Reference wavenumber

Following the general procedure, we replace the K and Q coefficients with appropriate approximations. We denote by kR = k(u>R) the reference wavenumber corresponding to the chosen reference frequency wr, and take... 

The principle of applying fuzzy logic to matching of spectra is that, given a sample spectrum and a collection of reference spectra, in a first step the reference spectra are unified and fuzzed, i.e., around each characteristic line at a certain wavenumber k, a certain fuzzy interval [/ o - Ak, + Afe] is laid. The resulting fuzzy set is then intersected with the crisp sample spectrum. A membership function analogous to the one in Figure 9-25 is applied. If a line of the sample spec-... 

The ubiquitous use of the word Tine to describe an experimentally observed transition goes back to the early days of observations of visible spectra with spectroscopes in which the lines observed in, say, the spectmm of a sodium flame are images, formed at various wavelengths, of the entrance slit. Although, nowadays, observations tend to be in the form of a plot of some measure of the intensity of the transition against wavelength, frequency or wavenumber, we still refer to peaks in such a spectmm as lines. 

So far as rule 2 is concerned, since AJ is conventionally taken to refer to J -J", where J is the quantum number of the upper state and J" that of the lower state of the transition, AJ = — 1 has no physical meaning (although it emerges from the quantum mechanics). It is commonly, but incorrectly, thought that AJ = +1 and AJ = — 1 refer to absorption and emission, respectively in fact AJ = +1 applies to both. Transition wavenumbers or frequencies are given by... 

It was predicted in 1923 by Smekal and shown experimentally in 1928 by Raman and Krishnan that a small amount of radiation scattered by a gas, liquid or solid is of increased or decreased wavelength (or wavenumber). This is called the Raman effect and the scattered radiation with decreased or increased wavenumber is referred to as Stokes or anti-Stokes Raman scattering, respectively. 

Spectroscopists usually talk in terms of wavenumbers rather than frequencies or energies. A wavenumber is an energy divided by hco, or a frequency divided by C(j, and so we refer to the classical vibrational wavenumber rUe given by... 

The monocationic form of the dimer 192 gives peaks at wavenumbers between those for the neutral and dicationic forms, and the peak width is broadened, which can be attributed to the rate of electron exchange between two electronic isomers, Red-Ox-Fe(CO)3 and Ox-Red Fe(CO)3, where Fe(CO)3 refers to an [(r 4-cyclopentadiene)Fe(CO)3]... 

Figure 2. IR spectra showing the substantial wavenumber shift between bands assigned to the V(H-H) vibration of coordinated molecular hydrogen in Mo(CO)5(H2), CrlCOj lH ), and W(CO) (H) in liquid Xe at -70°C. Note that the three traces were recor in separate experiments and that the absorbance scale refers to the Mo trace [28].

The enhancement factors mz and mx can be calculated exactly by Hansen s formulas for optics of thin multilayer film [10]. The results of the calculation for our experimental systems are shown in Figure 9 as a function of wavenumber. Three lines for the mz values and those for the mx values refer to the refractive indices of the LB film, 1.4, 1.5, and 1.6. The mx values are very small and about one percent of the mz values. This means that the electric field generated by the RA measurements is practically perpendicular to the film surface, as was mentioned above. 

The form of the scalar energy spectrum for larger wavenumbers will depend on the Schmidt number. Considering first the case where Sc 1, the range of wavenumbers between kc2 and kdi is referred to as the inertial-diffusive sub-range (Batchelor et al. 1959). Note that this range can exist only for Schmidt numbers less than Scid, where... 

This filtering preprocessing method can be used whenever the variables are expressed as a continuous physical property. One example is dispersive or Fourier-Transform spectral data, where the spectral variables refer to a continuous series of wavelength or wavenumber values. In these cases, derivatives can serve a dual purpose (I) they can remove baseline offset variations between samples, and (2) they can improve the resolution of overlapped spectral features. 

Surface species Wavenumbers (cm ) and intensities Surfaces Temperature range [Pg.32]

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