Dias parameter

Benzenoid (chemical) isomers are, in a strict sense, the benzenoid systems compatible with a formula C HS. Several invariants, including the Dias parameter, are treated and relations between them are given. Many of the relations involve upper and lower bounds. The periodic table for benzenoid hydrocarbons is revisited and new aspects of it are pointed out. In this connection some new classes of benzenoids are defined extreme-left, protrusive and circular. Extensive tables of enumeration data for benzenoid isomers are presented. Some of their forms are displayed in figures. 

The Dias parameter, ds [7], is an invariant for benzenoid systems and defined in terms of other invariants by... 

Fig. 1. Examples of benzenoids with various Dias parameters (ds) heavy lines indicate internal edges...

In the periodic table for benzenoid hydrocarbons [7] the formulas C HS are arranged in an array with coordinates (ds, ,). The Dias parameters (ds) are found on a horizontal axis (increasing from left to right), while the numbers of internal vertices ( ) are on a vertical axis (increasing downwards). The table extends infinitely to the right and downwards. To the left the formulas form a line in the shape of an uneven staircase, which shall be referred to as the staircase-like boundary. 

The Dias parameter is constantly zero (ds = 0), which means that the formulas are found in the same column, where C10H8 (naphthalene) is at the top. There is no limitation as to how far down one can get in this way, moving steadily away from the staircase-like boundary. 

The C HS formulas on the staircase-like boundary are those of most interest in the present chapter. Therefore an extensive listing of these formulas is given here see Fig. 9. The values of the Dias parameter (ds), which are indicated in the figure, are supposed to facilitate the identification of the positions of the different formulas in the periodic table for benzenoid hydrocarbons the same is the case for the h values. 

The invariant (Dias 1982a 1982b 1987) has been referred to as the Dias parameter (BrunvoU and Cyvin SJ 1990). The interpretation given in the above listing does not apply to benzene (CeHe = 0, h = 1), which has = —1. However, the functions in terms of other invariants (see below) may be taken as a general definition of d. ... 

Figure 2 exemplifies the reduced connectivity for some 0- and i—polyhexes, actually the same systems which were used previously for the exemplification of the Dias parameter in Cyvin SJ and Brunvoll (1989). 

A variety of Naphthol AS pigments are polymorphous they display at least two crystal modifications. The list includes P.R.9,12, and 187. A wide variety of dia-zonium compounds and coupling components with different substitution patterns have been developed in order to alter the properties of the resulting Naphthol AS pigments. This is particularly true for parameters such as fastness to solvents, in... 

To see if this drum size can be significandy reduced using the approach proposed in this article, some additional information is needed and the following is assumed inlet nozzle angle 0,=3O deg. inlet nozzle dia. vapor-droplet velocity ( , 56.6 ft/s hence. t/ = L cos 0,=49 ft/s, and Lp— stn 0,=28.6 ft/s. (The parameters 0( and dn can. of course, be adjusted. The effects of varying these parameters will be discussed.)... 

Phase identification was done on the basis of both d-spacing and the peak height intensity of all the x-ray lines. These values were compared with values obtained for the end-member (unsubstituted) compounds and also calculated by means of the Lazy-Pulverix computer program (9). Precision lattice parameters were obtained by the Debye-Scherrer method with a 114.6 mm dia. camera and filtered Cr Ka radiation standard least-squares methods were used. 

Calculated and experimental maleic anhydride yields for the three fluid bed reactors involved in the scale-up of the Mitsubishi process are shown together in Figure 7. The yield value for the 45 cm dia. reactor was used to determine the reaction rate constant k, but the calculations for the 15 cm dia. bed and for the laboratory reactor with 4 cm diameter were performed without any parameter fitting. The calculation for the 15 cm bed is surprisingly close to the measurement whereas there is some deviation between theory and experiment on the laboratory scale the reason of which ist not quite clear. It should be noted however that in the laboratory reactor 1-butene was used as feed while on the pilot scale C -fractions of the naphtha cracker i.e. mixtures of various hydrocarbons were used. 

Chart Packing FP Fp lource (ref. number) Data rams (ret numher) System Pressure Plow parameter Dia. in Packed ht. feet No. of data paints... 

When different inhibitory effects on microbial activity need to be compared, it is also necessary to determine the parameters that would state the influence of the antimicrobial compound (Ferreira, Loureiro-Dias, and Loureiro, 1997). 

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