Note on Constant-Deciation Prisms

A note on domination and total domination in prisms

Recently, Azarija et al. considered the prism G K2 of a graph G and showed that γt(G K2) = 2γ(G) if G is bipartite, where γt(G) and γ(G) are the total domination number and the domination number of G. In this note, we give a simple proof and observe that there are similar results for other pairs of parameters. We also answer a question from that paper and show that for all graphs γt(G K2) ≥ 4 3...

A Note on Artin’s Constant

P p(pi−1) , where the summation is over first N prime pi, k ∈ Z+. The classical summation formula is as follows: A = limN→∞Σ(N), where Σ(N) = 1 N ∑ φ(pi−1) pi−1 . The changes needed for arbitrary g are addressed in Theorem 1, a good exercise in basic analytic and algebraic number theory. The same procedure can be applied to other number-theoretic constants like A (see, e.g., [Ni]). In Theorem 2...

A note on a curious formula for Euler’s constant

In this short note we will use the residue theorem to establish a formula for Euler’s constant. In particular, we offer a slightly generalized version of an interesting infinite series due to Flajolet, Gourdon, and Dumas. 1 Properties of γ Recall that γ is usually defined in terms of the partial sums of the harmonic series: γ := lim n→∞ 

Note on thermodynamic fermion loop under constant magnetic field

The one-loop effective potential of a thermodynamic fermion loop under constant magnetic field is studied. As expected, it can be interpreted literally as a dis-cretized sum of (D−2)-dimensional energy density above the Dirac sea. Large/small mass expansions of the potential are also examined.

A note on Constant - RoundZero - Knowledge Proofs for NPAlon