Equivalence points, distance between

Let the distance between the injection point and the peak maximum (the retention distance on the chromatogram) be (y) cm and the peak width at the points of inflexion be (x) cm. If a computer data acquisition and processing system is employed, then the equivalent retention times can be used. 

Geometrically, column-centering of X is equivalent to a translation of the origin of column-space toward the centroid of the points which represent the rows of the data table X. Hence, the operation of column-centering leaves distances between the row-points unchanged. 

The region within which k is considered (—n/a first Brillouin zone. In the coordinate system of k space it is a polyhedron. The faces of the first Brillouin zone are oriented perpendicular to the directions from one atom to the equivalent atoms in the adjacent unit cells. The distance of a face from the origin of the k coordinate system is n/s, s being the distance between the atoms. The first Brillouin zone for a cubic-primitive crystal lattice is shown in Fig. 10.11 the symbols commonly given to certain points of the Brillouin zone are labeled. The Brillouin zone consists of a very large number of small cells, one for each electronic state. 

Five points can be arranged on the surface of a sphere such that they are all equivalent, only in a planar pentagonal arrangement, which does not maximize the distance between the points. In other words, there is no regular polyhedron with five equivalent vertices. There are two... 

The condition for a time-like difference vector is equivalent to stating that it is possible to bridge the distance between the two events by a light signal, while if the points are separated by a space-like difference vector, they cannot be connected by any wave travelling with the speed c. If the spatial difference vector r i — r2 is along the z axis, such that In — r2 = z — z2, under a Lorentz transformation with velocity v parallel to the z axis, the fourth component of transforms as... 

Janssens et al. [38, 40] used photoemission of adsorbed noble gases to measure the electrostatic surface potential on the potassium-promoted (111) surface of rhodium, to estimate the range that is influenced by the promoter. As explained in Chapter 3, UPS of adsorbed Xe measures the local work function, or, equivalently, the electrostatic potential of adsorption sites. The idea of using Kr and Ar in addition to Xe was that by using probe atoms of different sizes one could vary the distance between the potassium and the noble gas atom. Provided the interpretation in terms of Expression (3-13) is permitted, and this is a point the authors checked [38], one thus obtains information about the variation of the electrostatic potential around potassium promoter atoms. 

Plots devised by Dixon to determine K, for tight-binding inhibitors, (a) A primary plot of v versus total inhibitor present ([/Id yields a concave line. In this example, [S] = 3 x Km and thus v = 67% of Straight lines drawn from Vo (when [/It = 0) through points corresponding to Vq/2, Vq/3, etc. intersect with the x-axis at points separated by a distance /Cj app/ when inhibition is competitive. When inhibition is noncompetitive, intersection points are separated by a distance equivalent to K. The positions of lines for n = 1 and n = 0 can then be deduced and the total enzyme concentration, [EJt, can be determined from the distance between the origin and the intersection point of the n = 0 line on the x-axis. If inhibition is competitive, this experiment is repeated at several different substrate concentrations such that a value for K, app is obtained at each substrate concentration. (b) Values for app are replotted versus [S], and the y-intercept yields a value for /Cj. If inhibition is noncompetitive, this replot is not necessary (see text)... 

The right-handed a-helix (ur) is one of the most common secondary structures. In this conformation, the peptide chain is wound like a screw. Each turn of the screw (the screw axis in shown in orange) covers approximately 3.6 amino acid residues. The pitch of the screw (i. e., the smallest distance between two equivalent points) is 0.54 nm. a-Helices are stabilized by almost linear hydrogen bonds between the NH and CO groups of residues, which are four positions apart from each another in the sequence (indicated by red dots see p. 6). In longer helices, most amino acid residues thus enter into two H bonds. Apolar or amphipathic a-helices with five to seven turns often serve to anchor proteins in biological membranes transmembrane helices see p. 214). 

Ioffe and Regel (1960) were the first to point out that small values of l such that kl < 1 /2rc are in fact impossible. This point is developed further in the next section. Moreover, when fci l/2rc, which in metals is equivalent to the condition i a where a is the distance between atoms, the Boltzmann approximation becomes a bad one because k is no longer a good quantum number. This occurs particularly... 

As a first approximation, the temperature depression for hydrate inhibition might be considered to be similar to the depression of the freezing point of ice by an equivalent mass fraction of the inhibitor. However, Nielsen and Bucklin (1983) derived an equation indicating that the hydrate depression temperature will always be less than the ice depression temperature by a factor equal to [(heat of fusion of ice)/(heat of hydrate dissociation)], which has a numerical value between 0.6 and 0.7 as a function of the hydrate structure. This is illustrated in Figure 4.2d, by the fact that at constant pressure, the ice depression temperature (i.e., distance between... 

Fig. 16. Example of tree-like representation for RNA secondary structure. Each hairpin structure is shown next to its equivalent tree. With such representations, a graph theoretic measure can measure the distance between these trees and help generate fitness values for a fitness landscape. For example, the distance between two structures may be defined as the minimal number of elementary graph operations (insert a point, switch an edge, etc.) needed to convert one tree into the other. Note that there are many variants of tree representations for RNA secondary structures and many definitions of graph distance. In low-resolution tree representations, several secondary structures can map to the same graph.

When conveying plastics a properly designed system is to take the shortest distance. The shortest distance between two points is a straight line. The maximum conveying distance is usually 800 equivalent ft (244 m). A gradual upward slope is never better than a vertical lift. When the plastic passes through a 45° or 60° elbow, it ricochets back and forth creating turbulence that destroys its momentum. 

Equivalent considerations for nonstatic, sheared systems demonstrate the kinematical possibility of such shearing motions. This requires, inter alia, that the distance between any two sphere centers remains larger than 2a. The static viewpoint can be generalized to such circumstances as follows Rather than considering the lattice deformation, it suffices to examine the deformed collision sphere. The latter body 3 is defined as the set of points... 

Unit layers are held together in various ways to produce a clay crystal. These are regular, rigid systems and the distance between equivalent points in adjacent unit layers, the c spacing or basal spacing, can be measured by X-ray diffraction and is used to identify the clay minerals (Figure 5). 

Discriminant analysis evaluates the distance between individual points and several centroids hypothesized to exist in the hyperspace defined by elemental concentrations. Davis (28) provides a clear and concise description of the algebra involved in two-group and multiple-group discriminant analysis, showing that discriminant functions are equivalent to the eigenvectors of W-1B, where W1 is the inverse of the within-group sums of products matrix, and B is the between-group sums of products matrix. The Mahalanobis distances from an unknown point to each of the alternative centroids... 

In the first complete linkage analysis, the interaction term (layers, 1/1, float) was assigned the same weight as any of the other relevant attributes. The algorithm yielded three clusters (Figure 3) when there was only one match (or equivalently, when the maximum distance between clusters was 12 no matches ). Two of these clusters accounted for only 13 of the 101 location points. Interestingly, 11 of these 13 points were precisely those and only those points that revealed no pseudomorphs. The other two points were those for which pseudomorphic evidence could not be identified. As such, these two small clusters were taken together to form the cluster of inde-terminates . When matches were increased to three, the big cluster of 88 location points was subdivided into three smaller clusters. A cluster could represent either a fabric type or a fabric pattern. 

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