Contour tracing

Wyko Trace. A surface profile contour trace. 

Figure 4. Projection of typical short-axis contours in the jc, y plane. The endocardial and epicardial contours traced from a two-dimensional echocardiographic short-axis image are superimposed on a radial (circular) grid. The intersection points between the radii and cardiac contours identify the location of finite element nodal points.

A surface with zero mean curvature being given, consider an arbitrary closed contour traced on it, satisfying only the conditions 1° that it circumscribes a finite portion of the surface, and 2° that this portion does not exceed the limit of stability, if the surface given has such limits bend a wire in such a manner that it takes exactly the closed contour in question slightly oxidize it by weakened nitric acid immerse it entirely in the glyceric liquid, and withdraw it you will find it occupied by a film representing the portion of surface in question. 

Thus B is a diagonal mati ix that contains in its diagonal (complex) numbers whose norm is 1 (this derivation holds as long as the adiabatic potentials are nondegenerate along the path T). From Eq. (31), we obtain that the B-matrix hansfomis the A-matrix from its initial value to its final value while tracing a closed contour ... 

In case of three conical intersections, we have as many as eight different sets of eigenfunctions, and so on. Thus we have to refer to an additional chai acterization of a given sub-sub-Hilbert space. This characterization is related to the number Nj of conical intersections and the associated possible number of sign flips due to different contours in the relevant region of configuration space, traced by the electronic manifold. 

The positions of the (—1) terms in the diagonal indicate which of the electronic eigenfunction flips sign upon tracing the closed contour under... 

Now imagine that we rotate the molecule about the internuclear axis. The curved contour will trace out a surface. If we draw a unit outward normal vector to this surface, it will be everywhere perpendicular to the gradient vector (because the gradient vector points along the trajectory). 

Johansson et al. (1995) illustrate the detection limits for the above type of specimens in terms of concentrations (ppm). Contours are shown in Figure 4.18 showing the dependence of the detection limit upon the trace element atomic number (Z) and the proton beam energy Ep. 

Fig. 3. Contour plot of the proton-detected local field (PDLF) spectrum of a static 5CB sample. The traces taken parallel to for each carbon site show distinct doublets that are related to individual C-H couplings. (Reproduced by permission of American Chemical Society.)...

FIGURE 10. Contour plot of two-dimensional nuclear Overhauser effect ll NMR (NOESY) of the protonated Schiff base of all-traos-retinal, in chloroform, with formate as the counterion. The intermolecular NOE cross-peak observed between H15 of the retinal and the counterion proton, at a mixing time of 0.4 s, is shown. Top trace f2 projection of the 2D NOE spectrum. Reproduced by permission of John Wiley Sons from Reference 36... 

Figure 629 (a) UV trace of the drug, (b) mass chromatogram of mJz 486 of an impurity component and (c) two-dimensional contour plot of the mass spectra from mIz 400 to mIz 550. Reproduced from [22] with permission of John Wiley and Sons Ltd. 

Instead of 3-D plots, traces of the binding isotherm surface through a plane parallel to the [L]/[I] plane (contour diagrams) or profile plots (traces through the p./[L] or /x/[l plane can be used to explain certain special conditions. 

Fig. 6.8 Concentration contours for flow past spheroids at Re = 100 and Sc = 0.7. Flow from right to left. Dashed lines are streamlines as in Fig. 6.1 with values of l//a U indicated. Dimensionless concentration values are marked on the solid lines which trace lines of constant concentration (M6).

Figures 13.7 and 13.8 are two examples of two-dimensional NMR spectroscopy applied to polymers. Figure 13.7 is the proton homonuclear correlated spectroscopy (COSY) contour plot of Allied 8207A poly(amide) 6 [29]. In this experiment, the normal NMR spectrum is along the diagonal. Whenever a cross peak occurs, it is indicative of protons that are three bonds apart. Consequently, the backbone methylenes of this particular polymer can be traced through their J-coupling. Figure 13.8 is the proton-carbon correlated (HETCOR) contour plot of Nylon 6 [29]. This experiment permits the mapping of the proton resonances into the carbon-13 resonances.

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