An expression in terms of (cyclotomic) harmonic sums can be simplified by the quasi-shuffle algebra in terms of the so-called basis sums. By construction, these sums are algebraically independent within the quasi-shuffle algebra. In this article we show that the basis sums can be represented within a tower of difference ring extensions where the constants remain unchanged. This property enables...

This document describes the SAT solver “CCAglucose2015”, which first empoys a preprocessor CP3, and then calls a hybrid solver combining a local search solver CCAnr and a complete solver glucose.

We show that the classical kernel and domain functions associated to an n-connected domain in the plane are all given by rational combinations of three or fewer holomorphic functions of one complex variable. We characterize those domains for which the classical functions are given by rational combinations of only two or fewer functions of one complex variable. Such domains turn out to have the ...

A new multi-state Harten–Lax–van Leer (HLL) approximate Riemann solver for the ideal magnetohydrodynamic (MHD) equations is developed based on the assumption that the normal velocity is constant over the Riemann fan. This assumption is same as that used in the HLLC (‘‘C’’ denotes Contact) approximate Riemann solver for the Euler equations. From the assumption, it is naturally derived that the R...

In C-tests the hypothesis of items local independence is violated, which doesn't permit to consider them as real tests. It is suggested to determine the distances between separate C-test items (blanks) and to combine items into clusters. Weights, inversely proportional to the number of items in corresponding clusters, are assigned to items. As a result, the C-test structure becomes similar to t...