WEAK TRANSLATABILITY

In relation with these avoided crossings, the radial coupling matrix elements present sharp peaks at respectively 5.4, 6.6, 7.55 and 9.5 a.u. (Fig. 5). We may notice that these radial couplings are almost insensitive to the choice of the origin of electronic coordinates. The most sensitive one is the g23 function at short internuclear distance range, but we may expect weak translational effects for such electron capture processes dominated by collisions at large distance of closest approach. 

We can carry the ideas in the proof that every recursively enumerable set is the value language of some monadic program scheme one step forward and show that in a certain sense we can translate monadic recursion schemes into monadic program schemes, this notion of translatability being weak translatability. 

There are alternative definitions of "weak translatability". The following definition is rather "strong". "Weaker" versions cunit condition (3). 

DEFINITION A scheme S is weakly translatable into a scheme S if... 

THEOREM 8.16 Every monadic recursion scheme is weakly translatable into a monadic program scheme. 

WEAK TRANSLATION OF A RECURSION SCHEME S INTO FLOWCHART SCHEME Let the subschema Abbreviate subscheme ... 

Weak translation of in vitro findings into the in vivo situation may be due to a variety of factors, e.g. shorter times of exposure of cells to l,25(OH)2D3 in vivo compared to incubation experiments in vitro. Furthermore, the stability of the compound may differ in vitro and in vivo. Importantly, the tissue distribution of l,25(OH)2D3 is far from homogenous in vivo. Thus, it may well be that peripheral blood - the compartment that is usually analyzed regarding effects of l,25(OH)2D3 - is not fully appropriate for that purpose. In addition, ex vivo data from previously 1,25 (OH)2D3-deficient patients, such as patients with chronic renal failure, cannot easily be extrapolated on patients with other types of diseases (e.g. chronic inflammation) or healthy volunteers. 

Collision-induced absorption from free pairs of molecules appear as broad lines or bands located at the wavenumbers of the pure-rotation or vibration-rotation transitions in the participating individual molecules. Figure 3.3.6 shows the spectrum for H2-H2 collisions (Bachet et al., 1983) [see also Courtin (1988)]. In the far infrared (below 200 cm ) a weak translational band is also present. In H2 the prominent features in planetary atmospheres occur at the pure-rotation / = 0 -> 2 and 1 3 transitions located at 354 and 587 cm . The widths of collision-induced features are extremely large, about 100 cm or more, because the time during the collision in which the partners are interacting is very short ( 10 seconds or less). The width of a spectral line is related to the reciprocal of the collision duration. 

It is time to create some data to play with. By creating the data ourselves, we will know exactly what its properties are. We will subject these data to each of the chemometric techniques so that we may observe and discuss the results. We will be able to translate our detailed a priori knowledge of the data into a detailed understanding of how the different techniques function. In this way, we will learn the strengths and weaknesses of the various methods and how to use them correctly. 

Chapter 3 is devoted to pressure transformation of the unresolved isotropic Raman scattering spectrum which consists of a single Q-branch much narrower than other branches (shaded in Fig. 0.2(a)). Therefore rotational collapse of the Q-branch is accomplished much earlier than that of the IR spectrum as a whole (e.g. in the gas phase). Attention is concentrated on the isotropic Q-branch of N2, which is significantly narrowed before the broadening produced by weak vibrational dephasing becomes dominant. It is remarkable that isotropic Q-branch collapse is indifferent to orientational relaxation. It is affected solely by rotational energy relaxation. This is an exceptional case of pure frequency modulation similar to the Dicke effect in atomic spectroscopy [13]. The only difference is that the frequency in the Q-branch is quadratic in J whereas in the Doppler contour it is linear in translational velocity v. Consequently the rotational frequency modulation is not Gaussian but is still Markovian and therefore subject to the impact theory. The Keilson-... 

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