Family INDEX

As an analogous detailed treatment of the P- and F-family would be beyond the scope of this paper, only examples of structure types for these families are discussed. Table 8a contains some structure types which may be described either in the F-family (index 1) as addition compounds or as belonging to main classes or subclasses of die P-famfly (index 8). An hypothetical structure type with symmetry Pm3m is listed too. The first three structure types of Table 8b are closely related to the perovskite structure. The... 

Composition Spacegroup Structure- formula Descrlptic F-Fomily Index 1 n in the P-Family Index 8... 

An important application of this type of analysis is in the determination of the calculated cetane index. The procedure is as follows the cetane number is measured using the standard CFR engine method for a large number of gas oil samples covering a wide range of chemical compositions. It was shown that this measured number is a linear combination of chemical family concentrations as determined by the D 2425 method. An example of the correlation obtained is given in Figure 3.3. 

We will often add an index e in order to refer to a family of solutions. 

World Patents Index DIALOG, ORBIT, Questel, STN Derwent Information Ltd. international limited bibliographic data patent families comprehensive English language abstracts of basic and some equivalent granted patents polymer and chemical stmcture indexing for subscribers drawings... 

Patent Citation Index DIALOG, Questel—ORBIT, STN Derwent Information Ltd. international examiners and inventors citations of eadier references and later citing patents Derwent tide, bibhographic, and family information... 

World Patents Index / APIPAT ORBIT Derwent Information Ltd. American Petroleum Institute international limited bibhographic data patent families comprehensive English language abstracts of basic patents aU Wodd Patents Index and APIPAT indexing for subscribers... 

A new initiative introduced by Derwent during 1995 is the Patents Citation Index, an on-line database of patent citations that includes both examiners citations and patentees citations to prior art from patent specifications. When given a known invention of interest, as represented by a patent family, the database can identify any patent against which it has been cited, as well as eadier patents cited by any member of that family. Limited citation... 

The ChemicalF hstracts database does not have an on-line family capabUity, but does pubHsh a patent index, with family data obtained from INPADOC. Printed patent indexes have been including family information since the 1960s, but the number of countries covered before 1970 was limited. 

Pure, low temperature organic Hquid viscosities can be estimated by a group contribution method (7) and a method combining aspects of group contribution and coimectivity indexes theories (222). Caution is recommended in the use of these methods because the calculated absolute errors are as high as 100% for individual species in a 150-compound, 10-family test set (223). A new method based on a second-order fit of Benson-type groups with numerous steric correctors is suggested as an alternative. Lower errors are claimed for the same test set. 

The use of Polya s Theorem in a specialized context such as the above, has led to the extension of the theorem along certain useful lines. One such derivation pertains to the situation where the boxes are not all filled from the same store of figures. More specifically, the boxes are partitioned into a number of subsets, and there is a store of figures peculiar to each subset. To make sense of this we must assume that no two boxes in different subsets are in the same orbit of the group in question. A simple extension of Polya s Theorem enables us to tackle problems of this type. Instead of the cycle index being a function of a single family of variables, the 5j, we have other families of variables, one for each subset. An example from chemical enumeration will make this clear. 

The second choice is a simpler solution. According to Sarko and Muggli,66 all 39 observed reflections in the Valonia X-ray pattern are indexable by a two-chain triclinic unit cell with a = 9.41, b =8.15 and c = 10.34 A, a = 90°, 3 = 57.5°, and y = 96.2°. Ramie cellulose, on the other hand, is completely consistent with the two-chain monoclinic unit cell. Also, there are significant differences between their high-resolution solid-state l3C NMR spectra, indicating that Valonia and ramie celluloses, the two most crystalline forms, reflect two distinct families of biosynthesis. On this basis, the Valonia triclinic and the ramie monoclinic forms are classified69 as Ia and Ip, respectively. It has been shown from a systematic analysis of the NMR spectra by these authors, and from electron-dif-... 

Kier and Hall used the valence 5 index from Eq. (3) to define the family of molecular connectivity indices "Xt [13-15] ... 

A suitable way to represent group-subgroup relations is by means of family trees which show the relations from space groups to their maximal subgroups by arrows pointing downwards. In the middle of each arrow the kind of the relation and the index of the symmetry reduction are labeled, for example ... 

For each index pair k, k of a pair f, f of nuclear families, a quantity cn is defined as follows ... 

For each index k and nuclear family ft with indices k and k" for which Cn 0 holds, three additional quantities are defined ... 

Here uf = u exp(277ig r) is, like w, periodic with the period of the lattice, and k = k - 27rg is a reduced wave vector. Repeating this as necessary, one may reduce k to a vector in the first Brillouin zone. In this reduced zone scheme, each wave function is written as a periodic function multiplied by elkr with k a vector in the first zone the periodic function has to be indexed, say ujk(r), to distinguish different families of wave functions as well as the k value. The index j could correspond to the atomic orbital if a tight-binding scheme is used to describe the crystal wave functions. 

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