INDEX indicators

Merkmal, n. characteristic, mark, sigri, symbol, indication, index, criterion. 

Production Indices, Index Sets, Control and Input Data... 

Figure 4.30. Solid zero-level lines for the orientation amplitudes pi- in the adiabatic limit for k from 2 to 6 dashed asymptotic values from Eq. (4.301). In multibranch graphs the numbers indicate index / the upper right graph shows the case k = 2 in the extended (0 scale.

Balaban, A.T., Mills, D. and Basak, S.C. (2002) Alkane ordering as a criterion for similarity between topological indices index J as sharpened Wiener... 

In order to decide whether thermal conditions are acceptable for a particular type of work, a number of indices (indexes) have been developed. These were developed in a number of ways, for example ... 

NOTE The array Xforest withC is an array of indices (indexes) specifying which row from Cforest (256x3 array) the pixel color is to be taken from. Cforest is a 256-by-3 matrix of real numbers between 0.0 and 1.0. Each row is an RGB vector that defines one out of 256 colors. The kth row of the colormap, Cforest, defines the color, where Cforest(k, ) = [r(k) g(k) b(k)] specifies the intensity of red, green, and blue. So, in indexed images, the pixel values are themselves indices (indexes) to a table that maps the index value to a color value. 

The predicted cumulative cash-flow curve for a project throughout its life forms the basis for more detailed evaluation. Many quantitative measures or indices have been proposed. In each case, important features of the cumulative cash-flow curve are identified and transformed into a single numerical measure as an index. 

Refractive index this is one of the most precise measurements that can be carried out on a petroleum cut. The ASTM method D 1218 indicates a reproducibility of 0.00006, which is exceptional. 

As a consequence, other than its use in the ndM method, the refractive index is very often used in process operations because it can indicate smaii differences in product quality that would be missed by other measurements. The only restriction is that the color of the sample should be less than 5 on the ASTM D 1500 scale. 

This usefulness of the correlation is twq-fpld first it provides information on the cetane indices that are not aViit le in the literature as in the cases of polynuclear aromatics and sulfur-containing aromatics, and second it helps provide an evaluation of the cetane index based on a few milligrams of sample, instead of the liter or so required for the motor method. 

The viscosity index is an empirical number, determined from the kinematic viscosities at 40 and 100°C it indicates the variation in viscosity with temperature. 

The exact calculation of the index is given in the ASTM D 2270 standard. The kinematic viscosity at 40°C (f/) of an oil whose viscosity index (V7) is being calculated is compared with those of two reference oils for which the viscosity indices are 0 and 100 respectively, and which have at 100°C the same kinematic viscosity as that of the oil being examined )... 

The luminometer index (ASTM D 1740) is a characteristic that is becoming less frequently used. It is determined using the standard lamp mentioned above, except that the lamp is equipped with thermocouples allowing measurement of temperatures corresponding to different flame heights, and a photo-electric cell to evaluate the luminosity. The jet fuel under test is compared to two pure hydrocarbons tetraline and iso-octane to which are attributed the indices 0 and 100, respectively. The values often observed in commercial products usually vary between 40 and 70 the official specification is around 45 for TRO. 

Neutralization index NFT 60-112 ISO 6618 ASTM D 974 Titration in presence of colored indicators... 

Drawdown and build-up surveys are typically performed once a production well has been completed, to establish the reservoir property of permeability (k), the well completion efficiency as denoted by its skin factor (S), and the well productivity index (PI). Unless the routine production tests indicate some unexpected change in the well s productivity, only SBHP surveys may be run, say once a year. A full drawdown and build-up survey would be run to establish the cause of unexplained changes in the well s productivity. 

The previous sections have considered the flow of fluid to the wellbore. The productivity index (PI) indicates that as the flowing wellbore pressure (Pwf) reduces, so the drawdown increases and the rate of fluid flow to the well increases. Recall... 

A similar form of indicator is the Profitability Index (PI), where the denominator is the maximum exposure of the project, and is applicable where the company is sensitive to the maximum exposure e.g. 

The Index n = k- ) - M + m is the current variable that indicates the sequence for the beam projections. Exploiting the current measurings y fn) one has to estimate the unknown image parameters a, with undefined conditions about their distribution and the noise FDD function. 

In describing a particular surface, the first important parameter is the Miller index that corresponds to the orientation of the sample. Miller indices are used to describe directions with respect to the tluee-dimensional bulk unit cell [2]. The Miller index indicating a particular surface orientation is the one that points m the direction of the surface nonual. For example, a Ni crystal cut perpendicular to the [100] direction would be labelled Ni(lOO). 

All tenus in the sum vanish if / is odd, so (00/) reflections will be observed only if / is even. Similar restrictions apply to classes of reflections with two indices equal to zero for other types of screw axis and to classes with one index equal to zero for glide planes. These systematic absences, which are tabulated m the International Tables for Crystallography vol A, may be used to identify the space group, or at least limit die... 

Figure Bl.21.1 shows a number of other clean umeconstnicted low-Miller-index surfaces. Most surfaces studied in surface science have low Miller indices, like (111), (110) and (100). These planes correspond to relatively close-packed surfaces that are atomically rather smooth. With fee materials, the (111) surface is the densest and smoothest, followed by the (100) surface the (110) surface is somewhat more open , in the sense that an additional atom with the same or smaller diameter can bond directly to an atom in the second substrate layer. For the hexagonal close-packed (licp) materials, the (0001) surface is very similar to the fee (111) surface the difference only occurs deeper into the surface, namely in the fashion of stacking of the hexagonal close-packed monolayers onto each other (ABABAB.. . versus ABCABC.. ., in the convenient layerstacking notation). The hep (1010) surface resembles the fee (110) surface to some extent, in that it also...

Figure C2.5.10. The figure gives tire foldability index ct of 27-mer lattice chains witli sets containing different number of amino acids. The sets are generated according to scheme described in [27], The set of 20 amino acids is taken as a standard sample. Each sequence witli 20 amino acids is optimized to fulfil tire stability gap [5]. The residues in tire standard samples are substituted witli four different sets containing a smaller number of amino acids [27]. The foldability of tliese substitutions is indicated by tire full circles. The open diamonds correspond to tire sequences witli same composition. However, tire amino acids are chosen from tire reduced representation and tire resultant sequence is optimized using tire stability gap [5].

The Hamaker constant can be evaluated accurately using tire continuum tlieory, developed by Lifshitz and coworkers [40]. A key property in tliis tlieory is tire frequency dependence of tire dielectric pennittivity, (cij). If tills spectmm were tlie same for particles and solvent, then A = 0. Since tlie refractive index n is also related to f (to), tlie van der Waals forces tend to be very weak when tlie particles and solvent have similar refractive indices. A few examples of values for A for interactions across vacuum and across water, obtained using tlie continuum tlieory, are given in table C2.6.3. 

Figure C2.15.13. Two-dimensional waveguide configurations, the darker shading indicates tire different indexes.

In empirical formulas of inorganic compounds, electropositive elements are listed first [3]. The stoichiometry of the element symbols is indicated at the lower right-hand side by index numbers. If necessary, the charges of ions are placed at the top right-hand side next to the element symbol (e.g., S "). In ions of complexes, the central atom is specified before the ligands are listed in alphabetical order, the complex ion is set in square brackets (e.g., Na2[Sn(OH)+]). 

The elements of an organic compound are listed in empirical formulas according to the Hill system [8] and the stoichiometry is indicated by index numbers. Hill positioned the carbon and the hydrogen atoms in the first and the second places, with heteroatoms following them in alphabetical order, e.g., C9H11NO2. However, it was recognized that different compounds could have the same empirical formula (see Section 2.8.2, on isomerism). Therefore, fine subdivisions of the empirical... 

Both tables, the atom and the bond lists, are linked through the atom indices. An alternative coimection table in the form of a redundant CT is shown in Figure 2-21. There, the first two columns give the index of an atom and the corresponding element symbol. The bond list is integrated into a tabular form in which the atoms are defined. Thus, the bond list extends the table behind the first two columns of the atom list. An atom can be bonded to several other atoms the atom with index 1 is connected to the atoms 2, 4, 5, and 6. These can also be written on one line. Then, a given row contains a focused atom in the atom list, followed by the indices of all the atoms to which this atom is bonded. Additionally, the bond orders are inserted directly following the atom in-... 

Figure 2-80. The permutation matrix oFthe reference isomer the second line gives the indices of the sites of the skeleton and the first line the indices of the ligands (e.g.. the ligand with index 3 is on skeleton site 3).

Hence, they take account of only the structure constitution (topology). One of the first and most frequently used topological indices is the Wiener index. It has the form of Eq. (3), where D,y are all the routes from atom i to atom j. 

Other quite frequently used indices are the Randic index and the information-topological indices such as the Bonchev index (see Chapter VIll, Section 1 in the Handbook), Up to now several hundred indices have been devised. 

A second disadvantage in the use of topological indices is that whereas the process of transformation of connectivity into one number is straightforward, the reverse process of reconstruction of connectivity from the index is not possible. 

Full structure search can be developed by using similar approaches to those employed in the case of 2D structure search. Thus, some topological indices can be modified in such a way that they include geometrical information. For example, the global index given by Eq. (4) can be modified to Eq. (11), where are real interatomic distances. 

Z eb index, Wiener index. Balaban J index, connectivity indices chi (x), kappa (k) shape indices, molecular walk counts, BCUT descriptors, 2D autocorrelation vector... 

---