INDEX straight line

Omega polynomials, their derivatives, and Cl and /q indices for anthracene (a) and phenanthrene (b). PI is the PI index. Straight line segments indicate orthogonal edge cuts. 

The shortest time occurs for light travels in straight lines in a constant index media. 

The relationship between film thickness of hexadecane with the addition of cholesteryl LCs and rolling speed under different pressures is shown in Fig. 25 [50], where the straight line is the theoretic film thickness calculated from the Hamrock-Dowson formula based on the bulk viscosity under the pressure of 0.174 GPa. It can be seen that for all lubricants, when speed is high, it is in the EHL regime and a speed index 4> about 0.67 is produced. When the rolling speed decreases and the film thickness falls to about 30 nm, the static adsorption film and ordered fluid film cannot be negligible, and the gradient reduces to less than 0.67 and the transition from EHL to TFL occurs. For pure hexadecane, due to the weak interaction between hexadecane molecules and metal surfaces, the static and ordered films are very thin. EHL... 

One of the apparent results of introducing couple stress is the size-dependent effect. If the problem scale approaches molecular dimension, this effect is obvious and can be characterized by the characteristic length 1. The size effect is a distinctive property while the film thickness of EHL is down to the nanometre scale, where the exponent index of the film thickness to the velocity does not remain constant, i.e., the film thickness, if plotted as a function of velocity in logarithmic scale, will not follow the straight line proposed by Ham-rock and Dowson. This bridges the gap between the lubrication theory and the experimental results. 

Conventional advice maintains that there is no benefit in adding P to soils that contain available P of index 3 (26-45 mg/kg P in the soil). Beyond this level, there is unlikely to be an increase in herbage yield (Lockhart Wiseman, 1993). However, the experiment cited above (Newton, 1993) showed a straight-line response up to levels of available P of 103 mg/kg (index 6). The equation derived from this work suggested that for every increase of 10 mg/kg available P in the soil,... 

Since members of a homologous series have incremental boiling point differences and if the amount of any homolog in the moving gas phase is related to vapor pressure at the temperature of the experiment, plots of log k vs. carbon number should also be a straight line. (The enthalpy of vaporization increases monotonically with carbon number.) This in fact is observed in gas-liquid equilibrium separation systems. It is the basis of retention index systems pioneered by Kovats for qualitative identification. 

Here, A and v 2 are fitting parameters amenable to physical interpretation using Equation 12.11. The point of present concern is that the isotope effect on polarizability can now be expressed in terms of isotopic differences in refractive index. It follows from Equation 12.14 that a plot of AR/R = [6n2/((n2—l)(n2 + 2))][An/n] vs. v2 gives an approximately straight line,... 

For binary mixtures, a straight line (isobole) is produced joining Di and D2 and passing through di, d-2). The interaction index (Cl) is 1, <1, or >1 when the combinations show zero interaction, synergism, or antagonism using dose addition, respectively. 

These results show a maximum deviation of -3 per cent to ethyleneglycol dinitrate, or 0.0008 in refractive Index from the straight line connecting the 100 per cent values. They also represent a maximum deviation of i 2 per cent, or 0.0005 from any of the points by which die curves were determined. The values at 15°C came the neatest to giving a smooth curve passing through all points, and this may be considered the optimum temperature at which to work... 

In Figure 3, a straight-line relationship between a retention index and molecular weight is illustrated for homologous series of n-alcohols, n-aldehydes, n-acetates, and n-hydrocarbons. The compound having molecular weight 130 and retention index 1180 corresponds to n-pentyl acetate. Since the relationship in Figure 3 holds for all types of related compounds, it is obvious that this technique could be widely used in identification of GC peaks. 

The straight lines permit the determination of the composition of potassium and sodium glasses by determining their density and refractive index and calculating their specific refraction. 

Rates of model reactions are more commonly used to determine relative rather than absolute surface acidities and a variety of acid-catalyzed reactions have been used for this purpose (1-3). Xylene isomerization is a particularly well-substantiated model reaction, thanks to work by Ward and Hansford (43). They demonstrated that the conversion of o-xylene to p- and /n-xylenes over a series of synthetic silica-alumina catalysts increases as the alumina content is increased from 1 to 7%. The number of strong Brdnsted acids in each member of the catalyst series was measured by means of infrared spectroscopy. Since conversion of o-xylene was found to be a straight-line function of the number of Br0nsted acids (see Fig. 9), rate of xylene isomerization appears to be a valid index of the amount of surface acidity for this catalyst series. This correlation also indicates that the acid strengths of these silica-alumina preparations are roughly equivalent. 

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