A three-valued function $f\: V\rightarrow \{-1,0,1\}$ defined on the vertices of a graph $G=(V,E)$ is a minus total dominating function (MTDF) if the sum of its function values over any open neighborhood is at least one. That is, for every $v\in V$, $f(N(v))\ge 1$, where $N(v)$ consists of every vertex adjacent to $v$. The weight of an MTDF is $f(V)=\sum f(v)$, over all vertices $v\in V$. The minus total domination number of a graph $G$, denoted $\gamma _t^{-}(G)$, equals the minimum weight of an MTDF of $G$. In this paper, we discuss some properties of minus total domination on a graph $G$ and obtain a few lower bounds for $\gamma _t^{-}(G)$.
The main goal of our prospective randomized study was
comparing compare the effectiveness of ventilation control
method „Automatic proportional minute ventilation (APMV)
“versus manually set pressure control ventilation modes in
relationship to lung mechanics and gas exchange. 80 patients
undergoing coronary artery bypass grafting (CABG) were
randomized into 2 groups. 40 patients in the first group No. 1
(APMV group) were ventilated with pressure control (PCV) or
pressure support ventilation (PSV) mode with APMV control. The
other 40 patients (control group No.2) were ventilated with
synchronized intermittent mandatory ventilation (SIMV-p) or
pressure control modes (PCV) without APMV. Ventilation control
with APMV was able to maintain minute ventilation more
precisely in comparison with manual control (p<0.01), similarly
deviations of ETCO2 were significantly lower (p<0.01). The
number of manual corrections of ventilation settings was
significantly lower when APMV was used (p<0.01). The
differences in lung mechanics and hemodynamics were not
statistically significant. Ventilation using APMV is more precise in
maintaining minute ventilation and gas exchange compared with
manual settings. It required less staff intervention, while
respiratory system mechanics and hemodynamics are
comparable. APMV showed as effective and safe method
applicable on top of all pressure control ventilation modes.