Contributions, additivity

Correspondingly, replacement of the phenol (Fig. 33) by m-cresol (with the methyl oriented partially along a, Fig. 35) is associated with an increase of only about 0.65 A in the length of the c axis. The methyl substituent is perfectly well accommodated within the expanded lattice, contributing additional interactions of dispersion without an apparent distortion of the previous ones. All intermolecular distances remain well within range of characteristic van der Waals values 49). 

The foregoing procedure can be used to solve a variety of steady, fully developed laminar flow problems, such as flow in a tube or in a slit between parallel walls, for Newtonian or non-Newtonian fluids. However, if the flow is turbulent, the turbulent eddies transport momentum in three dimensions within the flow field, which contributes additional momentum flux components to the shear stress terms in the momentum equation. The resulting equations cannot be solved exactly for such flows, and methods for treating turbulent flows will be considered in Chapter 6. 

The second argument offered in [359] was based on the observation of 71Ga / j 1 rates at different temperatures that were faster than those calculated assuming Korringa relaxation as the only mechanism. However, this observation cannot be used to exclude the presence of Korringa relaxation, since additional mechanisms can always contribute additively to relaxation rates. Indeed, exactly such behavior has been observed for 71Ga MAS-NMR of h-GaN co-doped with Ge and Mn, where... 

The molecular mass would be too high because the nonvolatile impurities would contribute additional mass. The contribution to volume would be negligible. 

In all hydrodynamic methods we have the effect of both the hydrodynamic and thermodynamic interactions and these do not contribute additively but are coupled. This explains why the theoretical treatment of [77] and of the concentration dependence of has been so difficult. So far a satisfactory result could be achieved only for flexible linear chains [3, 73]. Fortunately, the thermodynamic interaction alone can be measured by static scattering techniques (or osmotic pressure measurement) when the scattering intensity is extrapolated to zero scattering angle (forward scattering). Statistical thermodynamics demonstrate that this forward scattering is given by the osmotic compressibility dc/dn as [74,75]... 

Hypericum not only has a long tradition of use as an antidepressant, but also a considerable amount of scientific research to support it. More research is needed, but it certainly works better than placebo and may be as efficacious as pharmaceutical antidepressants. The mechanism of this effect is not certain although monoamine reuptake mechanisms are most likely involved. Various other mechanisms may contribute additive or synergistic effects. 

The neat chloroform proton Tj data are in substantial agreement with those of Bender and Zeidler.— Unlike chloroform relaxation, which Is almost exclusively by intramolecular dipole-dipole relaxation, relaxation has Intermolecular as well as intramolecular contributions. By means of dilution with CDCI3 one can obtain separately the intramolecular and the various intermolecular contributions.— Additional intermolecular terms must be included in the presence of polymer. Expressed in terms of relaxation rates. 

The xenon atoms adsorbed in a zeolitic pore experience different perturbations which contribute additively to the experimental chemical shift, 5obs [1] ... 

Phase purity of the sample. Crystalline impurity phases present in a powder sample (e.g. residual amounts of starting materials from a synthetic procedure) contribute additional peaks to the experimental powder XRD pattern. As a result, the pattern may look substantially different from that of a pure sample of the main phase. Clearly, careful inspection should be carried out to assess the presence of impurity phases, particularly with regard to residual amounts of unreacted starting materials. 

Sherwood was one of the early workers to recognize the importance of turbulence (S15, S16, S17) in material transport. He summarized the progress in this field some years ago (S13) and contributed additional experimental work (L7, M2, M3). Kirkwood and Crawford (K7) set forth the relationships for transport in homogeneous phases with particular emphasis upon the interrelation of material and thermal flux. These contributions have laid a satisfactory basis for work in the field which has been well summarized from a macroscopic standpoint by Sherwood and Pigford (S14). 

The viewpoint parallels that of many other theories of condensed state behavior. The van der Waals theory develops an equation of state for dense gases from the assumption that each molecule moves in an average field provided by its neighbors and that the molecules contribute additively to the pressure. The Flory-Huggins thermodynamic theory of concentrated polymer solutions proceeds similarly. Chains select configurations on a lattice partially occupied by... 

The sorption of a penetrant by a class (a) membrane can be treated most simply, if the processes of sorption in the polymer matrix and into each kind of specific sorption site within it can be treated as mutually independent and hence additive. Under these conditions, each sorbed species may similarly be expected to contribute additively to the total diffusion flux. Hence, if there are N — 1 kinds of specific sorption sites, the overall sorption and permeability or diffusion coefficients can be written as... 

The photoequilibrium (114) (118) (see section III-A) and the irreversible rearrangement (118) - (120) contribute additional examples of photochemical isomerizations of cyclopropyl ketones to enones. The triplet nature of these isomerizations of (118) has been demonstrated by complete... 

The IR spectra of hydroxy adds are not very different from the spectra of the corresponding carboxylic acids. The additional hydroxyl groups usually produce minor displacements of the carbonyl vibrational bands to higher energies and, of course, contribute additional characteristic... 

For small peptides, the amount of color increases with the size of the peptide. The presence of any of five amino acid residues (tyrosine, tryptophan, cysteine, histidine, and asparagine) in the peptide or protein backbone further enhance the amount of color produced, because they contribute additional reducing equivalents for further reduction of the phos-phomolybdic/phosphotungstic acid complex. With the exception of tyrosine and tryptophan, free amino acids will not produce a colored product with the Lowry reagent however, most dipeptides can be detected. In the absence of any of the five amino acids listed above, proteins containing proline residues have a lower... 

The isolated silver atom formed in this reaction could take part in latent image formation either by diffusion to a latent sub-center or by thermal dissociation with the transfer of an electron to the conduction band. Hence, it is theoretically possible that the absorption of one photon by the silver halide results in two latent image silver atoms. Reduction centers larger than Ag2 could not contribute additional silver to the latent image in this way until their size had been decreased to two atoms by reaction with holes. 

Delay Due to Resistive Losses. On electrically long, lossy lines, the signal rise time is degraded by dispersion in the interconnection. Dispersion delays and attenuates the high-frequency components of the signal more than the low-frequency components because of the frequency-depen-dent resistance of the interconnection. The rise time degradation contributes additional delay before the switching threshold is reached at the end of the line. 

Chow and Mak came to a similar conclusion on investigating the chiroptical properties of dendrimers containing enantiomerically pure threitol building blocks obtained from tartaric acid as spacers between the achiral phloroglucin branching units (see Fig. 4.73) [27]. They found that the chiral spacers in the dendrimer scaffold do not influence one another and contribute additively to the overall rotation. Moreover, they also observed that on introduction of both enantiomers one (R,R)-threitol unit precisely compensated the rotational contribution of one (S,S)-threitol unit, provided that the enantiomeric building blocks were located at equivalent positions within the dendrimer scaffold. However, CD-spectroscopic data revealed that the contribution of the exterior threitol units to the total rotation must be slightly different from that of the interior units. 

The determination of r is made easier because of several aspects of Eq. (4.32). It is not necessary to know the real zero point (/ = 0) of the relaxation curve moreover, a physical property such as absorbance or conductance related to concentration is measured in relaxation studies rather than actual concentrations. With first-order reactions, one does not need to know the proportionality constant between the physical property and the concentration of the respective species. This is valid only if one or all of the species present in the system contributes to the physical property (Bernasconi, 1976). Another basic feature of chemical relaxation that should be mentioned is that the forward and backward reactions of Eq. (4.1) contribute additively to r l (Bernasconi, 1976). Thus, it is the faster of the two processes which contributes most to r-1. 

With the advent of dry wall finishes that replace the wet plaster wall finish, additional fire safety problems were presented. The lime, cement, and gypsum plaster previously used provided an incombustible surface and afforded some fire protection to the wood or steel framing of the building but many of the dry wall finishes are themselves combustible, offer little if any resistance to fire, and tend to increase the intensity of a fire by contributing additional fuel. 

---