The Number System

A prerequisite for engineering calculations is the understanding of the number system. The reader may refer to the free on-line Web source http //mathworld.wolfram.com/topics/NumberTheory.html for the details. 

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The numbering system of tetracyclines is used for synthetic intennediates. 

The stmcture of vitamin A [11103-57-4] and some of the important derivatives are shown in Figure 1. The parent stmcture is aH-Zra/ j -retinol [68-26-8] and its lUPAC name is (all-E)-3,7-dimethyl-9-(2,6,6-trimethyl-l-cyclohexen-l-yl)-2,4,6,8-nonatetraen-l-ol (1). The numbering system for vitamin A derivatives parallels the system used for the carotenoids. In older Hterature, vitamin A compounds are named as derivatives of trimethyl cyclohexene and the side chain is named as a substituent. For retinoic acid derivatives, the carboxyl group is denoted as C-1 and the trimethyl cyclohexane ring as a substituent on C-9. The stmctures of vitamin A and -carotene were elucidated by Karrer in 1930 and several derivatives of the vitamin were prepared by this group (5,6). In 1935, Wald isolated a substance found in the visual pigments of the eye and was able to show that this material was identical with Karrer s retinaldehyde [116-31-4] (5) (7). 

A classification based first on ion specificity, then on stmctural features has been suggested for the polyethers (7). Another method uses the presence of unsaturation or of aromatic groups in the molecular skeleton (8). In this review the compounds are classified based on the number of carbons in the backbone according to the numbering system proposed in reference 9. The carbon backbone or skeleton refers to the longest chain of contiguous carbons between the carboxyl group and the terminal carbon. 

The nomenclature of penicillins requires special comment. Compound (2) can be named as follows (a) penicillin G (b) benzylpenicillin (note that the term penicillin may refer to the compound class (1), to the structural fragment (3) or, especially in the medical literature, to compound (2) itself) (c) 6/3-phenylacetamidopenicillanic acid (d) 2,2-dimethyl-6/3-phenylacetamidopenam-3a -carboxylic acid (e) (2S,5i ,6i )-3,3-di-methyl-7-oxo-6-(2-phenylacetamido)-4-thia-l-azabicyclo[3.2.0]heptane-2-carboxylic acid and (f) [2S-(2a,5a,6/3)]-3,3-dimethyl-7-oxo-6-[(phenylacetyl)amino]-4-thia-l-azabicyclo-[3.2.0]heptane-2-carboxylic acid. The numbered system shown in (2) is the one most commonly used in the penicillin literature and will be used in this chapter note that different number is used when (2) is named according to (e) and (f) above. 

This reference system is considered to be more useful than the conventional superscript number method since it enables the reader to see immediately in which year and in which journal (at least for the more common journals whose letter codes soon become familiar) the work cited was published. The reader is thus able to go directly to the original literature reference without having to consult a bibliography. It also provides the author and editor with the considerable advantage of being able to add or delete references up to the final submission of the manuscript without altering the numbering system. 

FIGURE 12.34 A general diagram for the structure of tRNA. The positions of invariant bases as well as bases that seldom vary are shown in color. The numbering system is based on yeast tRNA R = purine Y= pyrimidine. Dotted lines denote sites in the D loop and variable loop regions where varying numbers of nucleotides are found in different tRNAs. 

Fluorinated compounds are frequently referred lo by code, such as F-l 15. To translate this code into a molecular formula, add 90 to 115. The firsl digit of the sum is the number of carbons the second, the number of hydrogens the third, the number ol fluorines chlorines complete the valences (i.e., C2F5CI is F-l 15 = 90 + 115 = 205. or C H Fj). A four-digit number is used for unsaturated molecules. See Tables 14.1-14.3 for the numbering system for chlorofluorocarbons. 

We re almost ready to start naming molecules. We finished learning about the individual parts of a name, and now we need to know how to identify how the pieces are connected. For example, let s say you determine that the functional group is OH (therefore, the suffix is -ol), there is one double bond (-en-), the parent chain is six carbon atoms long (hex), there are four methyl groups attached to the parent chain (tetramethyl), and the double bond is cis. Now you know all of the pieces, but we must find a way to identify where all of the pieces are on the parent chain. Where are all of those methyl groups (and so on). This is where the numbering system comes in. First we will learn how to number the parent chain, and then we will learn the rules of how to apply those numbers in each part of the name. 

And we indicated the position of the double bond with the numbering system. But then we saw that there are often two ways for the atoms of a double bond to connect to each other in 3D space. We saw a system for distinguishing these possibilities, using the terms cis and trans ... 

The two structures differ in only one place, the orientation at position 4. The numbering system is the same for both sfructures, so the proposed structure of galactose meets the specifications of the problem. 

Fig. 16.6 The 1,3-diphenyl propane skeleton of flavonoids and the numbering system for flavonoids. Three structural features optimise the radical scavenging properties of a flavonoid (i) an orto-dihydroxy structure of the B-ring (catechol) (ii) 2,3 double bond in conjugation with a 4-oxo group (iii) 3- and 5-hydroxy groups (Bors and Saran, 1987).

The numbering system and normal stereochemistry of the steroids of interest to this chapter are as follows ... 

This chapter extends the information provided by the two preceding reviews (1,2) to the literature that appeared within the years 1976-1986, focusing on spectral data, structural elucidation, synthesis, biosynthesis, and pharmacology. Some references that appeared in the foregoing reviews are omitted from this chapter with exception of those related to the present treatise. Although previously presented in Volume 16 of this treatise (2), the numbering system of the hasubanan skeleton (la) and the hasubanalactam skeleton (lb), which is used in this chapter except for the most part of Section V, is represented anew. 

Fig. 1. Schematic diagram of two glucopyranose units of a cycloamylose molecule illustrating details of the o-(l,4) glycosidic linkage and the numbering system employed to describe the glucopyranose rings.

The numbering systems of mononuclear 1,2,5-thiadiazole 1 and 2,1,3-benzothiadiazole 2 are given below. 2,1,3-Benzothiadiazole, also referred to as benzo[l,2,5]thiadiazole, was often called piazthiole in the early literature. 1,2,5-Thiadiazole was also referred to as 2,5-diazathiophene. Both reduced and oxidized derivatives of 1,2,5-thiadiazole are known. 7... 

Four deuteriated retinols, 26-29, with 3 to 5 deuterium atoms have been synthesized29 for metabolism of vitamin A studies in humans30. Deuterium has been introduced into appropriate intermediates, used in the reaction scheme shown in equation 12, by base-catalysed exchange with 2H20 or perdeuterioacetone. The numbering system for retinol (vitamin A alcohol) is shown in equation 12. 

Table 10-6 presents one type of basic HAZOP form. The first column, denoted Item, is used to provide a unique identifier for each case considered. The numbering system used is a number-letter combination. Thus the designation 1 A would designate the first study node and the first guide word. The second column lists the study node considered. The third column lists the process parameter, and the fourth column lists the deviations or guide words. The next three columns are the most important results of the analysis. The first column lists the possible... 

This is one of the quirks in the numbering system. Physically and psychologically, a minus means less (less shielding), and DOWNfield is further left on the paper yet the value of <5 goes UP. Another system uses the Greek tau (t) — that s 10.0-<5. So <50.0 (ppm) is lO.Ot. Don t confuse these two systems. And don t ever confuse deshielding (or shielding) with the proper direction of the chemical shift. 

Nylon (polyamide fibers). The chemical structure of the nylon fiber looks just like the nylon resin. The polymerization processes are the same the numbering systems are the same and the two most important nylon fibers are the same nylon, 6 and 66. The difference is the length of the molecule in comparison to the cross-section. Thats regulated by the polymerization process conditions. 

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