Square plots

Oxygen isotopes in achondrites (above) and primitive achondrites (below). The 8 notation and units are explained in the caption for Figure 6.4. Most achondrites define mass fractionation lines parallel to, but slightly offset from the terrestrial line. Aubrites and lunar samples plot squarely on the terrestrial line. Primitive achondrites generally do not define oxygen mass fractionation lines, but are scattered and resemble their chondrite precursors. 

Figure 2. The vibrational energy transfer rate, UVA. from reactive states to nonreactive states at energy E is plotted (squares) above the barrier energy of 5500 cm for cyclohexane chair-boat isomerization. Also plotted (circles) is the corresponding transmission coefficient, K(E), calculated with Eq. (9).

FIGURE 7.1 Selectivity for the gas pair CO2/CH4 as a function of CO2 permeability and the Robeson plots (squares for CMS membranes, solid circles for TR polymers, triangles for FSC membranes, and solid diamonds for PIMs). (Robeson plots from Ref. [5] data from Refs. [8-13].)... 

Figure 3 Small-angle neutron scattering data of protonated PS dissolved In deuterated PS plotted as Zimm plot. Squares c=0.5% circles c=5%. The data were taken from WIgnall, G. D. Ballard, D. G. H. Schelten, J. J. Macromol. Sci. Phys. 1976, B12, 75. ...

In many process-design calculations it is not necessary to fit the data to within the experimental uncertainty. Here, economics dictates that a minimum number of adjustable parameters be fitted to scarce data with the best accuracy possible. This compromise between "goodness of fit" and number of parameters requires some method of discriminating between models. One way is to compare the uncertainties in the calculated parameters. An alternative method consists of examination of the residuals for trends and excessive errors when plotted versus other system variables (Draper and Smith, 1966). A more useful quantity for comparison is obtained from the sum of the weighted squared residuals given by Equation (1). 

Barnes and Hunter [290] have measured the evaporation resistance across octadecanol monolayers as a function of temperature to test the appropriateness of several models. The experimental results agreed with three theories the energy barrier theory, the density fluctuation theory, and the accessible area theory. A plot of the resistance times the square root of the temperature against the area per molecule should collapse the data for all temperatures and pressures as shown in Fig. IV-25. A similar temperature study on octadecylurea monolayers showed agreement with only the accessible area model [291]. 

Using the curve given by the square points in Fig. XVI-2, make the qualitative reconstruction of the original data plot of volume of mercury penetrated per gram versus applied pressure. 

Plot the data according to the BET equation and calculate Vm and c, and the specific surface area in square meters per gram. 

A succinct picture of the nature of high-energy electron scattering is provided by the Bethe surface [4], a tlnee-dimensional plot of the generalized oscillator strength as a fiinction of the logaritlnn of the square of the... 

One of the most important fiinctions in the application of light scattering is the ability to estimate the object dimensions. As we have discussed earlier for dilute solutions containing large molecules, equation (B 1.9.38) can be used to calculate tire radius of gyration , R, which is defined as the mean square distance from the centre of gravity [12]. The combined use of equation (B 1.9.3 8) equation (B 1.9.39) and equation (B 1.9.40) (tlie Zimm plot) will yield infonnation on R, A2 and molecular weight. 

Figure B2.4.2. Eyring plot of log(rate/7) versus (1/7), where Jis absolute temperature, for the cis-trans isomerism of the aldehyde group in fiirfiiral. Rates were obtained from tln-ee different experiments measurements (squares), bandshapes (triangles) and selective inversions (circles). The line is a linear regression to the data. The slope of the line is A H IR, and the intercept at 1/J = 0 is A S IR, where R is the gas constant. A and A are the enthalpy and entropy of activation, according to equation (B2.4.1)...

Figure B2.4.6. Results of an offset-saturation expermient for measuring the spin-spin relaxation time, T. In this experiment, the signal is irradiated at some offset from resonance until a steady state is achieved. The partially saturated z magnetization is then measured with a kH pulse. This figure shows a plot of the z magnetization as a fiinction of the offset of the saturating field from resonance. Circles represent measured data the line is a non-linear least-squares fit. The signal is nonnal when the saturation is far away, and dips to a minimum on resonance. The width of this dip gives T, independent of magnetic field inliomogeneity.

Thus, by plotting as a function of in tire limit of small q tire mean square of tire end-to-end distance can be... 

Figure C2.5.8. Plot of the folding times Tp as a fimction of cr nfor tlie 22 sequences. This figure shows tlrat under tire external conditions when tire NBA is tire most populated tlrere is a remarkable correlation between ip and The correlation coefficient is 0.94. It is clear tlrat over a four orders of magnitude of folding times Xp = expf-a, / Oq) where CTq is a constant. The filled and open circles correspond to different contact interactions used in C2.5.1. The open squares are for A = 36.

Figure C2.17.12. Exciton energy shift witli particle size. The lowest exciton energy is measured by optical absorjDtion for a number of different CdSe nanocrystal samples, and plotted against tire mean nanocrystal radius. The mean particle radii have been detennined using eitlier small-angle x-ray scattering (open circles) or TEM (squares). The solid curve is tire predicted exciton energy from tire Bms fonnula.

Figure 8, Wavepacket dynamics of the butatriene radical cation after its production in the A state, shown as snapshots of the adiabatic density (wavepacket amplitude squared) at various times. The 2D model uses the coordinates in Figure Ic, and includes the coupled A andX states, The PES are plotted in the adiabatic picture (see Fig. lb). The initial structure represents the neutral ground-state vibronic wave function vertically excited onto the diabatic A state of the radical cation,...

In this illustration, a Kohonen network has a cubic structure where the neurons are columns arranged in a two-dimensional system, e.g., in a square of nx I neurons. The number of weights of each neuron corresponds to the dimension of the input data. If the input for the network is a set of m-dimensional vectors, the architecture of the network is x 1 x m-dimensional. Figure 9-18 plots the architecture of a Kohonen network. 

Plot tin g the same orhitnl as its den sily. wh ich is the square ol the wave riinctioii, eniphasi/es the difference in magnitude al the different sites. 

Plot the probability density obtained from E in Problem 9 as a function of r, that is, simply square the function above with an appropriate scale factor as determined by trial and error. Comment on the relationship between your plot and the shell structure of the atom. 

Plotting the left side of Eq. (3-22) as a function of gives a curve with as the slope and E° as the intercept. Ionic interference causes this function to deviate from lineality at m 0, but the limiting (ideal) slope and intercept are approached as OT 0. Table 3-1 gives values of the left side of Eq. (3-22) as a function of The eoneentration axis is given as in the corresponding Fig. 3-1 beeause there are two ions present for each mole of a 1 -1 electrolyte and the concentration variable for one ion is simply the square root of the concentration of both ions taken together. 

Plotting the same orbital as its density, which is the square of the wave function, emphasizes the difference in magnitude at the different sites. 

When you request an orbital, you also request a plot of either the orbital itself or of its square. The orbital /j is a signed quantity with... 

The overall standard deviation, S, is the square root of the average variance for the samples used to establish the control plot. 

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