Distance defined

Several practical issues of the scatterometer must be considered in the case of characterizing nominally smooth surfaces. The incident laser beam may be collimated, but more commonly it is brought to a focus at a distance defined by the arc in which the detector rotates. In addition, a deflection mirror or an optical fiber might be used to direct light to the detector element. These features permit measurements close to the specular and transmitted beams, and this is critical to folly characterize the scattered light. This is especially significant since the scattered light intensity... 

Row-standardization forces points in 5 on a (hyper)sphere about the origin. In SP, angular distances after row-standardization are the same as those defined by row-centering. Distances defined in S by row-standardization are different from... 

Principal coordinates analysis 31.6.1 Distances defined from data... 

The Minkowski distance defines a class of distance functions which are characterized by the parameter r (Section 30.2.3.2) ... 

If initial solute uptake rate is determined from intestinal tissue incubated in drug solution, uptake must be normalized for intestinal tissue weight. Alternative capacity normalizations are required for vesicular or cellular uptake of solute (see Section VII). Cellular transport parameters can be defined either in terms of kinetic rate-time constants or in terms of concentration normalized flux [Eq. (5)]. Relationships between kinetic and transport descriptions can be made on the basis of information on solute transport distances. Note that division of Eq. (11) or (12) by transport distance defines a transport resistance of reciprocal permeability (conductance). 

One measure of the conformational properties of the chains are the components of the mean-square end-to-end distance, defined as... 

R Sachs scaled distance, defined by equation 6-25 (unitless)... 

But if affinity was like gravity, electricity, or, to a lesser extent, magnetism, it could not be identical to them. An important difference was that affinity was selective or "elective." Elementary chemical substances chose friends and foes on the basis of kind, not just the quantity of a thing and its distance. Defining affinity in the nineteenth century, Wurtz called it the "force which... 

Most of the standard clustering algorithms can be directly used for clustering the variables. In this case, the distance between the variables rather than between the objects has to be measured. A popular choice is the Pearson correlation distance, defined for two variables xj and xk as... 

Nevertheless it must be pointed out that, in calculating (k ), the value taken in practice is often the ratio of the corrected retention distance (the distance in centimeters on the chart, between the dead point and the peak maximum) to the dead volume distance (the distance in centimeters on the chart, between the injection point to the dead point on the chromatogram). This calculation assumes the extra column dead volume is not significant and, unfortunately, in almost all cases this is not true, (k ) values calculated in this way will be in error and should not be used for solute identification. Where computer data processing is used and no chart is available the distances defined above would be replaced by the corresponding times. 

If a Cauchy sequence converges, using the distance defined by x -xm, in a scalar product space, then it is a Hilbert space. 

The overlapping occurs within a distance defined by 2 (depending on the angle y). Taking the mean of over all angles y gives a mean overlapping volume. 

One of the major differences between two-coordinated sulfur and selenium is the tendency of the latter to increase its coordination number, as can be seen from the fairly strong intermolecular interactions between selenium rings in the various crystal structures. The shortest intermolecular distance observed (335 pm in y-Se8) is 65 pm shorter than the van der Waals distance (400 pm) but still 101 pm longer than the single bond distance defined above. In the case of sulfur rings the shortest observed intermolecular contact (323 pm in Si0 (88) is 37 pm shorter than the van der Waals distance (360 pm) but 101 pm longer than the single bond in S8. 

DISTANCES are in Angstroem increments of distances/pharmacophore distances define the bins to be filled... 

In aqueous solutions, the situation is clarified by the solvent. This solvent keeps the complex ions apart at mean distances, defines them as independent stable entities, and permits probing radiation (e.g., visible light) to pick them out from the surroundings (Fig. 5.5). 

Figure 2 Average NQR frequency difference of coordinated ortho-chlorine and noncoordinated (free) ortho-chlorine atoms in 2,6-dichlorophenolato(0,C/) complexes of metals, as a function of the excess M-Cl distance, defined as the average observed M-Cl distance minus the normal M-Cl single bond distance in octahedral complexes, from A. G. Orpen, L. Branner, F. H. Allen, O. Kennard, D. G. Watson, and R. Taylor, J. Chem. Soc., Dalton Trans. 1989, S1-S83...

Some difficulties in comparing the experimental kinetic data with the outer-sphere reorganization energy calculated from the Marcus formula (28) result from several assumptions made in this theory. The reactant was assumed to have a spherical shape with a symmetric charge distribution. No field penetration into the metal was considered. Also, the spatial dispersion of the dielectric permittivity of the medium was not taken into account. In fact, the positions and orientations of dipoles around a given ion are correlated with each other therefore the reorientation of one dipole, under the influence of the external field, changes to some extent the reorientation of other dipoles within the distance defined by the correlation length. 

An initial network configuration was set up by randomly choosing sizes for all sites and bonds, while observing the imposed twofold size distribution. Sites were placed at the nodes of the cubic lattice and bonds in between the nodes. Node to node distance was constant (i.e. equal to the diameter of the largest site) the length of each bond was adjusted to a value enough to connect its two neighbouring sites. This particular selection of bond-site distance defined the porosity of the network. 

A repeating pattern is formed by the repetition of some unit at regular intervals along one, two, or three (non-parallel) axes which, with the repeat distances, define the lattice on which the pattern is based. For a 1-dimensional pattern the lattice is a line, for a 2-dimensional pattern it is a plane network, and for a 3-dimensional pattern a third axis is introduced which is not coplanar with the first two (Fig. 2.1). 

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