Genuine modes

The translational and rotational degrees of freedom, which do not change the relative positions of the atoms in the molecule, are often called nongenuine modes. The remaining 3TV - 6 (or 3N - 5) degrees of freedom are called genuine vibrations or genuine modes. 

Surprisingly the first attempts to measure displacements originating from genuine periodic or quasi-periodic perturbations were carried out in vivo. Those studies took advantage of the internal pulsatile motions provided by heart beating. As soon as 1982 small displacements from aortic pulsations were visualized in liver on M-mode scans.69 It was shown that such displacements could be calculated from correlated successive A-scans,70 with an application on liver.71,72 Correlation techniques were also applied on M-mode images to quantitatively estimate motions and deformations of fetal lung.73,74... 

The question is, what do we need for approximation of the relaxation process (8). The answer is obvious for approximation of general solution (8) with guaranteed accuracy we need approximation to the genuine eigenvectors ("modes") with the same accuracy. The zero-one asymptotic (5) gives this approximation. Below we always find the modes approximations and not quasimodes. 

In order to use the F-G matrix method to maximum advantage, it is first necessary to set up linear combinations of internal coordinates which provide the proper number of functions, transforming according to each of the irreducible representations spanned by the 3N - 6 normal modes of genuine... 

Symmetry Types of the Normal Modes. For this nonlinear four-atomic molecule there are 3(4) -6 = 6 genuine internal vibrations. Using a set of three Cartesian displacement coordinates on each atom, we obtain the following representation of the group C3l, ... 

The character table shows that the rotations and translations belong, respectively, to the TXg and TXu representations. After deleting these, we obtain the following list of genuine normal modes, grouped according to the activities of their fundamentals ... 

Authenticity A condition that proves a record is authentic and/or genuine, based on its mode (the method by which a record is communicated over space or time) on its form (format and/or media that a record takes when received) state of transmission (the primitiveness, completeness, and effectiveness of a record when initially set aside after being made or received) and manner of preservation and custody (DOD 5015.2-STD). 

The removal of 1,2,4,5-tetramethylbenzene and isoropylbenzene from Equation 17.3 as outliers can be justified. Inspection of the data reveals that the bioluminescence response for 1,2,4,5-tetramethylbenzene is very low (-2.02), and much lower than for similar compounds (e.g. 1,2,3,4-tetramethylbenzene has a light level of 0.15). This implies that the compound is not an inducer of the ipb pathway and it is not part of the homologous series of compounds on which the model is based. It is fundamental to the development of QSARs that they are based on a genuinely homologous series (i.e., the chemicals elicit a biological response through the same mode of action). 

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