Combined contour plot

In Figure 4.13 the relation between disintegration time and mixture composition is depicted. With the application of more than one criterion a combined contour plot (Figure 4.14) can be made, where parts of the factor space that do not satisfy our demands, are shaded. So the unshaded area is the region where mixtures can be found that will satisfy our demands. 

Figure 4.14 Combined contour plot of the crushing strength and the disintegration time = = disintegration time > 20 s /// = crushing strength < 100 N 0= remaining area...

To obtain pictures of the orbital ip = R0< >, we would need to combine a plot of R with that of 0, which requires a fourth dimension. There are two common ways to overcome this problem. One is to plot contour values of ip for a plane through the three-dimensional distribution as shown in Figures 3.8a,c another is to plot the surface of one particular contour in three dimensions, as shown in Figures 3.8b,d. The shapes of these surfaces are referred to as the shape of the orbital. However, plots of the angular function 0 (Figure 3.7) are often used to describe the shape of the orbital ip = RQ because they are simple to draw. This is satisfactory for s orbitals, which have a spherical shape, but it is only a rough approximation to the true shape of p orbitals, which do not consist of two spheres but rather two squashed spheres or doughnut shapes. 

In this example with only three components, the optimum could have been determined by simply overlaying the individual response contour plots. This approach would be difficult, if not impossible, if the formulation would have many responses or contain four or more components. By contrast, the combination of the desirability function and the Complex algorithm permits an optimization of a multiresponse formulation having many constrained components in addition to providing the basis for sensitivity analysis. 

The initial wavepackets are built combining the rovibrational bound states with these NACMES s and derivative terms, as expressed in Eq.(17). In Eig.4 the contour plots associated to the initial wavepackets for the EP of the ground vibrational levels of A and B electronic states are shown. The most relevant features is the node appearing along r, the HP vibration. This is the reaction coordinate at... 

Fig. 2.59. Tracing out the carbon skeleton of C10H20O by a two-dimensional INADEQUATE experiment in combination with two DEPT experiments (100.6 MHz (a b) 400 mg in 1 mL, (c-e) 50 mg in 0.4 mL of deuteriochloroform at 30CC measuring time for (a) 14 h transform time 50 min) (a) contour plot of the INADEQUATE matrix (b) subspectra of all 13C — 13C bonds u k (c) proton-decoupled 13C NMR spectrum (d -e) DEPT experiments for generation of a CH carbon subspectrum (d) and for separation of CH2 carbon atoms (negative) from CH and CH3 groups (positive).

Combined function, surface, and level-zero contour plot for (3.6)... 

The m function runadiabNiso relies on adiabNiso3dplot, which combines our 2 = F(a, y) surface plot and a simplified version of the level-zero contour plot. 

Figure 4.12 (a) Surface response plot of a light cycle oil analysed by GC X GC. The column set was a BPX5-BPX50 combination, with the second column being 0.8 m in length. A 6 s modulation time was used, in conjunction with a l°C/min temperature programme rate. The cycle oil has been reformed to remove the cyclic alkanes, (b) The same data as in (a), but presented as a contour plot in this case. 

By using the FI direction as the time axis, the separation process, combined with the structure information in the F2 direction, can be investigated. Figure 7.2.6 shows the contour plot of the separation of five plasticizers, recorded by using a 400 MHz spectrometer with a 120 pi flow cell. The separation was... 

Figure 2 The Raman echo has the ability to distinguish single from multiple solvent interactions, (a) (b) Two-dimensional contour plots of the log of the Raman-echo correlation function, In Cre(ti, T3). Case 1 A combination of two interactions one in the fast modulation limit [T2 = 3.47 ps Equation (8)], and one in the slow modulation limit A, = 1.30 cm-1, r( = 40.9 ps Equation (9). Case 2 A single interaction with intermediate modulation (same as Fig. lb). The echo signals clearly differ for these two cases. However, the Raman lines have identical FWHM s (5 cm-1), and the Raman FID signals (c) are difficult to distinguish experimentally.

The relationship between the response and the variables is visualized by a response siuface or contour plot to see the relative influence of the parameters, to find an optimum parameter combination, and to predict experimental results for other parameter, for two variables, When k = 2 the empirical model from the general Eq. (2) becomes... 

A fine example of the use of pulse radiolysis technique in combination with steady-state product distribution is the recent study by Schuler and co-workers to probe charge distribution in aromatics. Their initial studies on biphenyf which were extended recently to phenof have been concerned with the determination of relative yields at o-, m- and -positions to examine the substituent effects on charge distribution. For example, Fig. 2 shows the contour plot of HPLC chromatographic data obtained in the OH radical reaction following the irradiation of phenol in the presence of the oxidant ferricyanide. Figure 3 shows the transient absorption spectra recorded in the reactions of OH and Ng radicals with phenol. The absorption... 

A contour plot is shown in Fig. 7.8. Note that this function is cylindrically-symmetrical about the z-axis with a node in the x, y-plane. The eigenfunctions 21 1 are complex and not as easy to represent graphically. Their angular dependence is that of the spherical harmonics 7i i, shown in Fig. 6.4. As deduced in Section 4.2, any linear combination of degenerate eigenfunctions is an equally-valid alternative eigenfunction. Making use of the Euler formulas for sine and cosine,... 

An example of the separation of coumarins with comprehensive normal-phase x reversed-phase LC systems has been published by Dugo etal for coumarins and psoralens in cold-pressed lemon oil. For the separation in the first dimension, the authors used a capillary normal-phase 1.0 mm X 300 mm 5 pm silica column with isocratic elution (eluent -hexane ACN (75 25)) at 20 pi min-1. In the second dimension, a monolithic 4.6 mm X 25 mm C18 silica column (including a 4.6 mm X 5 mm guard column) was employed with linear gradient elution (eluent A water and eluent B ACN) at 4 ml min-1. The interface between the first and the second dimension was a 10-port, 2-position valve equipped with two storage loops. The incompatibility of the solvents that were used in the two dimensions (NPC and RPC) and its effects in the separation were overcome by using a combination of a capillary column in the first dimension and an analytical monolithic column in the second dimension. With this NPC X RPC system, 11 heterocyclic compounds were analyzed and depicted in 2D contour plots. 

A graphical approach was also used by Millet and Pons to analyse anisotropy of rotational diffusion in proteins. The values of Z)j and DJD compatible with R IRi ratios are presented as a contour plot. The intersection of the contour plots for different residues provides the values of anisotropy parameters compatible with experimental data. The obtained parameters can be used as starting values for further optimisation. The method is apphcable to axially symmetric rotation. A combination of approximate and exact methods was used by Ghose et al. to reduce the computational time of the determination of rotational diffusion tensor from NMR relaxation data. The initial values of the tensor components and its orientation are evaluated from the approximate solution, which substantially reduces the search space during the exact calculations. The method was applied for the estimation of relative domain orientation of a dual domain protein. 

---