Erratum: Variable Integrals Method. II

Computation of Fresnel Integrals. II

This paper describes an improved method for computing Fresnel integrals with an error of less than 1 × 10(-9). The method is based on a known approximate formula for a different integral which is due to Boersma and referenced by Abramowitz and Stegun.

Variable Transformations for Nearly Singular Integrals in the Boundary Element Method

The Boundary Element Method (BEM) or the Boundary Integral Equation (BIE) method is a convenient method for solving partial differential equations, in that it requires discretization only on the boundary of the domain [2]. In the method, the accurate and efficient computation of boundary integrals is important. In particular, the evaluation of nearly singular integrals, which occur when computi...

Envelope tomography of long-period variable stars⋆ II. Method

A tomographic method is described that makes it possible to follow the propagation of shock waves across the photosphere of long-period variable stars. The method relies on the correlation of the observed spectrum with numerical masks probing layers of different atmospheric depths. The formation depth of spectral lines is derived from synthetic spectra of non-variable red giant stars. When appl...

Erratum

Algebraic Cycles and Motivic Iterated Integrals Ii

This is a sequel to [FJ]. It will give a more natural framework for constructing elements in the Hopf algebra χF of framed mixed Tate motives according to Bloch and Křiž [BK]. This framework allows us to extend the results of [FJ] to interpret all multiple zeta values (including the divergent ones) and the multiple polylogarithms in one variable as elements of χF . It implies that the pro-unipo...