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In this paper, we study the approximation of d-dimensional ϱ -weighted integrals over unbounded domains R + d or R d using a special change of variables, so that quasi-Monte Carlo (QMC) or sparse grid rules can be applied to the transformed integrands over the unit cube. We consider a class of integrands with bounded L p norm of mixed partial derivatives of first order, where p ∈ [ 1 , + ∞ ]. The main results give sufficient conditions on the change of variables ν which guarantee that the transformed integrand belongs to the standard Sobolev space of functions over the unit cube with mixed smoothness of order one. These conditions depend on ϱ and p. The proposed change of variables is in general different than the standard change based on the inverse of the cumulative distribution function. We stress that the standard change of variables leads to integrands over a cube; however, those integrands have singularities which make the application of QMC and sparse grids ineffective. Our conclusions are supported by numerical experiments. [ABSTRACT FROM AUTHOR]

We prove upper bounds on the star discrepancy of digital ( t, m, 2)-nets and ( t, 2)-sequences over Z 2. The main tool is a decomposition lemma for digital ( t, m, 2)-nets, which states that every digital ( t, m, 2)-net is just the union of 2tdigitally shifted digital (0, m - t, 2)-nets. Using this result we generalize upper bounds on the star discrepancy of digital (0, m, 2) -nets and (0, 2) -sequences. [ABSTRACT FROM AUTHOR]

We prove upper bounds on the star discrepancy of digital ( t, m, 2)-nets and ( t, 2)-sequences over Z 2. The main tool is a decomposition lemma for digital ( t, m, 2)-nets, which states that every digital ( t, m, 2)-net is just the union of 2tdigitally shifted digital (0, m - t, 2)-nets. Using this result we generalize upper bounds on the star discrepancy of digital (0, m, 2) -nets and (0, 2) -sequences. [ABSTRACT FROM AUTHOR]

The corrosion of tantalum was investigated in sub- and supercritical oxidizing solutions of hydrochloric, sulfuric and phosphoric acid at temperatures between 360 and 500 °C. The corrosion rates in HCl and H2SO4 increased strongly above the critical temperature of water, which was attributed to a phase transformation from vitreous to crystalline Ta2O5. Corrosion rates in H3PO4 were low at all temperatures due to the formation of a top phosphate layer. [ABSTRACT FROM AUTHOR]