Parallel components

The integer numbers (ni,K2) are used as indices to label the spot. The parallel component of the corresponding wave vector is ... 

The relative slopes of tanT (maximum or minimum). A, and reflectivity for the parallel component depend on the position relative to the Brewster angle (greater or lower). Thicker films on both types of substrate lead to dominant interferences. 

FIG. 14 (a) Plot of the normalized parallel component of the mean gyration radius i gll/i gb (open symbols), and end-to-end distance i /i gb (full symbols), vs the ratio D/i gb [19] (chain lengths N = 128, 256, 512 are distinguished by different symbols). The dashed straight line indicates the asymptotic slope of the scahng function for small D/i gb, namely —2(z/2 — (h) The same for the perpendicular components. 

With a modulated light source, the phase difference between the perpendicular and parallel components of the emission is measured. The time delay of the perpendicular component of emission is longer than that of the parallel component because the molecule requires a certain period of time to rotate into the perpendicular orientation where it can be detected through the perpendicular polarizer. 

The quality of the ) states has been tested through their energy and also their transition moment. Moreover from the natural orbitals and Mulliken populations analysis, we have determined the predominant electronic configuration of each ) state and its Rydberg character. Such an analysis is particularly interesting since it explains the contribution of each ) to the calculation of the static or dynamic polarizability it allows a better understanding in the case of the CO molecule the difficulty of the calculation and the wide range of published values for the parallel component while the computation of the perpendicular component is easier. In effect in the case of CO ... 

Moreover, for the observables depending on external electric field, its specific effect has to be investigated the electric field induces new terms in the nuclear Hamiltonian, due to the change of equilibrium geometry and the nuclear motion perturbation. Pandey and Santry (14) has brought to the fore this effect and calculated the correction which only concerns the parallel component. It is represented by the following expression ... 

Now with the 2p valence polarization, it is possible to partly describe the polarizability since the first step of calculation with the unperturbed wavefunction, especially the parallel component which is generally easier to calculate in CPHF. The optimized... 

When the distance r between the two points approaches 4(aAaB)l/6, the parallel component an goes to infinity and will be negative for shorter distances. 

Schematic representation of product distribution versus time for parallel-series combination of reactions—Case II parallel component added slowly. (Adapted from Chemical Reaction Engineering, Second Edition, by O. Levenspiel. Copyright 1972. Reprinted by permission of John Wiley and Sons, Inc.)...

As easily seen, the vector PA is always parallel to the surface plane and the sin-face-parallel component of the vector Ps vanishes for the structures having collinear projections of molecular axes onto the surface plane (

[Pg.68]

As is obvious from the above relation, the screening effect of the substrate on interactions causes, in the limiting case z —> 0, the change in the surface-normal components by a factor of 2e/( +e) and in the surface-parallel components by a factor of 2/(1 + ), i.e., the renormalization ratio is equal tO . As the substrate dielectric constant increases, the interaction of surface-parallel components monotonically decays to zero, whereas the interaction of surface-normal components is enhanced reaching the maximum, viz. the interaction with a double dipole moment, for a metal (at e -> oo).130 Analogous renormalization factors are also of significance in the treatment of island-like particles on a dielectric substrate.131 With such effects included, formula (3.3.9) can be rewritten as ... 

This rule is easily memorized because for parallel components the probabilities are multiplied. The total reliability for parallel units is given by... 

The other field components can be easily derived from Ez and Hz4. Introducing (12.2) into (12.3) yields all the field components in the y th layer. The parallel component of the fields Ez, Hz, Eq, H must be continuous at the interfaces separating successive layers. This requirement can be written in from of a transfer matrix, connecting the amplitude vector A B C D in the /th and / + 1 layers ... 

Equation (20) contains the matrix elements between the initial and final states of the (Q — G) component of the He surface potential gradient VI7. The potential gradient can be thought of vector with normal component d[7g /d2 and parallel component i(Q —G) Vq q. Because in general dt/g c/ i(G — the major contribution to the scattering cross-... 

BO energy curves of pertinent states we can expect the parallel component an to have singularities atR = 0.9873 and 15.4482 bohr whereas the perpendicular a at / = 1.8886 and 2.9055 bohr. Because all three interacting states have the same dissociation limit, A tends to zero when oo and we can also expect that both polarizability components will escape to infinity with growing R. 

Comparing the SOPPA and SOPPA(CCSD) results one can see that both methods predict correlation corrections which are comparable to the results obtained at the CCSD or RAS iSD level. However, it is clear that SOPPA(CCSD) is in better agreement with these more expensive methods. The SOPPA(CCSD) results for HF, for gip and goop in H2O are close to the respective MP3 results. In case of NH3 and the parallel component of the g tensor of H2O, where the correlation corrections are somewhat smaller, 1.5%, SOPPA(CCSD) predicts values close to the CCSD numbers. 

In FFC relaxometry, one is concerned with the time evolution of the parallel component M of the nuclear magnetization of a sample or, in more complex cases, of one or more of its constituents. The primary goal of the signal detection is to estimate M and not, like in NMR spectroscopy, to analyze the FIDs in any detail beyond a simple solid/liquid phase distinction. 

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