  Motivated by recent results and questions of D. Raghavan and S. Shelah, we
present ZFC theorems on the bounding and various almost disjointness numbers,
as well as on reaping and dominating families on uncountable, regular
cardinals. We show that if $\kappa=\lambda^+$ for some $\lambda\geq \omega$ and
$\mathfrak b(\kappa)=\kappa^+$ then $\mathfrak a_e(\kappa)=\mathfrak
a_p(\kappa)=\kappa^+$. If, additionally, $2^{<\lambda}=\lambda$ then $\mathfrak
a_g(\kappa)=\kappa^+$ as well. Furthermore, we prove a variety of new bounds
for $\mathfrak d(\kappa)$ in terms of $\mathfrak r(\kappa)$, including
$\mathfrak d(\kappa)\leq \mathfrak r_\sigma(\kappa)\leq \mathrm{cof}([\mathfrak
r(\kappa)]^\omega)$, and $\mathfrak d(\kappa)\leq \mathfrak r(\kappa)$ whenever
$\mathfrak r(\kappa)<\mathfrak b(\kappa)^{+\kappa}$ or $\mathrm{cof}(\mathfrak
r(\kappa))\leq \kappa$ holds.
