Contour plot and

Fig. 28. Contour plot and instanton trajectory for PES (4.28) with the parameters of fig. 25, ojqP = 35.

The contour plots and MEPs for both cases are demonstrated in fig. 56. The MEP in the total configuration space obeys the equation... 

From which compound were the INADEQUATE contour plot and C NMR spectra 21 obtained Conditions (CD3)2CO, 95 % v/v, 25 °C, 100 MHz. (a) Symmetrised INADEQUATE contour plot with C NMR spectra (b) H broadband decoupled spectrum (c) NOE enhanced coupled spectrum (gated decoupling) (d) expansion of multiplets of (c). 

In order to understand the relationship between the mixture component, physical properties and consumer acceptance of the lipstick, various lipstick formulations have to be produced. The physical properties of each formulation should be studied. The consumer acceptance towards the product also should be investigated. However, only a part of this work will be discussed in this paper. Here, natural waxes, oils and solvent have been used to produce natural ingredient based lipstick formulations based on the formulation suggested by the statistical mixture design. Contour plot and response surface graph were formed in order to understand the relationship between the mixture component and physical characteristic of the lipstick. 

Figure 13-10. The potential of mean force (kcal/mol) as a function of D1 and D2 (A) shown as a 20-level contour plot and colored by the free energy values...

FIGURE 2 CONTOUR PLOT AND SEARCH TRAJECTORY FOR TEST DATA (INITIAL ESTIMATES k1 s 1.5 /min, k2 = 1.5 A/mol/min)... 

Figure 6. Contour plot and cuts along the velocity and range axis of the ambiguity function/bistatic pair dominance case.

Fig. 7. Contours plots and projections of 2-D (left) and P F (right) HetCor...

Figure 4.12 Contour plot and levels of the crushing strength of the...

Fig. 4.4. A histogram of fluorescence and contour plots (plotted according to different line assignments) of the same data. Comparison between the histogram and the contour plots allows us to see at what altitudes the contour lines have been drawn for each contour plot and why the resulting displays look so different.

The simulated double-quantum coherence 2D INADEQUATE spectrum of 2-chlorobutane is shown in Figure 13.18. The normal 13C spectrum is plotted along the top. Only the cross peaks appear in the contour plot, and each cross peak appears as a doublet (a pair of dots) at this level of resolution. The separation between these dots, about 35 Hz in this case, is /Cc- Each pair of correlated (by one-bond coupling) cross peaks is indicated by a separate dotted horizontal line, with the midpoint of each line on the diagonal. The F axis is the double-quantum frequency, essentially the sum of the 8v values of the two coupled nuclei. 

Figure 4 Sample contour plots and partial three-dimensional views of nonlinear two-dimensional functions (a) f(x1,x2) = exi(4x12 + 4xlx2 + 2xzz) (b) f(xux2) = ext(xi - lx2)2.

Fig. 6.13 Representations of the valence m.o.s of HF (only one of the two tt orbitals is shown) by contour plots and a three-dimensional grid in the case of the vacant (anti-bonding) m.o. Plot of DD (density difference) illustrates the detailed structure of the difference map between the total electron density and the atomic contributions if no bond was formed (full lines for increase of electron density and dotted lines for decrease).

Be certain you understand these choices in each image you examine (or create ). These same issues appear in Chapter 5 when we discuss the wave functions for electrons in atoms, called atomic orbitals. Throughout this book, we have taken great care to generate accurate contour plots and isosurfaces for them from computer calculations to guide your thinking about the distribution of electrons in atoms and molecules. 

We present quantitative, computer-generated plots of the solutions to the particle-in-a-box models in two and three dimensions and use these examples to introduce contour plots and three-dimensional isosurfaces as tools for visual representation of wave functions. We show our students how to obtain physical insight into quantum behavior from these plots without relying on equations. In the succeeding chapters we expect them to use this skill repeatedly to interpret quantitative plots for more complex cases. 

The shale smear map was constructed by overlaying the shale map and the displacement contour plot, and shading in the area from the footwall cutoff of a shale bed down to the displacement contour equal to 7 times the thickness of the shale bed. This area represents the surface of the fault where the shale smear will be continuous and will be a significant barrier to hydrocarbon migration. Where the displacement value is >7 times the thickness of the shale bed, the smear is likely to be discontinuous and is unlikely to be a barrier to hydrocarbon migration. This mapping of shale smear is repeated for all thick shale units. 

Figure 2.1.3 Contour plot of the 2D 500.1 MHz H detected H/ Sn shift correlation (HSQC) of a sample of a reaction mixture containing three different tin-boron compounds. The mixture could not be analyzed by direct Sn NMR methods. (Adapted from Reference 152.) The f, projection shows the Sn NMR spectrum with its broad lines as a result of Sn,"B) 1000 Hz. The overlapping Sn resonances are well resolved in the contour plot, and the unstable species Me3SnB(OMe)2 (marked by lines towards f, and F2) can be readily identified. The insert shows the influence of relatively slow B quadrupolar relaxation in [Me3SnBH I giving rise to fairly sharp Sn NMR signals. (Reproduced from Reference 204, with permission form Wiley-VCH.)...

Select the desired quantities for contour plots and surface plots ... 

From which compound were the INADEQUATE contour plot and C NMR spectra 19 obtained ... 

From the total sample set (48 samples), 45 samples were used as calibration samples. The three samples excluded from the calibration set were selected on the basis of a representative variation of their active ingredient concentrations, and finally used as unknown test samples to predict the content of their active ingredients. Partial least squares (PLS) models for each active ingredient were developed with the Unscrambler Software (version 9.6 CAMO Software AS, Oslo, Norway) from the MSC-pretreated median spectra of all pixels of each of the 45 calibration sample images. Based on these calibration models, the predictions of the active ingredient content for each pixel of the imaging data of the three test samples and their evaluation as histograms, contour plots and RGB plots was performed with Matlab v. 7.0.4 software (see below). 

Fig. 7. Contour plot and expansion of a 2D- P, Fe H) correlation of exo- and endo- T -Cp)(Tj -l-sy/i-methylaIlyl)(PF )]Fe. TTie tilt in the cross-signal of the major isomer (bottom) in cales that the passive couplings 7(P,F) in P2 and /(Fe,F) in FI are of opposite sign. Reproduced, with permission, from ret 79. Copyright 1988 American Chemical Society.

The surface representing the model is called the response surface. Graphically, the response surface can be visualized by drawing 2D contour plots or 3D response surface plots (7). A 2D contour plot shows the isoresponse lines as a function of the levels of two variables, while a 3D response surface plot represents the response, on a third dimension, as a function of the levels of two variables. An example of a 2D contour plot and a 3D response surface plot is shown in Figure 2.18. When more than two factors... 

FIGURE 2.18. Graphical representation of the response resolntion of Table 18 (28) as (a) 2D contour plot and (b) 3D response surface plot. The response is presented as a function of factors 1 (A) and 2 (B), while factor 3 (C) is fixed at nominal level (Table 2.3). 

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