Spatial representation characterized

Working memory is traditionally divided into two major domains verbal and visuo-spatial. However, there is an ambiguity with respect to how this division is characterized. It has been defined in terms of sensory modality—auditory vs. visual-spatial representations, and it has also been... 

In the previous section we used quaternions to construct a convenient parameterization of the hybridization manifold, using the fact that it can be supplied by the 50(4) group structure. However, the strictly local HOs allow for the quaternion representation for themselves. Indeed, the quaternion was previously characterized as an entity comprising a scalar and a 3-vector part h = (h0, h) = (s, v). This notation reflects the symmetry properties of the quaternion under spatial rotation its first component ho = s does not change under spatial rotation i.e. is a scalar, whereas the vector part h — v — (hx,hy,hz) expectedly transforms as a 3-vector. These are precisely the features which can be easily found by the strictly local HOs the coefficient of the s-orbital in the HO s expansion over AOs does not change under the spatial rotation of the molecule, whereas the coefficients at the p-functions transform as if they were the components of a 3-dimensional vector. Thus each of the HOs located at a heavy atom and assigned to the m-th bond can be presented as a quaternion ... 

To be able to calculate 3D descriptors, amino acids have to be characterized by (x, y, z) Cartesian coordinates. Being the a-carbon present in all coded amino acids, the Cartesian coordinates of that atom are selected as the coordinates of the whole amino acid. From the peptide topological representation and/or the corresponding geometrical representation (using only a-carbon spatial coordinates), several constitutional, topological and geometrical descriptors can be calculated. 

When these compounds and many other PAHs were chromatographed to see if retention time could be used as another characterizing tool, an unexpected result was found. Even though the PAH structures were ostensibly similar (if conventional graphical representations were compared), their true spatial configurations must be very different. These conformational differences resulted in vastly different spectral and chromatographic characteristics. 

The solutions of the Schrodinger equation show how / is distributed in the space around the nucleus of the hydrogen atom. The solutions for t are characterized by the values of three quantum numbers (essentially there are three because of the three spatial dimensions, x, y and z), and every allowed set of values for the quantum numbers, together with the associated wave function, describes what is termed an atomic orbital. Other representations are used for atomic orbitals, such as the boundary surface and other diagrams described later in the chapter, but the strict definition of an atomic orbital is its mathematical wave function. 

Figure 19.22. Schematic representation of a set-up developed in-house for simultaneous SSITKA experiments and catalyst characterization by in situ time- and spatially-resolved UV/Vis spectroscopy.

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