Degeneration factor

Visual inspection of the estimated factors is not to be trusted in the presence of degenerate factors, which occur when two or more factors are collinear in one or more of the three ways. When this is the case, in the concentration way or Z-way, the PARAFAC model is still valid, but the rotational uniqueness of the X-way and Y-way protiles of the degenerate factors is lost. This often results in estimated protiles that are hard to interpret. If the collinearity occurs in the X-way or Y-way, the PARAFAC model may not be appropriate, and the constrained Tucker3 model should be used instead. Collinearity in the X-way or Y-way can be checked by successively performing PCA on data unfolded to an / x (J K) matrix, and then to a. / x (l K) matrix. If there are no collinearities in the X- or Y-ways, the optimal number of factors determined by both unfoldings will be the same. 

The gj are degeneration factors, Fgeo a geometrical correction factor. The partition function of a classical gas is QcUss = 1 /N (V[/A)NQ. ... 

Distribution spectrum for the secondary particles at the thickness of the liquid column equal to h (h a, b and a b), connecting both degeneration factors factor of force frequency degeneration caused by wave-damping factor and factor of characteristic frequency degeneration caused by change of the liquid column thickness, can be expressed in the following form [1-2] ... 

A is an adjustable constant of proportionality. Thus, the degeneration factor due to the vacancies present around a molecule would be written as ... 

This corresponds to the hjpothesis that each arrangement of molecules in the pure components splits at mixing into Nl/NilN l distinct arrangements which differ only in the " mutual localization " of molecules 1 and 2. The effect of mixing is to introduce a supplementary degenerancy factor. This special kind of degeneracy may be called a localisation degeneracy, because it is essentially due to the existence of different relative localisations in space of the two kinds of molecules. 

The sum excludes m = n, because the derivation involves the vector product of (n Vq H n) with itself, which vanishes. The advantage of Eq. (43) over Eq. (31) is that the numerator is independent of arbiriary phase factors in n) or m) neither need be single valued. On the other hand, Eq. (43) is inapplicable, for the reasons given above if the degenerate point lies on the surface 5. 

Because the rotational energies now depend on K (as well as on J), the degeneracies are lower than for spherical tops. In particular, because the energies do not depend on M and depend on the square of K, the degeneracies are (2J+1) for states with K=0 and 2(2J+1) for states with K > 0 the extra factor of 2 arises for K > 0 states because pairs of states with K = K and K = -K are degenerate. 

Copper is required for all forms of aerobic and most forms of anaerobic life. In humans, the biological function of copper is related to the enzymatic action of specific essential copper proteins (66). Lack of these copper enzymes is considered a primary factor in cerebral degeneration, depigmentation, and arterial changes. Because of the abundance of copper in most human diets, chemically significant copper deficiency is extremely rare (67). 

The sum in the denominator relates to the quantum states. The formula is often written in terms of energy levels rather than quantum states in the case that some of the energy levels are degenerate, with degeneracy factors gi then the formula can be modified to refer to energy-level populations directly ... 

Ferrara N, Damico L, Shams N, et al (2006) Developmemt of Ranibizumab, an anti-vascular endothelial growth factor antigen binding fragment, as therapy for neovascular age-related macular degeneration. Retina 26 859-870... 

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