Maximum slope

These three systems describe a set of crystallization curves that cross at 6 = 0.5 and t = 10 sec. For the case where m = 2, the time span over which the change occurs is widest (1430 sec from 9 = 0.1-0.9) and the maximum slope is flattest... 

Figure 6.35 illustrates how anharmonicity mixes the two vibrations Vj and V3 of CO2. If the molecule starts from the point X and proceeds to B it will tend to follow the line of maximum slope shown. In doing so it deviates considerably from the dashed line representing and so involves an admixture of Qi and Qj. 

The permeabiHty = B jH is important information for soft magnetic materials. The most often quoted values ate the initial permeabiHty and the maximum permeabiHty ]1. These correspond to the initial and maximum slopes of the virgin magnetization curve, respectively (Fig. 1). Because the value of at S/H = 0 needs to be extrapolated from measurements at finite H, the value often is quoted ia commercial catalogues at specific B or H The quoted values usually are relative to the free-space value p.Q. 

Ba.lla.sted. A ballasted roof assembly consists of a membrane or membrane and substrate material (insulation, sHp sheet, etc) loosely laid over a deck with the assembly held in place using ballast. A minimum ballast weight of 48.9 kg/m or 10 pounds per square foot (PSF) is used. The ballast can consist of smooth rounded stone, cmshed stone (a separator sheet must be used between the cmshed stone and the membrane), or pavers (both standard and lightweight). Both stone and pavers come in a wide variety of colors. The membrane is affixed to the building only at the deck perimeter (roof edge) and at various penetrations. Wall and penetration flashings are typically fuUy adhered and sealed to prevent water entry into the roof assembly. The maximum slope a ballasted system should be installed over is 16.7 cm/m. 

When plotted as a function of drop size (Fig. 9), the contact angle was found to decrease with increasing drop height. A different analysis of these data was performed in the original paper. In that case the maximum slope near the drop edge was used, as well as a direct inversion of the droplet shape. The data could be fit to an empirical 1/z function. In the present analysis we use the method of the effective contact angles defined earlier, together with Eq. (18). For the Flamaker constant A, we calculated a value of approximately -2 X 10 ° J. However, the best fit to Eq. (18) is for a pure exponential decay of the form ... 

Obtain the required pipe size using the required flow and the maximum slope.31... 

The equilibrium data from Table 10.2 are plotted in Figure 10.6a. It can be seen that this does not form a straight-line relationship overall. Figure 10.6a shows the operating line of maximum slope that touches the equilibrium line at xR = 0.1576 kg AA/kg Water. The slope of this line is the ratio of feed to extraction flowrates. If the liquids are immiscible, then the flowrate of solute-free feed (F) is equal to the flowrate of the... 

Notes (1) Mean of four diameters, no diameter > 0.05% of mean diameter. (2) Maximum slope less than 1% from perpendicular relative roughness < 10 4d over a circle not less than 1.5d. (3) Visually does not reflect a beam of light, finish with a fine radial cut from center outward. 

Figure 54-1, however, still shows a number of characteristics that reveal the behavior of derivatives. First of all, we note that the first derivative crosses the X-axis at the wavelength where the absorbance peak has a maximum, and has maximum values (both positive and negative) at the point of maximum slope of the absorbance bands. These characteristics, of course, reflect the definition of the derivative as a measure of the slope of the underlying curve. For Gaussian bands, the maxima of the first derivatives also correspond to the standard deviation of the underlying spectral curve. 

Equation (3) is plotted with two different time scales in Figures 1 and 2 for values somewhat typical of an elastomer. All the initial deformation takes place in the spring at a later time the dashpot starts to relax and allows the spring to contract. Most of the relaxation takes place within one decade of time on both sides of the relaxation time, but this is shown clearly only in Figure 2. On the logarithmic time scale, the stress-relaxation curve has a maximum slope at the time / = T and the stress ratio cr/cr is 0.3679 ore. The stress relaxation may also be given in terms of a stress-relaxation modulus Er(t) ... 

The sensitivity in detecting the index of refraction change can be estimated using the maximum slope of the resonance and a minimum detectable change in the... 

The universal interferometric response of a balanced two-port interferometer is shown in Fig. 11.2 as a function of the fixed phase offset between the two waves. The maximum slope of the intensity curve occurs when the fixed phase offset between the waves is an odd integer of = re/2. These conditions of maximum slope are called the conditions of phase quadrature. There are two quadrature conditions per cycle, with opposite slopes and hence opposite signed responses to modulated phase. These are the positions of maximum phase-to-intensity transduction and are the operating points for interferometric detection of protein or DNA on spinning discs. 

MAXSLOPE (Grove Meehl, 1993) stands for MAXimum SLOPE and is another procedure that can be applied to two variables. MAXSLOPE was developed for a somewhat different purpose than other CCK methods. The primary goal of MAXSLOPE is to present data graphically in a manner that makes apparent whether a taxonic pattern is present or not, rather than... 

The end point in a titration is a little different from the end of a reaction. What is desired is to know when all the add is titrated. This happens when the titration curve, shown in Figure 10.1, reaches its maximum slope. This change occurs at a pH of 7 for a typical strong acid-base titration), but occurs at pH... 

In most cases, a curve is not drawn and the end point is taken as the milliliters (mL) used just when the color change takes place. There should be a half-drop of titrant difference between the change from one color to the next. In many cases, the color change is very light but distinctive. If the titration curve is plotted, then the end point can be determined by inspection or by taking the first or second derivative of the data to find the point of maximum slope. 

Where transitions using maximum slope do not intersect inside or outside surface, as shown by phantom outlines, maximum slopes shown or alternate radii shall be used. 

Figure 4. Formation condition for porous silicon solid line - peak current density, dotted line - current density at the maximum slope (see Figure.2).18...

The simplest and the most commonly used method is to plot the cell voltage E, millivolts (mV), versus the volume (ml) of titrant added. Ultimately, the end-point is determined from the point of maximum slope of the curve i.e., the point of inflexion, as depicted in Figure 16.1 (a). However, the degree of accuracy and precision with which this point of inflexion can be located from the plotted graph largely depends on the individual number of data points observed in the close proximities of the end-point. 

If no product is withdrawn from the still, that is D = 0, then the column is said to operate under conditions of total reflux and, as seen from equation 11.47, the top operating line has its maximum slope of unity, and coincides with the line x = y. If the reflux ratio is reduced, the slope of the operating line is reduced and more stages are required to pass... 

The locations of the maximal slope of 0 and are clearly discernible in the maxima in the plots of the slopes of the BI. Thus, in Fig. 3.4, the maximum slope of 0 is always at the point logjQ X. = 0, but as q increases the location of the maximum slope of 0 moves leftward. Note that 0 is similar in shape to the Langmuir isotherm, but the form of 0/ is quite different. As can be seen from the lower panel of Fig. 3.4, in this particular case there are two points at which the curve... 

For 5 > 2 there is only one point of maximum slope, but for 5 < 0 there are two points of maximum slope. 

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