Perturbation spectrum

In order to finish the calculation, let us assume we are in the almost de Sitter case, that is, that w — 1. In this case, one has by definition 

Moreover, when w —1, one also has H Const, and dt p Const (because H2 (x pcj V and w -1 Const implies that the kinetic term is also constant, being proportional to the potential term). Therefore we have 

There exists an exact solution to this equation that can be given in term of Haenkel functions, which here can be expressed analytically 

In order to fix the integration constants A(k) and B(k), we shall impose that the usual Minkowskian solution is valid at early times, i.e., when hr/ - I (when the Hubble parameter is negligible compared to the mode frequency). This gives 

For the scalar modes, we want to relate this exact solution to the asymptotic form 

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In addition to a fluorescence perturbation, the Cd(II)-5d combination also uniquely yields aperturbation in the ultraviolet (UV) spectrum. A difference spectrum obtained by subtracting a fractional amount of an uncomplexed 5d spectrum from the perturbed spectrum is the mirror image of a fluorescence difference spectrum obtained by similar means. Moreover, excitation at 400 nm (where 1-4 are weakly absorbing but where moderate absorption is seen in the difference spectrum) gives rise to an emission spectrum with identical shape and Amax (456 nm) to that of the fluorescence difference spectrum. Thus, evidence points to the existence of two equilibrating ground state species as the physical basis for the chelatoselective emission. Bouas-Laurent has reported a related observation in methanol where a red-shifted CHEF was observed for a T1(I) 7r-complex.(14)... 

Also many epicycles are possible one could consider inflation with several scalar fields, which usually produce isocurvature fluctuations, inflation with a non smooth potential, in which case the slow roll conditions may not be satisfied at some epochs, which then translates into features in the perturbation spectrum (step-like, or with a break in the spectra index), etc. 

Irradiation of lower molecular weight samples in the fluid N phase at 313 or 366 nm led to an unusual result [21]. In the first few seconds of irradiation the perturbed spectrum of the N phase exhibited hyperchromism (an increase in absorbance) and its shape became similar to that of the spectrum of the isotropic melt. This effect is also observed upon triplet sensitization which, like 366-nm irradiation, suppresses photo-Fries rearrangement [28]. It has not yet been proved that this effect is accompanied by a phase change from N to I induced by photoproducts essentially acting as impurities in the mesophase. The effect could be at the microscopic level where formation of a cyclobutane dimer or other photoproduct could interrupt H-type aggregated chromophore stacks, or confor-... 

HCl in liquid xenon at T 185° K. has been studied (29). A spectrum consisting of three broad maxima is observed in the region where HCl vapor absorbs. The maxima have been interpreted as arising from a vibrational transition where the rotational angular momentum can increase by one quantum, decrease by one quantum, or remain the same. In the gas phase only the first two kinds of transitions are allowed. The third type of transition is expected when an unsymmetrical electrostatic field, such as that existing locally in the liquid, is present. In this case the major contribution to the field arises indirectly from the HCl dipole which induces a dipole in the neighboring polarizable xenon. This reaction field can act back on the HCl dipole. The field is unsymmetrical because of the defect structure of the liquid state. When there is high symmetry, as in the case of HCl in solid xenon (2S), the perturbed spectrum does not occur ... 

The normal procedure for visualizing these enhancements is to record a reference spectrum in which the intensities are unperturbed. In terms of z-magnetizations this means that 7 ref = 7°. The difference spectrum, defined as (perturbed spectrum - unperturbed spectrum) corresponds to the difference... 

For the CH3F, the possibility of a model atom approximation will be also discussed. The C-F group will be considered as a model atom. Stretching vibrational frequencies calculated in this work of up to 4 quanta of excitation will be compared with the predictions of the local-mode model for the CH3 group only [26] and with the resonant perturbed spectrum of the molecule observed by Law [26]. 

In order to demonstrate crystalline polymorphy more fully. Figure 12 shows the results of three Rhizoclonium cellulose experiments, like those of Figure 11, in which three different lines were initially perturbed. Spectrum 12A is the parent spectrum (like spectrum HA). The remaining six spectra, in pairs, consist of profiles of an original population perturbation (like spectrum HE) caused by the Dante inversion followed by the... 

This equation is only valid for small-amplitude disturbances, when the approximation C/a 1 holds. When this expression for p is equated to (1.23) at r = a and simplified in the linear approximation, the amplitude. A, disappears, and we are left with a characteristic relationship between the growth rate and the wave number determining the perturbation spectrum. Solving for the growth rate, we have ... 

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