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Quadratic coefficients

It is obvious that to be able to estimate the quadratic coefficients, p, in equation (14), it is necessary to have at least three distinct levels or settings for the variables. This suggests that a suitable design for estimating the coefficients of the second-order model would be a single replicate of a three-level full factorial design in p variables. This design... [Pg.26]

Carbon dioxide. Collision-induced absorption in carbon dioxide shows a discernible density dependence beyond density squared, even at densities as low as 20 amagats [34]. Over a range of densities up to 85 amagats the variation of the absorption with density may be closely represented by a (truncated) virial series (as in Eq. 1.2, with I(v) replaced by a(v)) of just two terms, one quadratic and the other cubic in density. The coefficient of g3 is negative. Relative to the leading quadratic coefficient, it is,... [Pg.106]

Fig. 3. Quadratic coefficient GB2 = G[JVsolvelJ32s0)Vem + Moiiite/82Soimc], obtained from the curves in Fig. 2, vs for complex [Ru(4,4 -C= CC6H4C= CC6H4N02)(PPh3)2(775-C5H5)]. Fig. 3. Quadratic coefficient GB2 = G[JVsolvelJ32s0)Vem + Moiiite/82Soimc], obtained from the curves in Fig. 2, vs for complex [Ru(4,4 -C= CC6H4C= CC6H4N02)(PPh3)2(775-C5H5)].
The quadratic coefficients, ba, describe the curvature of the response surface in the X direction. [Pg.10]

Figure 4. Hyper-Rayleigh scattering signal for 5 in chloroform at different number densities in unit of 10 cm 3 (A) 3.0, (B) 6.0, (C) 30, and (D) 301. (Inset) Quadratic coefficient 1(2 CO) f(co) vs. number density of 5. Figure 4. Hyper-Rayleigh scattering signal for 5 in chloroform at different number densities in unit of 10 cm 3 (A) 3.0, (B) 6.0, (C) 30, and (D) 301. (Inset) Quadratic coefficient 1(2 CO) f(co) vs. number density of 5.
The interfacial (excess) heat capacity is another Interfacial characteristic that we decided to disregard. The reason for doing so is not in its intrinsic interest. On the contrary, as with bulk heat capacities, they reflect the structure, or ordering (see e.g. FIGS I, sec. 5.3c). However, it is very difficult to establish these values experimentally. Basically the second derivative of the interfacial tension with respect to the temperature at a constant pressure is needed (see sec. 1.2.7), and to obtain this extremely preeise measurements are needed. The spread in the quadratic coefficient B in [1.12.1) indicates the uncertainty, even for a well-studied liquid like water. Yang and Li showed, by a thermodyncimic ancdysis, that for LL interfaces this heat capacity is related to the two bulk heat capacities, the inter-... [Pg.199]

As expected, the relative significance of the standard regression coefficient B3 is considerably less than those of the standardized linear and quadratic coefficients, Bi and B2. [Pg.169]

The quadratic coefficient flu describes the curvature along the Xj axis, and B22 describes the curvature along the X2 axis. The quadratic coefficients can be positive or negative and they can have different numerical values. Quadratic response surface models can therefore describe a variety of curved surfaces allowing analysis of surfaces which are convex and have a maximum or which are concave and have a minimum response as well as surfaces which are saddle-shaped. [Pg.41]

The standard error of the coefficients in the canonical model will be approximately the same as for the linear and quadratic coefficients in the original model when a rotatable design has been used. [Pg.282]

It is instructive to follow the differences in the respective linear and quadratic coefficients of the function and first derivative terms in each equation, in the order of number of factors in the corresponding square roots, or of Eqs. (36, 64, 69, 49,54 and 59) in Ref. [4] for P starting with the -dependent coefficient, their successive values are + I), I — l)( + 2), I — 2) + 3), i - 3) (t + 4) for the respective species b is shifted by one-half up or down in Eq. (56) and by three halves down or up in Eq. (53), and stays the same in the other cases however, for the derivative, the quadratic term has the negative coefficients 3,5, 7, and 9, while the respective constant terms are I and 3, and the linear terms only appear in Eqs. (53 and 56) again. The changes in the -dependent coefficients and in the anergy parameters are not exclusively for the most asymmetric molecules. Their counterparts also appear for molecules wifh any asymmetry, as shown in our Section 4.2.3. [Pg.155]

A study of the Zeeman effect of the PL lines of the excitons bound to group-III acceptors in silicon by Karasyuk et al. [75] has allowed us to obtain the ground-state (/-factors and the quadratic coefficients (72 and (73 of these acceptors. [Pg.405]

Table 8.20. Comparison of the experimental 77-factors g and g 2 of the acceptor ground state in silicon obtained from different sources with calculated values. The values obtained from ESR under stress by Shimizu and Tanakac have been converted into the zero-stress 77-factors by Neubrandb. The last two columns give the quadratic coefficients of the Zeeman Hamiltonian (8.20)... Table 8.20. Comparison of the experimental 77-factors g and g 2 of the acceptor ground state in silicon obtained from different sources with calculated values. The values obtained from ESR under stress by Shimizu and Tanakac have been converted into the zero-stress 77-factors by Neubrandb. The last two columns give the quadratic coefficients of the Zeeman Hamiltonian (8.20)...
Table 3. The One-Dimensional Ring Puckering Function for Cyclobutanone. Quartic and Quadratic Coefficients, Barrier Heights and Equilibrium Displacements, in cm 1 and A. Table 3. The One-Dimensional Ring Puckering Function for Cyclobutanone. Quartic and Quadratic Coefficients, Barrier Heights and Equilibrium Displacements, in cm 1 and A.
For simplicity, assume that vab is the geometrical mean of va and vb, i.e., the Berthelot law, and extend the free energy derived from Equation 2.f22 in the power series of Sa and, S),. The zero determinant of the quadratic coefficients gives the pseudo-second-phase-transition temperature as follows... [Pg.108]

The highest power of the series terms chosen to define each isotherm reflected the extent of the nonideality. For the ethylene isotherms, a cubic series was used for temperatures from 0° to 25°C and a quadratic series was used for temperatures from 75° to 175°C. At 50°C, a quadratic series as well as a cubic series were used. For the helium isotherms, a quadratic series was used with the virial coefficient of the quadratic term treated as a constant obtained from published values rather than as a parameter. The other parameters were evaluated more accurately with the quadratic coefficient treated as a constant rather than as a parameter since the contribution of this term was so small for our range of pressures. The term functioned only as a virial remainder. In the helium data analyses, the parameters were common to all of the data. For the ethylene data analyses, only the virial coefficient parameters were common to all of the data an initial density parameter was required for each sequence... [Pg.296]

See Particle Listings for quadratic coefficients an alternative parameterization related to jtjt scattering)... [Pg.1752]

In general, we should obtain the optimized torsion angles and the quadratic coefficients of energy with respect to dihedral angles. In this chapter, we assume that we can neglect the dihedral term of the potential energy in the Mg subsystem. [Pg.530]

In Table 31.2, our results of the bond lengths which give the minimum energy of the Mg subsystem and the quadratic coefficients ATb of the energy of the Mg subsystem... [Pg.534]


See other pages where Quadratic coefficients is mentioned: [Pg.167]    [Pg.455]    [Pg.457]    [Pg.27]    [Pg.247]    [Pg.47]    [Pg.29]    [Pg.167]    [Pg.90]    [Pg.103]    [Pg.168]    [Pg.455]    [Pg.457]    [Pg.39]    [Pg.52]    [Pg.269]    [Pg.451]    [Pg.294]    [Pg.62]    [Pg.62]    [Pg.213]    [Pg.328]    [Pg.1754]    [Pg.1700]    [Pg.154]    [Pg.529]    [Pg.529]    [Pg.529]    [Pg.529]    [Pg.529]    [Pg.535]   
See also in sourсe #XX -- [ Pg.153 ]




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