The angle defect, which is the standard way to measure the curvatures at the vertices of polyhedral surfaces, goes back at least as far as Descartes. Although the angle defect has been widely studied, there does not appear to be in the literature an axiomatic characterization of the angle defect. In this paper a characterization of the angle defect for simplicial surfaces is given, and it is sh...

The angle defect, which is the standard way to measure curvature at the vertices of polyhedral surfaces, goes back at least as far as Descartes. Although the angle defect has been widely studied, there does not appear to be in the literature an axiomatic characterization of the angle defect. We give a characterization of the angle defect for simplicial surfaces, and we show that variants of the...

Methanol (CH3OH) is a colorless liquid with a mild odor. The wide ranges of applications, toxicity and clinical implications of methanol have made necessary to develop reliable and high-performance methanol sensors. In this paper, WO3 thin films were deposited on SiO2/Si substrates by e-beam evaporation technique under normal and oblique angles and then post-annealed at 500 °C with a flow of ox...

Chiral molecules are characterized by a specific rotation angle, the angle through which plane-polarized light is rotated on passing through an enantiomerically enriched solution. Recent developments in methodology allow computation of both the sign and the magnitude of these rotation angles. However, a general strategy for assigning the individual contributions that atoms and functional groups...

The geometry of natural branching systems generally reflects functional optimization. A common property is that their bifurcations are planar and that daughter segments do not turn back in the direction of the parent segment. The present study investigates whether this also applies to bifurcations in 3D dendritic arborizations. This question was earlier addressed in a first study of flatness of...

We studied the between-therapist reliability and the validity of four instruments in measuring lumbar spine curvature and pelvic tilt. The four instruments and their measurements were 1) a tape measure to measure the change in lumbar curvature during trunk flexion; 2) a gravity goniometer to measure pelvic angle and lumbar curvature during stance, trunk flexion, and trunk extension; 3) a parall...