Further Subdivisions

When the considered acyclic categories have terminal and/or initial objects, there exist further subdivision results that are sometimes useful. Both results are corollaries of the main Theorem 10.21. 

this subdivision of A(C) A D) coincides with the restrictions of these subdivisions of tc A(C) A D) and to A C) A D). The statement (10.15) follows from this.  

---

There is an ever-increasing number of further subdivisions, or what I would call hyphenated branches of chemistry or chemically related sciences. Whether chemical-physics or chemical-biology is more meaningful than physical chemistry or biological chemistry may depend on the point of view one wants to look from. 

Esters of medium volatility are capable of removing the water formed by distillation. Examples are propyl, butyl, and amyl formates, ethyl, propyl, butyl, and amyl acetates, and the methyl and ethyl esters of propionic, butyric, and valeric acids. In some cases, ternary azeotropic mixtures of alcohol, ester, and water are formed. This group is capable of further subdivision with ethyl acetate, all of the ester is removed as a vapor mixture with alcohol and part of the water, while the balance of the water accumulates in the system. With butyl acetate, on the other hand, all of the water formed is removed overhead with part of the ester and alcohol, and the balance of the ester accumulates as a high boiler in the system. 

ATOM The smallest unit of an element incapable of further subdivision in the course of a chemical reaction. 

Chemicals are composed of atoms, discrete particles of matter incapable of further subdivision in the course of a chemical reaction. They are the smallest units of an element. Atoms of the same element are identical and equal in weight. All specimens of gold have the same melting point, the same density, and the same resistance to attack by mineral acids. Similarly, all samples of iron of the same history will have the same magnetism. Atoms of different elements have different properties and differ in weight. 

With the development of increasingly sophisticated analytical techniques it has become possible to determine substances present in quantities much lower than the 0.01 per cent upper level set for trace constituents. It is therefore necessary to make further subdivisions trace corresponds to 102-104/tg per gram, or 102-104 parts per million (ppm), microtrace to 102—10 1 pg per gram, (10 4-10 7 ppm), nanotrace to 102—10 1 fm per gram (10 7-10 1° ppm). 

The distinction between a- and P-adrenergic receptors was first proposed by Ahlquist in 1948 based on experiments with various catecholamine derivatives to produce excitatory (a) or inhibitory (P) responses in isolated smooth muscle systems. Initially, a further subdivision into presynaptic a2- and postsynaptic oq-receptors was proposed. However, this anatomical classification of a-adrenergic recqrtor subtypes was later abandoned. 

Further subdivision of a five-digit slice utilizes lower-case Roman numerals in parentheses (i), (ii), (iii), etc. It is often found that as a consequence of the organization, cognate material is located in different chapters but in similarly numbered pieces, i.e., in parallel sections. Section numbers, rather than page numbers, are the key by which the material is accessed through the various indexes. 

The material included in this chapter has been organized by oxidation state, with further subdivision into ligand donor type, and was obtained from reports published in primary research journals. The article will cover coordination complexes of copper in three oxidation states Cum, Cu11, and Cu1. The sections dealing with specific ligand donor types cut across several structural types. In view of the all-inclusive nature of the previous review of CCC(1987), no effort will be made here to present a comprehensive account. Instead, specific cases will be chosen for discussion because they exemplify important concepts concerning the relationship of ligand structure to metal complex properties. 

The literature cited in this article covers references listed in chemical abstracts to the end of 1961 and in current chemical papers after that. A degree of selection has been exercised in omitting some references that are now of limited value. Although metal nitrosyls are included in the scope of this chapter, no kinetic data on their decomposition is available and they will not be considered further. The data on metal carbonyls is limited and will be dealt with in the first section. The decomposition of metal alkyls and aryls has been extensively investigated. These compounds will be discussed in groups based on the position of the central metal atom in the periodic table and, when warranted, a further subdivision will be made based on the attached organic radicals. 

Anatomically, the nervous system is divided into the central nervous system (CNS) consisting of the brain and the spinal cord and the peripheral nervous system comprised of neural cells forming a network throughout the body. The peripheral system is itself subdivided into two sections the somatic system, where control of skeletal muscles allows movement and breathing, and the autonomic system which controls the actions of smooth muscle, cardiac muscle and glandular tissues. Further subdivision of the autonomic system based on anatomical and biochemical factors creates the sympathetic and parasympathetic nervous systems. 

The EC system of classification is based on the division of enzymes into six major classes according to the reaction they catalyse (Table 3.1). Each class is subdivided. In class 1, oxidoreductases, this is done according to the nature of the electron donor 1.1 with CHOH group as donor 1.2 with aldehyde or 0x0 group as a donor 1.3 with CH2-CH2 group as donor, etc. A further subdivision is achieved by consideration of the electron acceptor 1.1.1 with NAD as acceptor 1.1.2 with cytochrome as acceptor 1.1.3 with O2 as acceptor, etc. Finally, each enzyme that catalyses a unique reaction is given a fourth number so that, for... 

Two chapters are devoted to silicate melts. One is an introduction to petro-genetic diagrams, extensively treated in petrology. Aqueous solutions are covered in a single chapter that basically deals with electrolyte solution theory and its applications, since any further subdivision seemed unnecessary. A single chapter was deemed sufficient to describe the up-to-date information about gases. The decision not to treat chemistry and equilibria in the earth s atmosphere was dic-... 

The presence or absence of 3-0x0 groups allows a further subdivision into types A and B, respectively. For type A, Fe402) core can be formally envisioned as resulting from a condensation (8)... 

Preference will generally be given to the cyclization step early precursors can often only be indicated. The further subdivision of the sections depends on the ring existing in the precursor (annulation onto the six- or seven-membered ring or transformation of other precursors). Instead of excessive subdividing reaction sequences reported in the literature, subsequent reactions of cyclized products will sometimes be included in the synthetic formula schemes of Section 2 they will later in due course be described in Section 4. 

Here, k is the rate constant for hydrolysis in the Stern region, Fstem and Fmic are the volumes of the Stern region and of the micelle, respectively, AvS and Pm are the water-to-Stern region and water-to-micelle partition coefficients, respectively. Equation (6) shows that, for the assumptions described above, the micellar rate constant is given by the rate constant for the reaction in the Stern region, multiplied by a factor representing the distribution of the reactant within the micelle. Further subdivision of the micellar pseudophase is (mathematically) possible " " " but may not be warranted. 

Correspondingly, the molecular-skeleton class is indicated in boldface characters in the captions, with a further subdivision into femilies of skeletons, marked with a line underneath. This allows us a quick view as to the taxonomic distribution of the natural products, which is complementary to their ecological distribution. 

Both coastal areas and open oceans are found in the immense Indo-Pacific and Atlantic zones. Moving eastward, the Indo-Pacific comprises a sector from southern Japan to Natal, up to the Tuamotu and Hawaii archipelagos. The North Pacific and South Pacific are further subdivisions of the Pacific Ocean. Further zonation defines the North Atlantic (including the coastal areas fromNorth Carolina to southern Greenland in tte west, and a sector from off the coasts of Senegal to Novaya... 

Structures of typical groups are shown in Fig. 1.21. Further subdivision is possible on the basis of the nature of the octahedral sheets (di- or tri-octahedral) and stacking sequences. 

Mare basalts include lavas that erupted from fissures and pyroclastic deposits that produced glass beads. Six of the nine missions to the Moon that returned samples included basalts. The mare basalts from different sites have distinctive compositions and are classified based on their Ti02 contents, and to a lesser extent on their potassium contents (Fig. 13.3). A further subdivision is sometimes made, based on A1203 contents. Mare basalts are compositionally more diverse than their terrestrial counterparts. Volcanic glass beads, formed by fire fountains of hot lava erupting into the lunar vacuum, were found at several Apollo sites and eventually were shown to be a constituent of virtually every lunar soil. The glasses are ultramafic in composition and formed at very high temperatures. 

---