, 2006)We study the problem of constructing good intermediate-rank lattice rules in the sense of having a low weighted star discrepancy. The intermediate-rank rules considered here are obtained by “copying” rank-1 lattice rules. ...