Every graph G can be represented by a collection of equi-radii spheres in a d-dimensional metric ∆ such that there is an edge uv in G if and only if the spheres corresponding to u and v intersect. The smallest integer d such that G can be represented by a collection of spheres (all of the same radius) in ∆ is called the sphericity of G, and if the collection of spheres are non-overlapping, then...

The fullerene-50 is a 'magic number' cage according to the 2(N + 1)(2) rule. For the three lowest isomers of C50 with trigonal and pentagonal symmetries, we calculate the sphericity index, the spherical parentage of the occupied π-orbitals, and the current density in an applied magnetic field. The minimal energy isomer, with D3 symmetry, comes closest to a spherical aromat or a superaromat. In ...

Typical simulations of packed bed active magnetocaloric regenerators rely on correlations of Nusselt number as a function of Reynolds number. These models are well understood for large ranges of Reynolds number, but experimental data is lacking as Reynolds number approaches zero. Within a typical magnetocaloric refrigeration cycle a zero fluid velocity or dwell condition is present. When a cycl...

Clinical and hemodynamic appearances of aortic regurgitation caused by serious aortic lesions (AR-Ao-group) seemed more deteriorated than those with isolated chronic aortic regurgitation (AR-group). Often postoperative course and operative outcome are smooth and satisfactory in the AR-Ao-group. To support this observation, serial changes of left ventricular (LV) function and LV sphericity were ...

This paper presents a review and analysis of the research that has been carried out on dynamic calibration for optical-fiber solids concentration probes. An introduction to the optical-fiber solids concentration probe was given. Different calibration methods of optical-fiber solids concentration probes reported in the literature were reviewed. In addition, a reflection-type optical-fiber solids...

This article teaches the multivariate analysis of variance (MANOVA) method for repeated measures analysis to researchers who are already familiar with regular analysis of variance (ANOVA) methods. Repeated measures designs are traditionally analyzed with mixed-model ANOVAS. However, sphericity violations markedly affect the true Type I error rates and power for the mixed-model tests. However, t...

Monosubstituted alkanes are counted as stereoisomers by means of Fujita’s proligand method (Fujita S (2005) Theor. Chem. Acc. 113:73-79, 113:80-86, Fujita S (2006) Theor. Chem. Acc. 115:37-53), where the numbers of primary, secondary, and tertiary ones are calculated after deriving respective functional equations. The procedures of counting are programmed by means of the Maple programming langu...