1 Motivation This Master's Thesis project considers software for solving periodic Sylvester-type matrix equations. Recently, the ScaLAPACK-style library SCASY was completed. SCASY is a parallel HPC software library that solves for 42 sign and transpose variant of 8 common standard and generalized Sylvester-type matrix equations (see Table 1) which builds on the Table 1: The Sylvester-type matri...

We derive a two-parameter family of generalized entropies, Spq, and means mpq. To this end, assume that we want to calculate an entropy and a mean for n non-negative real numbers {x1,...,xn}. For comparison, we consider {m1,...,mk} where mi = m for all i = 1,...,k and where m and k are chosen such that the l and l norms of {x1,...,xn} and {m1,...,mk} coincide. We formally allow k to be real. Th...

L'ubomíra Balková We describe factor frequencies of the generalized Thue–Morse word t b,m defined for b ≥ 2, m ≥ 1, b, m ∈ N, as the fixed point starting in 0 of the morphism ϕ b,m (k) = k(k + 1). .. (k + b − 1), where k ∈ {0, 1,. .. , m − 1} and where the letters are expressed modulo m. We use the result of Frid [4] and the study of generalized Thue–Morse words by Starosta [6].

In this paper generalized Ramsey numbers of complete graphs K m versus the set h; n; ki of (n; k)-graphs are investigated. The value of r(K m ; hn; ki) is given in general for (relative to n) values of k small compared to n using a correlation with Turr an numbers. These generalized Ramsey numbers can be used to determine the local densities of graphs not containing a subgraph K m .