Normal curves

Examples of (a) straight-line and (b) curved normal calibration curves. 

The constant is called the modulus of elasticity (E) or Young s modulus (defined by Thomas Young in 1807 although the concept was used by others that included the Roman Empire and Chinese-BC), the elastic modulus, or just the modulus. This modulus is the straight line slope of the initial portion of the stress-strain curve, normally expressed in terms such as MPa or GPa (106 psi or Msi). A... 

The Metrohm E 636 Titroprocessor (Fig. 5.12) offers in principle the same possibilities as the Mettler MemoTitrators, but with some additional features concerning its operation, illustrated by the schematic diagram in Fig. 5.13, using the usual microprocessor terminology62 1, CPU 2, RAM 3, ROM 4, Bus 5, I/O interface 6,16-place alphanumeric display 7, numerical push-buttons 8, function and control buttons 9, card reader (for routine analysis) 10, alphanumeric thermoprinter for curves (normal and first derivative) and data on... 

Fig. 14 pH-titration curves normalized fluorescence intensity versus pH ( exc = 630 nm) of Square-650-pH, Square-650-pH-IgG, and Square-650-pH- . coli conjugates... 

Thus, %F is defined as the area under the curve normalized for administered dose. Blood drug concentration is affected by the dynamics of dissolution, solubility, absorption, metabolism, distribution, and elimination. In addition to %F, other pharmacokinetic parameters are derived from the drug concentration versus time plots. These include the terms to describe the compound s absorption, distribution, metabolism and excretion, but they are dependent to some degree on the route of administration of the drug. For instance, if the drug is administered by the intravenous route it will undergo rapid distribution into the tissues, including those tissues that are responsible for its elimination. 

During the analysis of real samples, the saturation limit of any impurity species is rarely reached. For that reason, the phase solubility curves normally... 

Fig. 25 STS curves (normalized I/V plots of LB monolayers of isomers 55 (crosses) and 56 (dots), deposited on an Au film over HOPG (highly oriented pyrolytic graphite), and scanned with a Pt/Ir nanotip. The films exhibit rectification in opposite quadrants of the plot, where the polarity is defined by the sign of the substrate electrode. Electron flow at forward bias in each case is from the acceptor to the donor [127]...

Fig. 9. Viscoelastic properties of ultrasound-treated ex vivo porcine muscle specimen. Muscle samples were coagulated with focused ultrasounds in selected regions. MRE using the method of Ref. 23 was carried out and shear moduli were calculated in normal and heated regions at different shear wave frequencies. Upper curve FUS-treated tissue. Lower curve normal tissue. Error bars are for standard deviations. (From Ref 47, reprinted by permission of Wiley-Liss, Inc., a subsidiary of John Wiley Sons, Inc.)...

Gas Chromatography Analysis of Water for Pesticides. All analyses for pesticides in water were done by gas chromatography. Solvents used for extraction were checked by gas chromatography for purity and interferences and all glassware used in the extraction was cleaned in a chromic acid/sulfuric acid mixture. Standards consisted of mixtures of various pesticides (actual commercial formulations) suspended or dissolved in water. These aqueous standards were extracted in the same manner as unknown solutions. The standard concentrations encompassed the concentration of unknowns to be determined. A standard curve normally consisted of a set of four pesticide concentrations. Blanks were run and an internal standard (eicosane) was used. The internal standard concentration was kept constant for all analyses. The conditions for GC analysis were guided by the pesticides expected in the water. For the more complex mixtures, such as those employed in the synthetic waste and those encountered in the field, a 6 ft., 3 percent SE-30 on GAS CHROM Q column sufficed. A typical chromatogram of a complex pesticide mixture is shown in Figure 2. ( )... 

Figure 6.39(a) shows the vs. T curve, normalized to the RT value, for a 100 nm thick a-/ -NPNN/glass film obtained from electron paramagnetic resonance (EPR) measurements with the static magnetic field applied perpendicular to the substrate plane. As previously shown in Fig. 3.19, the molecular a -planes are parallel to the substrate s surface. The data points closely follow the Curie-Weiss law = (T — w)/C, where C stands for the Curie constant. In this case w — —0.3 K, indicating that the net intermolecular interactions are weakly anfiferromagnetic. No hint of a transition at low temperature is observed. These results coincide with those derived from SQUID measurements on a single a-p-NPNN crystal (Tamura etal, 2003), where 0.5 < w < 0, which are displayed in Fig. 6.40. 

A new calibration curve must be implemented every time a new stock of internal standard solution is prepared, and at least twice per year. New calibration curves are validated by the following criteria for acceptability point-to-point comparison (<10% difference from the previous calibration curve), coefficient of linear regression (>0.99), intercept and slope (<10% difference from previous calibration curve). Normal and abnormal control samples are calculated against the new and the old curve and compared to the current quality control (QC) mean as the final step in the validation of the new curve. The new calibration curve is then used with subsequent runs if the curve validation is acceptable. Curves are unique to each instrument and therefore must be established for each instrument prior to clinical use. 

Figure 21.2—Gaussian distribution. As the number of measurements increases and the width of the interval remains relatively narrow, the envelope of data points (frequency vs measurements) resembles that of a Gaussian curve (normal distribution). The bottom figure represents two series of results with two different means. If the number of measurements is very small, it is not possible to estimate the average distribution. At the bottom right, the reduced form of the Gaussian distribution is shown.

Gaussian curves (normal distribution functions) can sometimes be used to describe the shape of the overall envelope of the many vibrationally induced subbands that make up one electronic absorption band, e.g., for the absorption spectrum of the copper-containing blue protein of Pseudomonas (Fig. 23-8) Gaussian bands are appropriate. They permit resolution of the spectrum into components representing individual electronic transitions. Each transition is described by a peak position, height (molar extinction coefficient), and width (as measured at the halfheight, in cm-1). However, most absorption bands of organic compounds are not symmetric but are skewed... 

Fig. 5.4 Effect of the exchange current density on the shape of the current-voltage curves normalized to the limiting current 7l (adapted from Bard and Faulkner, 2001, p. 107)...

The sign of the curvature K tells us on which side of the curve the center of the curvature lies. If K > 0, then the center of the curvature lies on the positive side of the curve normal. It lies on the negative side of the curve normal if K < 0. If K = 0, then the line of constant illumination is really a straight line. 

Fig. 4.20 Influence of the electrode radius (rs and rA values indicated on the curves) on DDPV curves for disc (solid line) and spherical (dashed line) electrodes with rs = rd in all the cases. Three different AE values are considered (a) —200 mV, (b) 0 mV, and (c) +200 mV. The curves normalized with respect to the peak current are also shown in the inserted graphs. T1/T2 = 50, AE = —50mV, ti = 1 s. T = 298 K. is given in Eq. (4.49). Reproduced with permission of [64]...

Potentiometric titration curves normally are represented by a plot of the indicator-electrode potential as a function of volume of titrant, as indicated in Fig. 4.2. However, there are some advantages if the data are plotted as the first derivative of the indicator potential with respect to volume of titrant (or even as the second derivative). Such titration curves also are indicated in Figure 4.2, and illustrate that a more definite endpoint indication is provided by both differential curves than by the integrated form of the titration curve. Furthermore, titration by repetitive constant-volume increments allows the endpoint to be determined without a plot of the titration curve the endpoint coincides with the condition when the differential potentiometric response per volume increment is a maximum. Likewise, the endpoint can be determined by using the second derivative the latter has distinct advantages in that there is some indication of the approach of the endpoint as the second derivative approaches a positive maximum just prior to the equivalence point before passing through zero. Such a second-derivative response is particularly attractive for automated titration systems that stop at the equivalence point. 

The classification of linings in the U.S. model building codes is based on the FSI and SDI (smoke developed index). The latter is based on the area under the light transmission versus time curve normalized to the area for red oak flooring, which by definition has an SDI of 100. There are three classes Class A for products with FSI < 25, Class B for products with 25 < FSI < 75, and Class C for products with 75 < FSI < 200. In all cases, the SDI must be 450 or less. Class A products are generally permitted in enclosed vertical exits. Class B products can be used in exit access corridors and Class C products are allowed in other rooms and areas. 

The theory was used to calculate kinetic curves for the polymerization of PTS deducing the ratio cJCp from the known conversion dependence of the lattice parameters. Time conversion curves normalized with respect to the time necessary to reach 50 percent conversion can be calculated for different values of the lattice mismatch using the crystal strain theory. For PTS a satisfactory fit of the experimental data of the thermal and y-ray polymerization can be obtained. However, further studies of the kinetics of the solid-state polymerization of PTS and other monomers provided results which cannot be explained by the theory. 

Fig. 28. Experimental form factor for Cr3+ in AI2O3 [after Ref. (20)]. The full lines are theoretical free ion curves normalized by 1.0 and 0.9...

Figure 10. DCP of promoted NiC obtained at different X values marked near the curves normalized to a single height Hpcp- Original DCP curves are given in Fig. 6. DCP of precipitated NiC is denoted by Pr. DCP of pellet failure has been moved up to 0.02.

Figure 16.22 Breakthrough curve normalized to the inlet concentration of CH4 and C)2 carried by helium through a 1 x 30 cm column packed with a microporous carbon (Kureha MAC). Dimensionless time, t = tug/L. Symbols show experimental results, the lines the calculated profiles with the models indicated. The variation of the gas velocity along the column was accounted for. Reproduced with permission from L.. P. van den Broeke, R. Krishna, Chem. Eng. Sci., 50 (1995) 2507 (Fig 12).

Fig. 15. X-ray diffraction intensity curves normalized to the same total intensity (a) sample I (b) sample II with different draw ratios (Z). (Figure 4 in the original literature Q. Chen, H. Kurosu, L. Ma and M. Matsuo, Polymer, 2002, 43, 1203.)...

FIGURE 138 MW distributions of two polymers shown in Table 43. Cr/silica-titania (8 wt% Ti02) with and without fluoride (1.5 F atoms nm 2) was activated at 600 °C, and tested at 95 °C with 0.5 mol L 1 1-hexene. Curves normalized by catalyst activity. 

FIGURE 139 MW distributions of polymers made with Cr/silica with, and without, 2.6 F atoms nm-2 added. After activation at only 400 °C, the catalysts were tested at 105 °C, and the resulting GPC curves normalized by the measured catalyst activity. 

For low-molecular strong electrolytes the concentration dependence of equivalent conductivity is simple and universal. From a well-defined limiting value the equivalent conductivity decreases monotonically with increasing concentration, although the conductivity curves normally exhibit a distinct curvature, as the decrease levels off at high concentrations. The decrease of equivalent conductivity in these solutions is a result of increased interionic friction, which increases as the interionic distances decrease with increasing concentration. 

Figure 7.10 illustrates the differences between conventional first-order and SCK diffusion reaction decay curves, normalized to the same half-life ri v The SCK curve applies to either an AB or a ZB. with [he partners in contact at time zero, lor an AB. both pair reaction and escape contribute to decay, but only pair reaction contributes for a ZB. 

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