### A combinatorial approach to evaluation of reliability of the receiver output for BPSK modulation with spatial diversity.

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A Content Distribution Network (CDN) can be defined as an overlay system that replicates copies of contents at multiple points of a network, close to the final users, with the objective of improving data access. CDN technology is widely used for the distribution of large-sized contents, like in video streaming. In this paper we address the problem of finding the best server for each customer request in CDNs, in order to minimize the overall cost. We consider the problem as a transportation problem...

It is proved that if a finite abelian group is factored into a direct product of lacunary cyclic subsets, then at least one of the factors must be periodic. This result generalizes Hajós's factorization theorem.

DOMINATING SET remains NP-complete even when instances are restricted to bipartite graphs, however, in this case VERTEX COVER is solvable in polynomial time. Consequences to VECTOR DOMINATING SET as a generalization of both are discussed.

We give a partial answer to a question of Carlitz asking for a closed formula for the number of distinct representations of an integer in the Fibonacci base.

For almost all infinite binary sequences of Bernoulli trials $(p,q)$ the frequency of blocks of length $k\left(N\right)$ in the first $N$ terms tends asymptotically to the probability of the blocks, if $k\left(N\right)$ increases like ${\mathrm{log}}_{\frac{1}{p}}N-{\mathrm{log}}_{\frac{1}{p}}N-\psi \left(N\right)$ (for $p\le q$) where $\psi \left(N\right)$ tends to $+\infty $. This generalizes a result due to P. Flajolet, P. Kirschenhofer and R.F. Tichy concerning the case $p=q=\frac{1}{2}$.

We study two topological properties of the 5-ary $n$-cube ${Q}_{n}^{5}$. Given two arbitrary distinct nodes $x$ and $y$ in ${Q}_{n}^{5}$, we prove that there exists an $x$-$y$ path of every length ranging from $2n$ to ${5}^{n}-1$, where $n\ge 2$. Based on this result, we prove that ${Q}_{n}^{5}$ is 5-edge-pancyclic by showing that every edge in ${Q}_{n}^{5}$ lies on a cycle of every length ranging from $5$ to ${5}^{n}$.