Measurement plots

Methods for the determination of solubility have been thoroughly reviewed [21,22], Solubility is normally highly dependent on temperature, and so the temperature must be recorded for each solubility measurement. Plots of solubility against temperature, as exemplified by Fig. 4 [23,24], are commonly used for characterizing pharmaceutical solids and have been extensively discussed [1,24]. Frequently (especially over a relatively narrow temperature range), a linear relationship may be given either by a van t Hoff plot according to [23]... 

Figure 8.6 Difference between real age and age estimated from skeletal measurements plotted as a function of real age in the Spitalfields population. (Adapted from Molleson and Cox, 1993 Figure 12.4, by permission of the CBA and the author.)...

Descriptions of the experimental scattering and microscopy conditions have been published elsewhere and are referenced in each section. Throughout this report certain conventions will be used when describing uncertainties in measurements. Plots of small angle scattering data have been calculated from circular averaging of two-dimensional files. The uncertainties are calculated as the estimated standard deviation of the mean. The total combined uncertainty is not specified in each case since comparisons are made with data obtained under... 

Figure 9.9 Predicted versus measured plot for urea crystallization temperature.

The predicted versus measured plot in Figure 9.9 shows the correlation between the acoustic signal and crystallization temperature, and hence its ability to predict it on-line. 

Figure 9.11 Predicted and measured plot for granule moisture contents, calibrated on data from 5 months of production. Sensor B was used in this model (eight PLS components). Cray curve measured, black curve predicted.

Raw Measurement Plot In Figure 4.48 the raw data for the four unknown samples are plotted with the mean of the training samples for the four classes (A-D). The mean is the average of the measurement vectors for all samples within a class and is used as a representation of the expected features for samples that belong to the respective class. The differences in the features may indicate the source of problems for unknowns where the classifications are suspect. Figure 4.48 confirms the other diagnostic tools, which indicate that ( ) unknown 1 is not a member of any class, ( ) unknown 2 is a member of class A, (c) unknown 3 is a member of class D, and (rf) unknown 4 is most like A but has different features. 

Raw Measurement Plot If an on-line analyzer were soning the containers, unknown 3 would have been rejected and the spectrum stored for further evaluation. The spectrum of this unknown is plotted in Figure 4.56 along with the average of the training set spectra for PVC and PET. Unknown 3 has features from both of these classes and, therefore, the classification results are not surprising. 

Raw Measurement Plot The taw data for the prediction samples is not usually plotted given that the diagnostics did not flag any samples as unusual. Tliey are displayed here because of the limited error detection of the other diagnostic tools. The pieprocessed data in Figure 5.87 do not re eal any unusual samples. 

Raw Measurement Plot Because no samples have been identified as outliers, the raw data are not plotted. 

Raw Measurement Plot The raw data for the four unknowns are plotted in Figures 5-20-5-23 and were discussed above. 

Raw Measurement Plot In multivariate calibration, it is normally not necessary to plot the prediction data if the outlier detection technique has not flagged the sample as an outlier. However, with MLR, the outlier detection methods are not as robust as with the full-spectrum techniques (e.g., CLS, PLS, PCR) because few variables are considered. Figure 5.75 shows all of the prediction data with the variables used in the modeling noted by vertical lines. One sample appears to be unusual, with an extra peak centered at variable 140. The prediction of this sample might be acceptable because the peak is not located on the variables used for the models. However, it is still suspect because the new peak is not expected and can be an indication of other problems. 

Figure 16.9 The ratio of the effective calorimetric enthalpy to the enthalpy calculated by the van t Hoff method from optical measurements, plotted against the temperature of denaturation. The symbols represent the following proteins , metmyoglobin A, ribonuclease O, cytochrome c O, a-chymotrypsin , lysozyme. Reproduced by permission from P. L. Privalov, Adv. Prot. Chem., 33, 167 (1979).

An example of the most common control chart, the Shewhart chart, is shown in Fig. 8-46. It merely consists of measurements plotted versus sample number with control limits that indicate the range for normal process operation. The plotted data are either an individual measurement x or the sample mean x if more than one sample is measured at each sampling instant. The sample mean for k samples is cal-... 

Once you finished the measurements, plot the optical density as a function of Calcofluor White concentration expressed in mg ml-1. What type of plot do you obtain, and why How do you expect to calculate the value of s from the plot you obtained The molecular weight of Calcofluor is equal to 942.7. Can you give the value of s in M-1 cm-1 ... 

Table 6.4 uses calculated diffusion coefficients to predict plot gradient. The plot gradient prediction would be more useful with measured D values, but factors greater than 2 between calculated and measured plot gradient are significant deviations from accepted theory, and the source of the difference is unlikely to be error in D values. Anomalies were found for two compounds with high log Pow which also exhibit a negative plot intercept, and for two carboxylic acids (2,4-D and acetic acid). 

Thermodynamic data, and especially AS values, are generally unreliable or lacking for important phosphate complexes. Until such AS data is measured, it can be estimated with fair accuracy using the Fuoss equation for monovalent and divalent-bonded complexes and the electrostatic model when trivalent and quadrivalent addends are associated. Unfortunately, published AG and AS data on HS , s2 , and Se and Te aquo-complexes are suspect or largely lacking (Barnes, H. L., Pennsylvania State University, personal communication, 1978). Both the stoichiometry and stability of such complexes remains in doubt. Once a few such data have been accurately measured, plots with EN (10) or Q (44) as a variable, or using hard and soft acid and base concepts (3, 40) should permit the useful estimation of many as yet un-... 

Results obtained with n-GaAs in NaOH are presented in Fig. 17. True in-situ STS measurements, plotted in the form of ii - U, curves, are solid lines. Since in tunneling mode the tip current is the sum ij + h, with ij the tunnel current, the faradaic component ip has been determined by retracting the tip far away from the surface (dotted line). The shape of STS curves is very similar to curves obtained in ex-situ... 

Figure 10. The logarithm of the linear growth rate G, based on polarized light microscopy measurements, plotted versus l/[T(T°i-T)] for HPX-C11 2 main direction ( ) lateral (O).

For each series of wavelength measurements, plot the mole ratio, x, of pyridine vs Aml- Using either software or a ruler, draw two straight lines following the increasing slopes to an apex. 

Construct a binding curve for each series of wavelength measurements, plot the change in absorbance, AAgoo vs total pyridine concentration (AA600 = measured absorbance at 600 nm for each solution minus A600 for 7.5 mM [Ni(salpd)], i.e., Stock 1. Note that this is equal to [A sm[M]t in equation (3.28). 

Fluorine has a high NMR sensitivity and, having similar chemical properties to protons, fluorine-substituted compounds are used widely in the pharmaceutical and medical industries. In addition to many studies carried out in the gas phase, the temperature dependence of the chemical shifts of liquid-state hexafluorobenzene, 1,4-ditrifluoromethylbenzene (DTFMB), 1,4-dibromo-tetrafluorobenzene (DBTFB) and CFCI3 have been measured.Plots of chemical shift vs. temperature were highly linear for hexafluorobenzene (0.0022 ppm K from 280 to 340 K) and CFCI3 (0.0048 ppm K from 220 to... 

Figure 6. Activation energy of the JG relaxation in the glassy state for different isobaric measurements plotted versus the related Tg(P). QN in tristyrene (5% and 10% wt. are indicated by open circles and solid squares, respectively), 5% wt. QN in PS800 (solid triangles), PPGE (solid stars), 5% wt CNBz in tristyrene (open stars), 17% ClBz in decalin from reff ] (solid down triangles). Dashed lines are the predictions according toEq. (3).

After each Meissner effect measurement plotted in Fig. 5, x(T) was measured from Tc to Tmax — 460-530C, where Tmax was the temperature necessary to remove enough oxygen for the next desired oxygen stoichiometry. Tmax increased with increasing x in YBa2Cu30y x. Some of the x(T) data are shown in Fig. 6, where x(T) data for a separately prepared sample of YBa2Cu30g (see experimental section) are also shown. 

A dynamic technique is described for obtaining surface elasticity (e0) vs. surface pressure (tt) curves which can be transformed into accurate tt—A curves for soluble monolayers. Small amplitude periodic area variations are used with a sufficiently high frequency to make monolayers effectively insoluble in the time of the experiment even though they behave as soluble in equilibrium measurements. plots are given for some nonionic surfactants. Straight line portions in these plots illustrate that surface interactions are too complex to be described by a Frumkin isotherm. In the limit of very low surface pressures there is no trace of an ideal gaseous region. Some examples show the implications of particular e0—rr curves for equilibrium and dynamic surface behavior. 

Control Chart. You will probably prepare this on the second day, after the method has been developed. You will be given an unknown (blind) sample. Make a measurement on it every 20 min throughout one laboratory period, intermittently with other measurements the team is making you should make at least eight measurements. Plot the determined concentration vs. time of day. After you have done this, and shown it to your instructor, obtain the known value from the instructor, and draw a horizontal line on the chart at that concentration. From the precision that Team B has determined for the method (at midrange), draw lines for iimer and outer control limits at 2 and 2.5 standard deviations, respectively. Are your values within the control lines Is there a trend in one direction ... 

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