Orientation definition, meaning

Definition (Orientation) An orientation of means the choice of a sequence (bo.bj.bj) of linearly independent vectors bj, i.e. the choice of an ordered basis of the space considered. Having chosen such an ordered basis (bo, b], bj), another ordered basis (cq, C], cj) is said to have thesome orientation if its determinant has the same sign,... 

One might hope to get somewhere with the idea of a geometrical structure by considering the development of the definition to deal with a system described in a frame fixed in the body. The idea here is to somehow fix a coordinate frame in the system and to define its orientation by means of 3 Eulerian angles, (j>m defined entirely in terms oi A — translationally invariant position variables associated with the nuclei. In such a coordinate system the Hamiltonian takes the general form... 

Data transposition is the process of changing the orientation of the data from a normalized structure to a non-normalized structure or vice versa. There are many definitions of normalization of data, and you should learn about normal forms and normalization. Here, in brief, normalization of data means the process of taking information out of the variable definitions and turning that information into row definitions/keys in order to reduce the overall number of variables. Normalized data may also be described as stacked, vertical, or tall and skinny, while non-normalized data are often called flat, wide, or short and fat. ... 

The term monolayer (ML) must be defined clearly. In the work presented here, two definitions are used for surface studies, one ML indicates one adsorbate for each surface atom. For studies of compound formation, a monolayer is a slice of the compound s crystal structure, composed of one atomic layer of each of the constituent atoms. This does not necessarily mean a one unit-cell thick deposit is formed, as most compounds have larger unit cells from the point of view of crystallography, dependent on the orientation (Figure 8). 

It may be noted that simple MOPAC AMI calculations suggest that the dipole moment of NOBOW is oriented antiparallel to the molecular arrow. As indicated in Figure 8.25, this means that for an up field, the molecular arrows are pointing down. Given the definition of the sign of P in FLCs, this also means that domains of the ShiCaPa phase with positive chirality have negative ferroelectric polarization, and vice versa. 

Several definitions depend on the measurement of a particle in a particular orientation. Thus Feret s statistical diameter is the mean distance apart of two parallel lines which are tangential to the particle in an arbitrarily fixed direction, irrespective of the orientation of each particle coming up for inspection. This is shown in Figure 1.1. 

An important consequence of the presence of the metal surface is the so-called infrared selection rule. If the metal is a good conductor the electric field parallel to the surface is screened out and hence it is only the p-component (normal to the surface) of the external field that is able to excite vibrational modes. In other words, it is only possible to excite a vibrational mode that has a nonvanishing component of its dynamical dipole moment normal to the surface. This has the important implication that one can obtain information by infrared spectroscopy about the orientation of a molecule and definitely decide if a mode has its dynamical dipole moment parallel with the surface (and hence is undetectable in the infrared spectra) or not. This strong polarization dependence must also be considered if one wishes to use Eq. (1) as an independent way of determining ft. It is necessary to put a polarizer in the incident beam and use optically passive components (which means polycrystalline windows and mirror optics) to avoid serious errors. With these precautions we have obtained pretty good agreement for the value of n determined from Eq. (1) and by independent means as will be discussed in section 3.2. 

The estimation of the surface area of finely divided solid particles from solution adsorption studies is subject to many of the same considerations as in the case of gas adsorption, but with the added complication that larger molecules are involved whose surface orientation and pore penetrability may be uncertain. A first condition is that a definite adsorption model is obeyed, which in practice means that area determination data are valid within the simple Langmuir Equation 5.23 relation. The constant rate is found, for example, from a plot of the data, according to Equation 5.23, and the specific surface area then follows from Equations 5.21 and 5.22. The surface area of the adsorbent is generally found easily in the literature. 

From its definition, the P-polynomial appears to depend on the particular projection of the link which we are working with. However, when this polynomial was defined it was proven that given any oriented link, no matter how it is deformed or projected, the link will always have the same P-polynomial [5, 6]. This means that two oriented links which are topologically equivalent have the same P-polynomial. In particular, if an oriented link can be deformed to its minor image then it and its minor image will have the same P-polynomial. 

The physical meaning of the constant s in equation (15) is less definite than the meaning of E. In bimolecular reactions, which demand a collision between two molecules before reaction can occur, s refers to the number of molecules colliding, and, as just explained, e E,RT is the fraction of molecules which are activated. The rate constant, k, when expressed in the proper units, is then equal to the number of activated molecules per unit volume colliding. This assumption that every collision of an activated molecule leads to reaction is valid only in a few cases and it is necessary to put another factor, a, into the equation to allow for a steric effect of some kind. Perhaps the activated molecules have to be orientated in a definite way when they collide, in order that reaction may occur. Equation (15) then becomes... 

Water and ionic compounds are very different types of substances, and it is not unnatural that they do not form solids of variable composition. The reason why water solutions of ionic substances exist is that the water molecules can rotate so as to be attracted to the ions this is not allowed in the solid, where the ice structure demands a fairly definite orientation of the molecule. But as soon as we think about solid phases of a mixture of similar components, we find that almost all the solid phases exist over quite a range. Such phases are often called by the chemists solid solutions, to distinguish them from chemical compounds. This distinction is valid if we mean by a chemical compound a phase which really exists at only a quite definite composition. But the chemists, and particularly the metallurgists, are not always careful about making this distinction for this reason the notation is misleading, and we shall not often use it. 

Probably the occurrence of this limiting value means that the long chains are orientated in the surface, so that the structure of the surfaces of the hydrocarbons, acids, and amines is practically the same, both in the arrangement of molecules and in the motions of the molecules. The orientation may be approximately perpendicular to the surface, but all that can be definitely stated is that it is probably the same for all the compounds. 

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