Vectorial information

The dipole moment is a fundamental property of a molecule (or any dipole unit) in which two opposite charges are separated by a distance . This entity is commonly measured in debye units (symbolized by D), equal to 3.33564 X 10 coulomb-meters, in SI units). Since the net dipole moment of a molecule is equal to the vectorial sum of the individual bond moments, the dipole moment provides valuable information on the structure and electrical properties of that molecule. The dipole moment can be determined by use of the Debye equation for total polarization. Examples of dipole moments (in the gas phase) are water (1.854 D), ammonia (1.471 D), nitromethane (3.46 D), imidazole (3.8 D), toluene (0.375 D), and pyrimidine (2.334 D). Even symmetrical molecules will have a small, but measurable dipole moment, due to centrifugal distortion effects. Methane " for example, has a value of about 5.4 X 10 D. 

The work of Laufer (L3) indicates that eddy viscosity is not isotropic in shear flow. For this reason it is unlikely that eddy conductivity is isotropic in such flows. Therefore, uncertainties in the application of eddy conductivities must arise when it is assumed that this transport coefficient is isotropic. Until additional experimental information is available, it appears reasonable to consider eddy conductivity as isotropic except in circumstances when the vectorial nature (J4, R2) of the eddy viscosity may be estimated. Such an approximation appears acceptable since the measurements available described the conductivity normal to the axis of flow, which is the direction in which most detail is required in the prediction of temperature distribution in turbulently flowing streams. Throughout the remainder of this discussion all eddy properties will be treated as isotropic. Such a simplification is open to uncertainty, and further experimentation will be required in order to determine the error introduced by neglect of the vectorial characteristics of these macroscopic transport quantities. 

The observant reader will have realized by now that the above experiment, which is a type of frequency modulation, provides no additional information beyond the simple H spectrum of acetone. Actually, that is the beauty of that experiment it has all of the elements of a 2-D correlation experiment and we can completely follow the activity of the net magnetization vector for acetone using simple vectorial models. Let us turn this prototype pulse sequence into a general format for all 2-D experiments. If we replace the first v/2 pulse with a generalized pulse that contains one or more pulses... 

The vectorial equation of the Topo-Information relationship is then expressed by the sum of the average perturbations JSIs ) associate with the primary sites Sp localized in the trace and by that of the average perturbations jSfs,-) associated with the interaction sites s, detected in the environment ... 

A simple approach to protein description consists of representing a protein by a sequence of properties of its constituent amino acids. Each amino acid is described by one ore more properties and therefore the total number of protein descriptors is given by the product of the number of amino acids in the protein and the number of selected amino acid properties. As this number of descriptors increases very fast with the size of proteins, this approach is usually applied to small- and medium-size peptides. Moreover, in QSAR studies that require uniform-length descriptors, it can be used only to describe a series of peptide analogues, vhich are peptide sequences with the same length. To enable QSAR studies of peptide sequences with different length, some method is required that is able to translate the peptide sequences into vectorial descriptors with the same number of variables. For example, ACC transforms were applied to compress information about principal properties of amino acids into peptide sequences with different length. 

Moreover, the RDF vectorial descriptor is interpretable by using simple rules and, thus, it provides a possibility of —> reversible decoding. Besides information about distribution of interatomic distances in the entire molecule, the RDF vector provides further valuable information for example, about bond distances, ring types, planar and nonplanar systems, and atom types. This fact is a most valuable consideration for a computer-assisted code elucidation. 

PathFinder fingerprints are vectorial descriptors encoding information about the molecular shape starting from a surface representation based on molecular interaction fields (MIFs) [McLay, Harm et al, 2006],... 

Several spectroscopic techniques are systematically used in chemistry for characterization and recognition of chemicals. This suggests that experimentally recorded spectra contain much information related to the molecular structure, which can be converted into molecular descriptors by proper algorithms. The signals obtained by nuclear magnetic resonance (NMR), namely, and H-NMR, and mass spectrometry (MS) are sharp enough to be easily transformed into vectorial descriptors. 

FLAP fingerprints (FLAP stands for Fingerprints for Ligands and Proteins) are vectorial descriptors encoding information about 3- and 4-point pharmacophores [Perruccio, Mason etal, 2006 Baroni, Crucianiet al, 2007]. The theory underpinning FLAP is similar to that of the TOPP descriptors. 

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