Similarity considerations

Similar considerations have been exploited for the systematic analysis of room-temperature and molecular-beam IR spectra in temis of intramolecular vibrational relaxation rates [33, 34, 92, 94] (see also chapter A3.13 V... 

Similar considerations apply to the size of system simulated. The samples involved are typically quite small... 

Since the total wave function must have the correct symmetry under the permutation of identical nuclei, we can determine the symmetiy of the rovi-bronic wave function from consideration of the corresponding symmetry of the nuclear spin function. We begin by looking at the case of a fermionic system for which the total wave function must be antisynmiebic under permutation of any two identical particles. If the nuclear spin function is symmetric then the rovibronic wave function must be antisymmetric conversely, if the nuclear spin function is antisymmebic, the rovibronic wave function must be symmetric under permutation of any two fermions. Similar considerations apply to bosonic systems The rovibronic wave function must be symmetric when the nuclear spin function is symmetric, and the rovibronic wave function must be antisymmetiic when the nuclear spin function is antisymmetric. This warrants... 

When a pure gas flows through a channel the accompanying fall in pressure is accounted for partly by acceleration of the flowing stream and partly by momentum transfer to the stationary walls. Since a porous medium may be regarded as an assembly of channels, similar considerations apply to flow through porous media, but in the diffusional situations of principal interest here accelerational pressure loss can usually be neglected. If more than one molecular species is present, we are also interested in the relative motions of the different species, so momentum transfers by collisions between different types of molecules are also important. 

The extent of displacement depends on the relative stabiUties of the complexes and the mass action effect of an excess of M For equivalent total amounts of M and M, K must be on the order of 10 for 99% complete displacement to occur. Similar considerations apply for the displacement of L from ML by U. The situation is quite analogous to the familiar competition of two bases for the hydrogen ion. 

Similar considerations might apply to bulking bmsh (2-6.3) and surface streamer (2-6.6) discharges which propagate across charged surfaces over distances up to about 1 m at source voltages less than 100 kV. 

For aromatics production, similar considerations apply. Maximum yields of xylenes and other heavy aromatics can be obtained in cyclic units, but, again, at somewhat higher investments. The process selection, thus, again requires the balancing of process credits versus debits for the specific application. For light aromatics (benzene-toluene) production, however, the situation tends to favor a... 

Only particular solvents are suitable for certain purposes. The choice depending, for instance, on their residual water content or their acid-base nature if Rf values are to be reproduced [1, 2]. Halogen-containing solvents may not be employed for the determination of chlorinated pesticides. Similar considerations apply to PAH analyses. Pro analyst grades are no longer adequate for these purposes. It is true that it would be possible to manufacture universally pure solvents that were adequate for all analytical purposes, but they would then be too expensive for the final user [3, 4]. 

For detonation flame arresters that are installed in manifolded vent systems, similar considerations as above apply to prevent overpressnre or vacnnm damage of atmospheric pressnre tanks. 

Similar considerations apply to best volume flow rates for samples of different molar mass. For high molar mass samples, flow rates should be reduced to avoid shearing the macromolecule in the column. Moreover, a reduced flow rate is necessary because the diffusion coefficients of large molecules will get pretty small. This means that the macromolecule will pass by a pore in the packing material without having the time to enter it, if the linear flow rate is too high. 

Similar considerations have been invaluable in devising synthetic routes to numerous other isomeric complexes of Pt" but. as can be seen in Hg. A, other considerations such as the relative stabilities of the different Pt-ligand bonds arc also involved. 

Similar considerations apply to the electric dipole moment the derivatives of the dipole integrals can be easily obtained whilst the derivatives of the density matrix require the use of coupled Hartree-Fock theory (e.g. Gerratt and Mills, 1968). 

Consider the following Coulomb contribution to the element of the Fock matrix (eq. (3.51)) similar considerations hold for the exchange contribution. 

Pyrazine-2-thione (213) and quinoxaline-2-thione (214) probably exist in the thione form since their ultraviolet spectra are different from those of the 2-methylthio analogs. The basicity of quinoxaline-2-thione is 1.4 pK units less than that of 2-methylthio-quinoxaline, and the ultraviolet spectra of the cations are dissimilar. Presumably quinoxaline-2-thione and its 2-methylthio derivative do not form similar cations (215, P = alkyl, H), and it would appear that either the thione gives the cation 216 or the 2-thioether gives the cation 217. Similar considerations apply to pyrazine-2-thione. 

Similar considerations apply to nitrogen-containing heterocycles carrying acidic groups, for example 2-hydroxypteridine, but the situation is further complicated by lactam-lactim tautomerism in the neutral species. Thus, hydroxypteridines exist predominantly as lactams, such as 6, in dynamic equilibrium with small amounts of lactims, such as 7. There is, in consequence, a decrease in the aromatic... 

If only one of the two aldehydes has an a-hydrogen, only two aldols can be formed and numerous examples have been reported, where the crossed aldol reaction is the major pathway. For two different ketones, similar considerations do apply in addition to the unfavorable equilibrium mentioned above, which is why such reactions are seldom attempted. 

Similar considerations apply to all other schemes to produce perpetual motion. No matter how it is designed, an isolated system will always tend toward a condition of thermal equilibrium, which never involves motion of objects on a human scale, and is thus not perpetual motion. ... 

Operations are similar to woodworking and collector selection involves similar considerations. See Item 13. 

At this point it should be noted that the free energies of half reactions can be added algebraically to evaluate AG, a on and similar considerations... 

Similar considerations also apply to the dielectric films formed on the metal surface during anodising, and, for example, in the case of the valve metals (Al, Ti, Ta, Nb, etc.) IR drops of hundreds of volts may be produced by the anodic oxide film formed on the metal surfaces. Paint films applied to a metal surface also exert resistance control see Section 14.3). 

Figure 1.3 la to c shows how an increase in the concentration of dissolved oxygen or an increase in velocity increases /Y and thereby increases. It has been shown in equation 1.73 that /Y increases with the concentration of oxygen and temperature, and with decrease in thickness of the diffusion layer, and similar considerations apply to. Thus Uhlig, Triadis and Stern found that the corrosion rate of mild steel in slowly moving water at... 

Similar considerations will apply to other metal hydroxides, and Table 1.17 gives the hydrolysis reactions and the equilibrium pHs for metal ions... 

Most cases of crevice corrosion take place in near-neutral solutions in which dissolved oxygen is the cathode reactant, but in the case of copper and copper alloys crevice corrosion can occur owing to differences in the concentration of Cu ions however, in the latter the mechanism appears to be different, since attack takes place at the exposed surface close to the crevice and not within the crevice in fact, the inside of the crevice may actually be cathodic and copper deposition is sometimes observed, particularly in the Cu-Ni alloys. Similar considerations apply in acid solutions in which the hydrogen ion is the cathode reactant, and again attack occurs at the exposed surface close to the crevice. 

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