Curvilinear triangle

This procedure is based on the use of unique sphere, with its tesserae defined in terms of a number of spherical triangles (from 60 to 940) derived by partition of the pentakisdodecahedron faces. The sphere is deformed to mimick the molecular shape, taking into account solvent excluded volume. The number of tesserae is automatically increased only in the portions of the surfaces where it is needed, keeping the shape of a curvilinear triangle. The gain in computational times reaches a 100 factor for the largest molecules. 

As mentioned earlier, near every vertex, there is a domain, namely the adjacent curvilinear triangle with G(c) > go, that is inaccessible from the inside, where G(c) > go, see Fig. 6.4C. An interesting question then arises how closely can this vertex, say Ai, be approached if the initial... 

At the junctions between three films, there are some thicker areas (called Plateau borders) whose cross-section is constant along the edge and has the shape of a curvilinear Plateau triangle formed by arcs of three adjacent circles. 

As shown in Fig. 6.3, Mishra et al. (1995) presented a tetrahedron as the spatial form of their metastable phase diagram, the comers of which represented MMA, PMMA, urethane prepolymer U , and PU. The PMMA contained 0.5 % tetraethylene glycol dimethacrylate, causing it to gel after about 8 % conversion see the Gi- U -PU plane. The phase separation curve for the ternary system MMA-PMMA- U (front triangle) on polymerization of only the MMA is indicated by the points C-D-A-E. Similarly, the phase separation curve for the MMA-PMMA-PU system (see rear triangle. Fig. 6.3) is represented by the points J-B-K-L. Thus, the entire tetrahedron volume is divided into two regions one phase separated and the other single phased, separated by the curvilinear constmction C-D-A-E-L-B-J. This surface exhibits a characteristic sail-like shape. 

Fig. 11.8A shows the curvilinear case of the coincidence between the time of intersection (aa=Ca he time of maximum tAs.max The coloring of this figure is mostly blue (grey), with a small yellow (white) domain near the left-bottom vertex. The top-left side of the triangle corresponds to the irreversible case studied by Yablonsky et al. (2010). Visually we can identify the boundary between yellow and blue on that side as Ic2 = /2. When the size of subdomains... 

Components of the curvilinear E- and A-waves, approximated as triangles, defined as the acceleration time (AT), deceleration time (DT), and peak height (Ep, ), were found to correlate with selected clinical pathologies such as ischemia, high blood pressure, or diabetes. Parameters such as the peak E to peak A ratio (E/A), which varied depending on disease, were empirical and found to be load dependent [1]. With no causal explanation for E-wave alteration, sensitivity and specificity for diagnosis of abnormal DF (diastolic dysfunction [DD]) was hindered. 

Fig. 4 Tetrahedron for the simultaneous IPN from PU and PMMA, showing the gelation plane of the PMMA and the curvilinear plane of phase separation. Inset experimental data for the phase separating part of the front left triangle, showing the appearance of turbidity during MMA polymerization as an indication of phase separation [4]...

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