On quasi-Pr\"{u}fer and UMtt domains

In this note we show that an integral domain $D$ of finite $w$-dimension is a quasi-Pr\"{u}fer domain if and only if each overring of $D$ is a $w$-Jaffard domain. Similar characterizations of quasi-Pr\"{u}fer domains are given by replacing $w$-Jaffard domain by $w$-stably strong S-domain, and $w$-strong S-domain. We also give new characterizations of UM$t$ domains.Comment: 6 Page

Review of sensors for remote patient monitoring

Remote patient monitoring (RPM) of physiological measurements can provide an efficient method and high quality care to patients. The physiological signals measurement is the initial and the most important factor in RPM. This paper discusses the characteristics of the most popular sensors, which are used to obtain vital clinical signals in prevalent RPM systems. The sensors discussed in this paper are used to measure ECG, heart sound, pulse rate, oxygen saturation, blood pressure and respiration rate, which are treated as the most important vital data in patient monitoring and medical examination

Cohen-Macaulay homological dimensions

We introduce new homological dimensions, namely the Cohen-Macaulay projective, injective and flat dimensions for homologically bounded complexes. Among other things we show that (a) these invariants characterize the Cohen-Macaulay property for local rings, (b) Cohen-Macaulay flat dimension fits between the Gorenstein flat dimension and the large restricted flat dimension, and (c) Cohen-Macaulay injective dimension fits between the Gorenstein injective dimension and the Chouinard invariant.Comment: To appear in Mathematica Scandinavic