Derived index numbers

The non-distillable part ND = 100 - AG4(K) of vacuum residues and bitumens is within the limits from 56 to 89 wt%, and for atmospheric residues from 33 to 40 wt%. For the conversion products ND depends on the distillation severity after conversion. ND increases for heavy products up to more than 75 wt%. Statistical evaluation results in the following data  

Statistical evaluation of the ratio CR/ND, which represents the crackable portion of the non-distillable part of the sample, gives the following results  

Vacuum residues, bitumens, and atmospheric residues (Samples 1-17) 0.80 5.1 

The lower value of the ratio CR/ND for products from conversion processes indicates that considerable amounts of these products have already been cracked and distilled. The high value CR/ND = 0.88 for the visbreaker residue, sample 21, demonstrates on the other hand that in that case the crack conditions were very light. 

The Conradson coke residue in the non-distillable part of the samples (CCR/ND) 100 is in the limits from 23 to 33 % for vacuum residues, bitumens, and atmospheric residues. The statistics result in a mean x = 27.3 % and a coefficient of variation V = 9.6 % (relative). The products from conversion processes scatter from 33 to 58 %. The furfural extract (sample 24) stands out because it does not possess any coke residue. 

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Table 4-16 Derived index Numbers from Thermogravimetry in Argon...

From the arguments in chapter 4.2.3.4 it may be deduced that while the derived index numbers of chapter 4.2.3.2, such as ND, CR, CCR/ND, and R800/ND may be of theoretical interest, other index numbers are relevant to the practice of refineries, and may also be obtained by thermogravimetry (see Tables 4-20 and 4-21). 

Table 4-20 Derived Index Numbers of Thermogravimetry in Inert Gas (I)...

The index numbers for thermogravimetry in inert gas, for the bitumens and their colloidal components are given in Tables 4-55 to 4-58. The only derived index number is the crackable part of the sample, CR, which is listed in Table 4-59. 

Naphthol AS derivatives that have retained commercial importance are listed in Table 10, together with their name, constitution, and Colour Index number (Sec. 2.1.2, p. 195). 

The index number refers to the principal quantum number and corresponds to the K shell designation often used for the electron of the normal hydrogen atom. The principal quantum number 2 corresponds to the L shell, 3 to the M shell, and so on. The notation s (also p, cl, f to come later) has been carried over from the early days of atomic spectroscopy and was derived from descriptions of spectroscopic lines as sharp, principal, diffuse, and fundamental, which once were used to identify transitions from particular atomic states. 

The 1,2,5-thiadiazole nucleus is numbered as in 4. The hydrogenated forms (5 and 6) are referred to as 1,2,5-thiadiazoline and 1,2,5-thiadia-zolidine according to the Patterson Ring Index. The benzo derivatives are numbered as in 7 and are named 2,1,3-benzothiadiazole though much of the early literature makes use of the name piazthiole. In an apparent confusion with the numbering system of the 2,1,3-benzothiadiazole some modem authors have used the name 2,1,3-thiadiazole in reference to the monocyclic derivatives. 

Azo dyes are classified according to a color index system based on usage and chemical constituents. These are subdivided into monoazo, disazo, trisazo, and polyazo derivatives with a specific assigned range of color index number. Another classification system involves dividing dyes into dyeing classes such as acid, basic, disperse, direct, mordant, and reactive dyes. Azo compounds are used extensively as dyes to color varnishes, paper, fabrics, inks, paints, plastics, and cosmetics. They are used in color photography. 

The PG are named with the letters A-J depending on the type of substitution at the cyclopentane ring. The index number indicates the number of double bonds in the side chain the index number 1 characterizes derivatives of (fl//-Z)-8,l 1,14-eicosatrienoic acid, the number 2 derivatives of (a//-Z)-5,8,ll,14-eicostetraenoic acid ( arachidonic acid), and the number 3 derivatives of (a//-Z)-5,8,l 1,14,17-eicosapentaenoic acid (timno-donic acid often found in marine vertebrates). The orientation of the OH group at C-9 is designated by the index a or / . 

The problem is simply exemplified by the extension of an imaginary patent covering aspirin and its derivatives. Indexing aspirin is not a difficult job - it can be done by structure. Registry Number, or name. However, if one replaces the alkyl group of this compound with a short list of other possibilities, the number of compounds covered can increase substantially. A further generalisation of the structure to cover any alkyl would mean that the patent covers an infinite number of structures. 

Tabic 4-1) using a series of empirical index numbers. Further characterization may be achieved using other index numbers derived from those aforementioned (Table 4-2). Quantitative statements concerning the kinetics of the pryrolysis and the oxidation behavior may be derived using DSC. 

The next sections of this chapter explore concepts, conceptualisation and conceptual profiling. This is then used as the basis for developing the idea of a derived index of fit-to-brand, which is illustrated using a number of case studies. 

Thus, the length G(x) of the orbit is equal to the index G / G of the stabilizer. Using this, we can derive the number of orbits ... 

Other Names Aniline, 4,4 -(3H-2,l-benzoxathiol-3-ylidene)di-, S,S-dioxide Benzenamine, 4,4 -(3H-2,1 -benzoxathiol-3-ylidene) -, S,S-dioxide o-Toluenesulfonicacid, a,a- (p-aminophenyl) -a-hydroxy-, y-sultone 3H-2,l-Benzoxathiole, benzenamine deriv. Anihnesulfonephthalein CA Index Name Benzenamine, 4,4 -(l,l-dioxido-3H-2,l-benzoxathiol-3-ylidene)fci5 -CAS Registry Number 4538-11-8 Merck Index Number Not listed Chemical Structure... 

Other Names Fluorescein, 2, 7 - w[[ (carboxymethyl)amino]melliyl]- Spiro[isobenzofuran-l (3H),9 -[9Fl]xantliene], glycine derivative 2,7-fi [iV,lV-to(carboxymethyl)aminomethylene]-fluorescein Acetic acid, [(3, 6 -dihydroxy-2, 7 -fluorandiyl)fci>(methylenenitrilo)]telra- Calcein Fluorescein complexon Fluorexon NSC 298193 Oftasceine CA Index Name Glycine, A7V -[(3, 6 -dihydroxy-3-oxospiro[isobenzofiiran-l(3II),9 -[9ir xanthene]-2, 7 -diyl) M(methylene)] is[N-(carboxymethyl)-CAS Registry Number 1461-15-0 Merck Index Number Not listed Chemical Structure... 

Other Names Spiro[isobenzofuran-l(3H),9 -[9H]xaiithene], 2,5-pyrrolidinedione derivative 5-(6)-Carboxyfluorescein diacetate succinimidyl ester CA Index Name 2,5-Pyrrolidinedione, l-[[[3, 6 -to(acetyloxy)-3-oxospiro-[isobenzofuran-l(3H), 9 -[9H]xanlhen]-5(or 6)-yl]carbonyl]oxy]-CAS Registry Number 150347-59-4 Merck Index Number Not listed Chemical Structure... 

Based on their analysis of test data from 11 references for sand in particle sizes ranging up to 1 inch (25.4 mm), in pipes with a diameter range from 1.5 inch to 22 inch, and in volumetric concentration up to 22%, Zandi and Govatos (1967) derived an equation for the index number (equation 4 13) in terms of the volumetric concentration, and some empirical parameters ... 

Reducing the Number of Partial Derivatives Index-1 Case The effort for the computation of sensitivity matrices can be reduced significantly observing that only directional derivatives in the directions of the degrees of freedom of the system are necessary. This leads to ideas used earlier also in the context of multistage least squares systems see [BES87]. 

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