Positive slope

Equation (6.8), to (d /dx)g. Figure 6.1 shows how the magnitude /r of the dipole moment varies with intemuclear distance in a typical heteronuclear diatomic molecule. Obviously, /r 0 when r 0 and the nuclei coalesce. For neutral diatomics, /r 0 when r qg because the molecule dissociates into neutral atoms. Therefore, between r = 0 and r = oo there must be a maximum value of /r. Figure 6.1 has been drawn with this maximum at r < Tg, giving a negative slope d/r/dr at r. If the maximum were at r > Tg there would be a positive slope at r. It is possible that the maximum is at r, in which case d/r/dr = 0 at Tg and the Av = transitions, although allowed, would have zero intensity. 

FIG. 22-55 Typical capital-cost schematic for membrane equipment showing trade-off for membrane area and mechanical equipment. Lines shown are from families for parallel hues showing hmiting costs for membrane and for ancillary equipment. Abscissa Relative membrane area installed in a typical membrane process. Minimum capital cost is at 1.0. Ordinate Relative cost. Line with positive slope is total membrane cost. Line with negative slope is total ancillary equipment cost. Curve is total capital cost. Minimum cost is at 1.0. 

A plot of the solubility of a certain compound (g/100 g H20) against temperature (°C) is a straight line with a positive slope. Is dissolving that compound an exothermic process ... 

B The positive slope of the solid-liquid boundary shows that monoclinic sulfur is more dense than liquid sulfur over the temperature range in which monoclinic sulfur is stable the solid is more stable at high pressure. 

Fig. 1. Methods of Huggins (positive slope), Kraemer (negative slope) (a), Schulz-Blaschke (b), and Martin (c). Data obtained from experimental measures for gelatin B at 37.4°C.

Negative slopes are flagged an W is to be interpreted in the sense that the slope is negative, and J decreases as I increases positive slopes remain unmarked. 

Figure 3.10 Illustrative example of linear regression between two artificial variables for six experimental units. For each unit, denoted by a different graphical symbol, a closely packed set of five observations with negative slope is measured. The whole data set, if fitted naively, would show a very significant positive slope.

Note that the lipophilicity parameter log P is defined as a decimal logarithm. The parabolic equation is only non-linear in the variable log P, but is linear in the coefficients. Hence, it can be solved by multiple linear regression (see Section 10.8). The bilinear equation, however, is non-linear in both the variable P and the coefficients, and can only be solved by means of non-linear regression techniques (see Chapter 11). It is approximately linear with a positive slope (/ ,) for small values of log P, while it is also approximately linear with a negative slope b + b for large values of log P. The term bilinear is used in this context to indicate that the QSAR model can be resolved into two linear relations for small and for large values of P, respectively. This definition differs from the one which has been introduced in the context of principal components analysis in Chapter 17. 

Figure 19. Variation in dimension of the X-fold cation site in alkali-feldspar for 2+ cations (), obtained by fitting the experimental data of Icenhower and London (1996) for Dca, >sr and Dsa at 0.2 GPa and 650-750°C. In performing the fits was set at 91 GPa for all runs. Error bars are 1 s.d. The positive slope is consistent with measured changes in metal-oxygen bond length from albite to orthoclase (cf Fig. 6). The solid line shows the best-fit linear regression given in Equation (35).

A straight line plotted in coordinates Igfl -. /e for a negatively charged ion 02 Yq <0) must have a positive slope which is consistent... 

As a consequence of the high conductivities of H30+ and OH in comparison with those of Na+ and Cl, eqns. 2.28 and 2.29 will yield straight lines with negative and positive slopes, respectively. In practice, therefore, both straight lines are drawn through a sufficient number of measuring points for extrapolation to yield an intersection at, the equivalence point. According to eqn. 2.30, at A (see Fig. 2.4) some curvature may occur as a consequence of the protolysis... 

The curve for the energy dependence as a function of k in Fig. 10.4 has a positive slope. This is not always so. When p orbitals are joined head-on to a chain, the situation is exactly the opposite. The wave function y/0 = Z.X, is then antibonding, whereas yKja is bonding (Fig. 10.5). 

Figure 3.3 The six apparent ionization constants of vancomycin plotted as a function of weight % methanol. Unfilled circles denote acid groups, and filled circles denote basic groups. Acids usually are indicated by positive slopes and bases, by negative slopes. [Avdeef, A., Curr. Topics Med. Chem., 1, 277-351 (2001). Reproduced with permission from Bentham Science Publishers, Ltd.]...

Fig. 21. Loss tangent, tan 3, for five partially crosslinked PDMS samples at different extents of reactions. For the liquid, a negative slope is observed. At the LST, tan 3 is independent of frequency. The loss tangent of the solid material exhibits a positive slope...

Which of the following lines have positive slope a. 

Amides and esters give a positive slope of about 1.2 on Hart et al. s (1967) plot, due to the reduction of the double bond character of C=0 by the mesomeric effect of NH2 and OH, which reduces the reactivity toward eh. 

Fig. 4. Physical significance of calculations of the potential energy gradient at the starting nuclear geometry. From left to right, negative slope, positive slope, and a calculation for the second excited state...

Data of thermal expansion do not always show a regular positive slope increasing with temperature, as those shown in Fig. 13.3 [57], Look, for example, in Fig. 13.4, at the data for a cold sintered SiC, a material specially suitable for the realization of high-quality mirrors for space astronomy [58],... 

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