Correspondence table

The item (Display) allows the user to chose between the graph and the corresponding table of data, see Fig. 5.7. 

This result (problem 14) allows the coefficients to be calculated. Thus, with a knowledge of the symmetry group and the corresponding table of characters, the structure of the reduced representation can be determined. Equation (37) is of such widespread applicability that it is referred to by many students of group theory as the magic formula. ... 

Optimum Conditions for Quasiliving Polymerization. Table I summarizes H -W relationships obtained under a variety of conditions. nThI corresponding table for MVE is almost identical. The observed relationships are classified into three categories ... 

In a relational database, we might have separate tables, Session, Instructor, and Client. Each object is one row in its corresponding table (see Figure 2.4). 

The role of lone pairs, the effect of their geometry and of electronegative substituents on coupling constants (mostly proton-proton) have been studied for oximes. Specific examples are given in the corresponding tables. 

The naturally occurring compounds in the flavan, flavan-3-ol, flavan-4-ol, flavan-3,4-diol, and proanthocyanidin classes, together with their plant sources, are listed in Table 11.2-Table 11.17. The lists are confined to new compounds reported in the post-1992 period or those that have been overlooked in the 1994 review, and therefore must be considered in conjunction with the corresponding tables of the Porter reviews to be comprehensive. Since many of the monomeric analogs have been published under trivial names these will be retained to facilitate electronic literature searches. Unfortunately, a considerable number of these potentially chiral compounds have been reported without assignment of absolute configuration, and are hence presented as such. 

Substituent increments are obtained as usual by subtracting the reference shifts of naphthalene (C-1,4,5,8 127.7 C-2,3,6,7 125.6 C-9,10 133.3 ppm) from the individual data of C-l to C-10 in the substituted derivatives given in Table 4.55. It turns out that comparable Zx, Zmthn, Zmrta, and Zpara increments in naphthalene and benzene differ substantially in magnitude, as exemplified in Table 4.56. In 1-substituted naphthalenes, C-9 increments are attenuated in favor of C-2 relative to comparable ortho effects known from benzene C-3 and C-1 in 2-substituted naphthalenes behave correspondingly (Table 4.56). This can be explained by the cannonical formulae c, which do not contribute so much to the actual molecular state due to disrupted % electron sextets. Full inter-... 

Current-potential curves of the oxidation of hydrogen peroxide with a vitreous-carbon electrode in an alkaline environment with a hydrogen peroxide concentration of (a) 0.15 mol I-1 and pH = 12.04 and (c) 0.44mol I-1 and pH = 12.80, and their corresponding table graphs with (b) an inclination of 0.50 and (d) an inclination of 0.48. 

To summarize, we thus introduce into the database three new external important information types the domain reverse resolution, the result of Whois queries and the network parameters. As a follow up, since these information characterize uniquely a given Source, we have decided to enrich the corresponding table with this information by adding attributes, the value of which point to new tables providing the imported information. This is represented in Figure 6. For instance, Network Id is a pointer to an entry in the table Network where a network address can be found together with an estimated CIDR value. 

Tables 4.10, 4.11, and 4.12 are the corresponding tables for pyruvate dehydrogenase, the citric acid cycle, the net reaction for the citric acid cycle, the net...

Present-day average values of the water runoff of the Dnieper, Southern Bug and Ingul rivers are amounted as 43.4, 2.2 and 0.58 km3 year 1 correspondingly (Table 8). 

Examples of Li MH use are found in reviews " " and in"" Table 1. Although LiAlH is a more powerful reducing agent than NaBH, the latter is used frequently in EtOH, while LiAlH requires ether. Comparison of Table 1 with the corresponding table in 1.10.7.1 shows that transition-metal hydrides can be prepared by the use of either reagent. 

Subsequently, move to the next column in the corresponding table. Identify reflections that belong to a specified combination of Miller indices listed in the column header and analyze whether or not the extinction conditions are met. This should further narrow the list of possible space groups. 

The principal bond arrangements are set out in Table 16.1 which has the same general form as the corresponding Table 11.1 for oxygen. For the sake of simplicity we have assumed sp hybridization in H2S though the interbond angle (92°) is nearer to that expected for p bonds. For other molecules SR2 see Table 16.2... 

Figure 11.18 shows an application of EXAFS on sulphided catalysts as used in hydrotreating processes [39]. The results in the corresponding table have been obtained by computer fitting. The great disadvantage of EXAFS is that data analysis is complicated and time consuming considerable expertise is required... 

To apply the Laplace transformation several theorems are required, which have been put together, without proofs, in Table 2.2. In addition a table of functions of t with their Laplace transforms a is also needed. This correspondence table is generated by the evaluation of the defining equation (2.111). 

Once the Laplace transform u(x,s) of the temperature () (x, /,) which fits the initial and boundary conditions has been found, the back-transformation or so-called inverse transformation must be carried out. The easiest method for this is to use a table of correspondences, for example Table 2.3, from which the desired temperature distribution can be simply read off. However frequently u(x,s) is not present in such a table. In these cases the Laplace transformation theory gives an inversion theorem which can be used to find the required solution. The temperature distribution appears as a complex integral which can be evaluated using Cauchy s theorem. The required temperature distribution is yielded as an infinite series of exponential functions fading with time. We will not deal with the application of the inversion theorem, and so limit ourselves to cases where the inverse transformation is possible using the correspondence tables. Applications of... 

Inverse transformation to the time region (u — , s — t) using a correspondence table (u —o ) or the general inversion theorem. 

In order to carry out the inverse transformation with the aid of correspondence tables, the numerator has to be expanded into a binomial series, giving... 

This is a series development which for large values of s or p = fsja rapidly converges. The inverse transformation using correspondence tables (No. 6 from Table 2.3 with x = 5, 35, 55,. ..) yields a series that is particularly suitable for small times t. This gives... 

If heat transfer from a fluid at 0 = 0g to the free surface, takes place at x = 0, Case c from Table 2.4, the temperature is also obtained from a correspondence table (No. 11 in Table 2.3). The solution is written in dimensionless form with the variables... 

The reverse transformation, with the assistance of a correspondence table, Table 2.3, provides us with... 

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