Order spectral

Besides this intercollisional interference process, there are other three-body processes which at elevated densities affect the observable spectra over a much wider range of frequencies, virtually at all frequencies at which absorption may be observed. With increasing density, one will be able to discern binary, ternary, and perhaps higher-order spectral contributions (even if cvxi2 1). These are caused by the dipoles induced in systems consisting of N interacting atoms or molecules, with N > 2. 

Classical approximations. While the computation of binary, low-order spectral moments, Eqs. 5.37 and 5.38, poses no special problems, we note... 

Z. Gburski, C. G. Gray, and D. E. Sullivan. Higher-order spectral moments in collision-induced absorption Inert gas mixtures. Chem. 

Since the A th order spectral moment p corresponds to the sum of all self-returning walks of length k in the line graph of the molecular graph Q, it can be expressed as the... 

Obviously, spectral moments p of the P order line graph Lj are the spectral moments of the edge adjacency matrix, and 0- order spectral moments po of any line graph L coincide with the number of vertices in the considered line graph. 

Matched signal detectors, such as spectral matched filter and matched subspace detectors (whether adaptive or non-adaptive), only exploit second order correlations, thus completely ignoring nonlinear (higher order) spectral inter-band correlations that could be crucial to discriminate between target and background. In this paper, our aim is to introduce nonlinear versions of MSD, OSD, SMF and ASD detectors which effectively exploit the higher order spectral inter-band correlations in a high (possibly infinite)... 

The H-nmr spectrum of phosphorinane (1) indicates that the proton on phosphorus is axial and gives no evidence of the presence of an equatorial isomer. Similar conclusions are drawn from the spectrum of phosphorinane 1-sulphide (2), but no conclusions can be reached concerning the proton on the phosphorus of phosphorinane methiodide (3) because of second--order spectral complications (J.B. Lambert and W.L. Oliver, Tetrahedron, 1971, 27, 4245). 

Ning T. and Bronzino J.D. 1989b. Bispectral analysis of the EEC in developing rats. In Proceedings of the Workshop Higher-Order Spectral Analysis, Vail, CO, pp. 235-238. 

As described in Chapter 3, grating spectrometers will respond to harmonically related wavelengths that is, if a grating spectrometer is adjusted to record spectral emission at 6000 A in the first order, spectral emission at 3000 A in the second order also will be recorded at 6000 A and emission at 2000 A will be recorded as third-order emission at the same 6000 A position. Overlapping spectral orders therefore may unnecessarily complicate the observed spectrum and, in some cases, interfere with spectral lines used for analytical purposes. 

A series of papers has appeared from Casy s laboratory dealing with the synthesis, stereochemistry, and conformations of some piperidin -ols. - Three diastereoisomeric l,2,5-trimethyl-4-phenylpiperidin-4-ols were isolated. Making the questionable assumptions (i) that the phenyl group will be equatorial in any chair conformation and (ii) that first-order spectral analysis is applicable, they arrive at configurational and conformational assignments different from those proposed earlier by a Russian group. Subsequent papers deal with acyl derivatives of the above compounds and the n.m.r. spectra of compounds in this series. Similar work has also been reported for ciS and tra 5-l,3-dimethylpiperidin-4-ols and their derivatives. ... 

The SI approach relies on the fact that a discretized spectrum deriving from an calculation and covering a large energy range, including the continuum, provides a reasonable approximation of, at least, the lowest order spectral moments S provided the extension of the basis set is sufficiently good ... 

Yang, D.M., Stronach, A.F., MacConnell, P. Penman, J. 2002. Third-order spectral techniques for the diagnosis of motor bearing condition using artificial neural networks. Mechanical systems and signal processing 16(2) 391 11. 

The approximate solution given in Eq. 30 provides accurate results for low and intermediate frequencies. Therefore the author considered the solution proposed by Vanmarcke and Gasparini (1977) given by Eq. 10 with the adjusted spread factor as further improvement of Eq. 19. As the peak factor evaluation depends on the whole power-spectral density function, which is intrinsically related to the spectral characteristics of the unknown response process (see Eqs. 9, 13, 14, and 20), the author developed an algorithm which enables to update the spectral characteristics of the response process every frequency step of definition of the frequency domain. The iterative scheme mainly differs from the procedure proposed by Sundararajan (1980) as not only the zeroth-order spectral moment is updated at each step but also the peak factor. To this aim the... 

If we examine Fig. 3 we see that only two of the four possible transitions are allowed, namely, those in which the nuclear spin does not change its orientation. The energy difference between these two transitions is defined as the hyperflne constant, usually symbolized by A in units of megahertz (MHz) or gauss (G). Since Ami = 0, the effect of the nuclear Zeeman term in the spin Hamiltonian will always cancel out for first-order spectral transitions. Thus, this term can be neglected in the Hamiltonian when one is considering only first-order spectra. However, it should be cautioned that if one considers spectra in which the perturbation theory approach must be carried out to second order or if one considers spin relaxation, which will be discussed later, the full spin Hamiltonian must be used. 

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